Best all time mathematicians/physicists.

[mprm86]

Who you think are the best mathematicians/physicists of all time? (the first five)

1. Einstein
2. Gauss
3. Newton
4. Euler
5. Archimides (I dont know how to write it in English)

[fourier jr]

in no particular order, here are some that come to mind off the top of my head:
- Hilbert
- Euler
- Erdos
- Gauss
- Archimedes
- Galois

i don't think i know enough physics to have an opinion about physicists. i guess you could go through the list of nobel prize winners to find a bunch of the best ever.

[Chrono]

I can go ahead and tell you that Riemann is my favorite mathematican. Gauss and Newton come at a pretty close second.

[fourier jr]

... oh yeah, I'll add Fourier also :biggrin:

[devious_]

Euler, Riemann, Cauchy, Leibniz and al-Khawarizmi are my favorite 5 (in no particular order).

[vsage]

Where's the love for ramanujan?

[James R]

Einstein, Gauss, Newton, Galileo, ...

Hard to pick number 5.

[DrKareem]

Einstein, Euler, Gauss, Newton...

[Chrono]

Where's the love for ramanujan?

Funny you should say that. I was thinking of adding him in as I was just coming to this post.

[mathwonk]

Riemann is my favorite, but that is possibly because I have read his works and thus know more about what he did, and hence am more impressed by it. I also agree on Gauss, Archimedes, Hilbert and Euler, having some familiarity with some of their works.

Galois was a genius, and gave a beautiful solution to a fascinating problem, and his life was very romantic, but the theory he created is arguably not tremendously important in mathematics. His lesser known but to me more important work, on abelian integrals, anticipated Riemann, and it is a tragedy that he did not live to fulfill his enormous scientific potential.

Anyone who would list Erdos in such a group, might well be asked to define what he means by "best". Certainly Erdos inspired a large number of young mathematicians to work on his problems, most of them elementary to state, and of somewhat specialized interest. Many of them were of course relatively trivial, but some were very difficult, and have truly inspired some wonderfully talented young mathematicians. I would say his work is somewhat unimportant, but his life gave a generous impetus to mathematics.

It is also puzzling to me to see a list such as "Einstein, Gauss, Newton, Galileo", followed by "can't think of a 5th", when Archimedes' mathematical works seem to contain Galileos' as a small subset, and precedes it by many hundreds of years.

I.e. Galileo's great work, "On two new sciences" comprises 1) strength of materials, and 2) the science of motion. His main results in the science of motion are easy corollaries of the methods of Archimedes for finding areas under parabolas.

Of course one can discuss endlessly such opinions, since we are all underqualified to judge such a question. Still it might be of interest for people to offer a hint of why they chose their candidates.

As to my choice of Riemann, Gauss himself praised Riemann's "gloriously fertile originality". Riemann began the now huge subject of algebraic geometry, by applying the methods of complex analysis and topology, which he essentially invented for the purpose, to the study of plane curves. He invented complex analysis on non planar surfaces, and proved the analog of the Mittag Leffler theorem for these new objects, his famous Riemann Roch theorem. His results on abelian integrals and abelian functions are among the most beautiful in all of mathematics, and have led to scores of years of study and generalization, including work by the amazing Grothendieck. Riemann introduced the idea of clasifyuing all geometric objectys of a given type by poiints of a geometric object tiself of the same kind, the powerful idea of "moduli", still an enormous field of study in many areas.

In another related arena, differential geometry, Riemann invented the study of higher dimensional space, and differential calculus on manifolds, generalizing ideas of Gauss from 2 dimensions to all dimensions. He invented the curvature tensor, a subject of great interest in these pages, and provided the mathematical foundations for Einstein's formulation of gravity in space.

In topology, invented by him to study algebraic curves over the complex numbers, he introduced the concepts of homology of curves, via the genus, as the minimum number of "loop cuts" that render a compact surface planar.

In number theory, he achieved perhaps his greatest general fame by his application of complex analysis to the study of prime numbers, introducing the zeta function to count primes, and making a simple conjecture still unpoproven to this day, and yet of enormous interest and application, the Riemann hypothesis, that all "non trivial" zeroes of the zeta function lie on the line Re(z) = 1/2.


By the way, I think Grothendieck deserves a place on some of these lists, if one is willing to include 20th century mathematicians. He singlehandedly revolutionized the subject of algebraic geometry and number theory, marrying them forever as previous generations had merely dreamed of doing. Andre Weil is very worthy of mention as well, and others.

[arildno]

" Archimedes' mathematical works seem to contain Galileos' as a small subset, and precedes it by many hundreds of years."

This statement, by itself, shows where Archimedes should be placed on ANY list of mathematicians (and, for that matter, physicists):
At the very TOP.

There are no one beside him, and, unfortunately, never will be.
We'll have to make do with Newtons, Einsteins, Gausss and suchlike..

[marlon]

Aristarchus...Copernicus basically took over his ideas on planetary motion and the heliocentric modell.

I would name Ptolemaeus as the worst physicist ever...
Gauss is the best mathematician...

regards
marlon

[arildno]

"I would name Ptolemaeus as the worst physicist ever..."
Good heavens, why?

Please note that his choice of a geocentric model over a heliocentric model was NOT based on respect for the Gods (or some such idea), but on a rational (but fallacious) argument:
Namely, that if the earth moved relative to the background, we would experience a perpetual wind.
It is only when the atmosphere is seen as co-moving with the earth that this argument loses its power.
This, however, is a result of a theory of gravitation&air, in which the matter comprising the air follows the earth due to gravitation.

To castigate Ptolemy for not reaching the insights of Galileo&Newton a thousand years earlier, is rather churlish..IMO.

[fourier jr]

Anyone who would list Erdos in such a group, might well be asked to define what he means by "best". Certainly Erdos inspired a large number of young mathematicians to work on his problems, most of them elementary to state, and of somewhat specialized interest. Many of them were of course relatively trivial, but some were very difficult, and have truly inspired some wonderfully talented young mathematicians. I would say his work is somewhat unimportant, but his life gave a generous impetus to mathematics.

"In over six decades of furious activity, he wrote fundamental papers on number theory, real analysis, geometry, probability theory, complex analysis, approximation theory, set theory and combinatorics, among other areas. His first great love was number theory, while in his later years he worked mostly in combinatorics. In 1966, with Selfridge, he solved a notorious problem in number theory that had been open for over 100 years, namely that the product of consecutive positive integers (like 4·5·6·7·8) is never an exact square, cube or any higher power. With Rado and Hajnal, he founded partition calculus, a branch of set theory, which is a detailed study of the relative sizes of large infinite sets. Nevertheless, he will be best remembered for his contributions to combinatorics, an area of mathematics fundamental to computer science. He founded extremal graph theory, his theorem with Stone being of prime importance, and with Rényi he started probabilistic graph theory..."
+ the prime number theorem, and all the problems he left behind

http://www.ams.org/new-in-math/erdosobit.html

[WORLD-HEN]

What about Godel?

[fourier jr]

yeah godel did some good stuff, from what I've read anyway (which isn't a lot)

i've got a related questions for everybody; who is the most underrated mathematician there ever was? by that I mean who are some "unsung heros?"

[marlon]

To castigate Ptolemy for not reaching the insights of Galileo&Newton a thousand years earlier, is rather churlish..IMO.

Untrue...
look at the work of Aristarchus,...this is my whole point

regards
marlon

[arildno]

Untrue...
look at the work of Aristarchus,...this is my whole point

regards
marlon
That would depend upon whether Aristarchus provided an acceptable argument against the perpetual wind objection.
I don't know if he did, perhaps you know about that?

[JasonRox]

It depends on what area of mathematics you are into. This changes everything.

[Cod]

I know Richard Feynman is more "new school", but would y'all consider him one of the greatest of all-time?

[JasonRox]

I have a few arguments:

Galileo is an idiot for not leaving Italy.
Keppler is an idiot for not collaborating with Galileo.
Newton is an idiot for being an arrogant prick.
Gauss is an idiot for being an anti-social/arrogant prick.
Archimedes is an idiot for refusing to follow a soldiers orders.

You can go on and find false with all of them. A lot of times the problem with these special people also took part as "slowing" down physics and mathematics.

What about all the idiots refusing to use Arabic Numbers?

History is full of idiots.

[Atheist]

Gauss and Feynman would be my favorites for maths/physics. While the first one is rather obvious (maybe not as THE best mathematical but certainly as a very successful one), Feynman would be there just out of a personal feeling and my respect for the Feynman graphs which brought the description of physical processes from pure formula description to another "level". Many people don´t even know that those pictures are just a term in an equation.

[JasonRox]

I thought about this and if I had to pick I would choose -

Isaac Asimov

I like him best because he got me into all of this. I read one of his non-fiction books and I got hooked onto science, which then lead me to math.

Probably didn't do anything great, but he sure did something for me.

[Chrono]

I thought about this and if I had to pick I would choose -

Isaac Asimov

I like him best because he got me into all of this. I read one of his non-fiction books and I got hooked onto science, which then lead me to math.

How could I ever forget the man who got me into physics and math - the great Michio Kaku.

[WORLD-HEN]

Are we talking about our favourite mathematicians/physicists or best mathematicians/physicists?

Richard Feynman was surely a very good teacher and also made some important contributions but i wouldnt consider him one of the best.

And about unsung heros, there are many ancient indian texts found which show that calculus was known long before archimedes,newton and leibniz.

[Integral]

This is really 2 separate lists. While Einstein was a great Physicist he was not a spectacular Mathematician. Any Physics that you do requires some math, on the other hand there is lots of Math that can be done with no Physics. It is not clear to me how you could compile a single list which incorporates the best of both.

[mathwonk]

dear fourier jr:
i agree that the author of erdos' obituary was enthusiastic about the man's work. so are the many people he inspired to do mathematics. I never met anyone before however who ranked him with gauss or archimedes. (nor anywhere near there.)

still, differences of opinion make the world go round.

best regards,

mathwonk

[mathwonk]

i would be interested in knowing more about any ancient indian texts that show calculus to have been known long before archimedes. what are they?

[Janitor]

Rated by a combination of quantity of work and quality of work, Euler must be at the top of the mathematician list.

[mathwonk]

the fact that the only 20th century mathematician mentioned here is erdos, suggests to me that the authors of these opinions do not know anything first hand about (20th century?) mathematics, but are only parroting what they read in the popular press.

essentially anyone in the mathematical community would have mentioned poincare, lebesgue, weyl, weil, mumford, thom, jones, bott, hironaka, wiener, hopf, artin, artin (yes, there are two of them), oka, grauert, lefschetz, hilbert (at least his famous congress talk was in 1900 and guided much of 20th century mathematics), zariski, cartan, enriques, serre, morse, atiyah, grothendieck, cohen, deligne, bombieri, brauer, igusa, fulton, chow, harish - chandra, kodaira, chern, tate, shafarevich, kontsevich, manin, washnitzer, witten, mori, sullivan, etc etc etc....

are these names known to readers of this site? if not, they qualify for unsung heroes, in the sense at least that the general public does not know who they are.

i recommend also to fans of gauss that, if they have not done so, they at least read some of his work "disquisitiones arithmeticae" (available in english translation), and to adherents of galileo that they read his "two new sciences", which is much easier and reads almost like a socratic dialogue. it is very striking that he obtains his results without even a decent notastion for numbers, representing each real number as the ratio of a pair of straight lines!

galileo shows for example that a projectile moving under the influence only of gravity travels in a path shaped like a parabola, ASSUMING THAT LINES DRAWN TO THE CENTER OF THE EARTH ARE PARALLEL, which he also observes is not quite true, since they meet at the earth's center. How many modern calculus books bother to point out this fact, before proving the otherwise false statement above? This shows the difference between reading the masters and their pupils, as abel put it, since regardless of their limitations in technique the old masters are possessed of amazing amounts of insight.

How many people are aware that galois last letter contained more than group theory and its application to solving equations? (the second half being an anticipation of riemanns theory of abelian integrals, including i believe the concept of the genus). you can only know this if you read it, and do not depend on textbooks (or websites) for an account of "galois theory".



huff puff

[WORLD-HEN]

Integral:

Do you mean that Einstein did not know a lot of math or do you mean he was not a good mathematician? He was surely good at mathematics but his main interest was physics so that would explain why he never made any discoveries in math.

Mathwonk :

Im not sure where you can find the translation but you could try searching for "Madhava" on google.

[mathwonk]

well looking up Madhava was interesting, except that he worked over 1,500 years later than Archimedes, not earlier.

[Janitor]

artin, artin (yes, there are two of them)... are these names known to readers of this site?

I have heard of about half of the names on your 20th century list. Hermann Weyl seems to be a favorite mathematician of physicists, I think because of his applications of symmetry ideas. I seem to remember from reading a biography of John Nash that there was a Professor Artin at Princeton. Would he be the one that Artinian rings are named after? (I think they were a favorite topic of the Unabomber!)

[Chrono]

Do you mean that Einstein did not know a lot of math or do you mean he was not a good mathematician? He was surely good at mathematics but his main interest was physics so that would explain why he never made any discoveries in math.

I always was under the impression that Einstein wasn't a good mathematician and concentrated in physics. Also, I remember reading that he had one of his theory's and didn't have the math to proove it, but did some research and found that Riemann did create the math. Anybody know the truth to this?

[mathwonk]

simply put, einstein was not a mathematician at all. he was a physicist. he never to my knowledge created any mathematics and never intended to do so. minkowski on the other hand was both.


hermann weyl was a famous matheamtician who worked significantly in linear groups and their reprsentations, a standard topic of theoretical physics.

Emil Artin was a German emigre to the US who is very likely the one Artinian rings are named after. Along with Nesbitt and Thrall he wrote a book on the topic of rings i beoieve. He worked at least in algebra, number theory, algebraic geometry, and wrote a nice book on algebraic topology. He seems to have illuminated every subject he touched. He was also a famous and excellent teacher. His son, Michael Artin is a contemporary algebraic geometer at MIT, of world stature, one of the architects of etale cohomology, whose book Algebra is perhaps the best introduction to abstract algebra available today.Enriques was one of the big three of classical Italian algebraic geometry, with Castelnuovo and Severi. Zariski was a Russian emigre, who studied with Enriques in Rome and came to the US, as did Lefschetz, the famous algebraic geometer and topologist. Mumford and Hironaka are Fields medalists who studied under Zariski. Michael Artin is also a student of Zariski I believe. John Tate and Serge Lang are two famous students of Emil Artin from Princeton. Tate is perhaps the more famous mathematician but Lang is better known to the public. Bott is one of the most famous topologists alive, and Marston Morse is extremely famous, especially for his method of studying topological manifolds by "flooding" them and studying the "shoreline' as the water rises, an extension of ideas of the great Lefschetz. Rene Thom is another Fiedls medalist, a famous differential topologist, and Grothendieck is an overwhelming force in algebraic geometry and number theory over the last 40 years. His foundations incorporated and replaced the partial ideas of all previous workers, whose contributions remain of great value within the context of his now universally accepted language.

I should also have mentioned Stephen Smale and William Thurston, but the list is so long one cannot name them all.

[fourier jr]

essentially anyone in the mathematical community would have mentioned poincare, lebesgue, weyl, weil, mumford, thom, jones, bott, hironaka, wiener, hopf, artin, artin (yes, there are two of them), oka, grauert, lefschetz, hilbert (at least his famous congress talk was in 1900 and guided much of 20th century mathematics), zariski, cartan, enriques, serre, morse, atiyah, grothendieck, cohen, deligne, bombieri, brauer, igusa, fulton, chow, harish - chandra, kodaira, chern, tate, shafarevich, kontsevich, manin, washnitzer, witten, mori, sullivan, etc etc etc....

more from the 20th century: nash, milnor, banach, smirnov, nagata, (mary ellen) rudin, smale, poincare, m & f riesz, thompson & feit, cook, wiles, swinnerton-dyer....

maybe it's too soon to tell with the 20th-century people and that's why nobody has mentioned them, i don't know.

re: artins, Emil was the more famous one, who was the first to do Galois theory using field extensions, and whom Artinian rings are named after. i don't know much about michael artin except that he's written an algebra book.

[Bin Qasim]

Hello guys,

I am new here. Good to see a place like this..... :smile:

no one included Muhammed bin Musa Al-Khawarizmi in thier list.....here is some info about this man....

http://members.tripod.com/~wzzz/KHAWARIZ.html

peace

[fourier jr]

a few more from the 20th century: caratheodory, hardy, littlewood, coxeter, noether, florence nightingale, sobolev, hausdorff, zorn, ramanujan, russell

[mad]

Wheres Leibnitz?

[devious_]

Hello guys,

I am new here. Good to see a place like this..... :smile:

no one included Muhammed bin Musa Al-Khawarizmi in thier list.....here is some info about this man....

http://members.tripod.com/~wzzz/KHAWARIZ.html

peace
Welcome to the forums. :smile:

Al-Khawarizmi was on my list, btw.

[gravenewworld]

Gauss, Euler, Einstein, Shrodinger, Bohr, Godel, Cauchy, Galois

[harsh]

I am surprised no one has mentioned Bernoulli's yet. He was an absolute genius.

As for physicist, I think Maxwell, Feynman, Fermi and Bohr are my picks

- harsh

[arildno]

I am surprised no one has mentioned Bernoulli's yet. He was an absolute genius.


- harsh
Which Bernoulli?
There were scores of them, hating each other.

[Chronos]

So many mathematicians, so hard to choose. Some made spectacular breakthroughs that were decades, even centuries ahead of their times. Hard to come up with a shortlist. Oh well, can't hurt to try [in roughly chronological order]
Pythagoras
Eudoxus
Archimedes
Diophantus
Ptolemy
Khayyam
Al-Khwarizmi
Fibonacci
Viete
Fermat
Newton
Leibniz
Euler
Galois
LaGrange
Cauchy
Cantor
Dirichlit
Gauss
Lie
Riemann
Hilbert
Godel
Grothendieck
Witten

[mathwonk]

i liked the bernoullis as well. they were apparently the first to study the integrals of functions like 1/sqrt(cubic polynomial), which are not elementary functions.

once whe teachiong calculus I xeroxed for my class a copy of a poage from an old text on this topic by the bernoulli's.


I admit I do not know who Cook and Smirnov are. And several of the others seem insignificant to me. And please, Russell was not a mathematician, but a logician and philosopher. His mathematical weight is nil.

I may be out on a limb alone here but also to me Nash is just a strong problem solver, but not a real theory maker like the great mathematicians Archimedes, Gauss, Grothendieck, etc etc , even if they did make a movie about him.

[jcsd]

Einstein often joked that his major discovery in maths was the summation convention! But he certainly wasn't a bad mathematician by any standard, otherwise he wouldn't of been able to understand much of his own work!.

I find it amazing though that Eulcid hasn't been mentioned once yet.

[fourier jr]

I admit I do not know who Cook and Smirnov are.
Cook conjectured that P=NP with a Russian whose name I can't remember, and Smirnov (& Nagata) proved the necessary & sufficient conditions that a topological space is metrizable. I'm not sure what else he did but that's why I put his name out there.

And please, Russell was not a mathematician, but a logician and philosopher. His mathematical weight is nil.
he worked on foundations of math, like Godel, and figured out what was wrong with the phrase "I am a liar" (self-referencing) which one of the Greek old-timers thought up.

I may be out on a limb alone here but also to me Nash is just a strong problem solver, but not a real theory maker like the great mathematicians Archimedes, Gauss, Grothendieck, etc etc , even if they did make a movie about him.
nash almost got a fields medal for the way he solved some partial differential equation, and made a huge development in game theory. i thought everybody knew about his non-cooperative games from the book/movie


re: euclid I've read that he wasn't a great mathematician but only compiled everything that was known at the time; i've also read that he was a really good mathematician. i guess maybe he should be on the list just for writing the elements. there's only one book that has been published more than euclid's elements, & I'm sure everyone knows what it is...

[JasonRox]

I find it amazing though that Eulcid hasn't been mentioned once yet.

He re-wrote everything that has already been done and organized it into a book.

Wow. I'm impressed. :rolleyes:

[mathwonk]

thank you for the explanations. however, to me proving necessary and sufficient conditions for metrizability seems a fairly trivial result. and just making a conjecture is a rather small contribution. I think there has to be more than that to deserve much notice.

being a mathematician myself i do not go to sensationalized movies supposedly about mathematicians' lives, although i did read some of the book on Nash, and an excellent book review of it by milnor. creating game theory sounds to me like an important thing, but i am personally pretty ignorant of the topic. i had thought von neumann was credited with that. at least that was the impression i got reading game theory as a teenager decades ago.

to me nash is known mostly for difficult and original results like the embedding theorem for analytic manifolds, and the structure theorems on the diffeomorphism type of real algebraic varieties. (His conjecture on these latter by the way has recently been disproved by Kolla'r, another outstanding 20th century mathematician.)

a mathematician views mathematical contributions through the lens of his own knowledge of the subject and its evolution, not by somebody else's written opinions. when it comes to someone like euclid, i have to pause, since his main contribution is writing a textbook, but there are some wonderful things in there. recently when teaching a course on number theory, proof and abstract algebra I read euclid's original discussion of some very basic concepts on divisibility in the translated original, available on a website. I rearned that he used the word "measures" for "divides" which gave me the geometrical perspective he had on divisibility. This illuminated for me after decades, the explanation for how one thinks of using the relation Ax+By = 1 to prove that if A divides Bn, where A,B are relatively prime, then A divides n, which I had always thought an algebraic trick. it became clear why there is a reciprocal relation between the largest length that will measure both of two given lengths (gcd), and the smallest length that can be measured using both of them (lcm). It also becomes more clear why there may be "incommensurable" lengths.

still archimedes is on another plane from euclid, in my opinion.

doing mathematics is not the same as teaching it, or knowing it, or using it, or writing about it. a written work of mathematics is not valued by how many copies it sells, or how long its shelf life is. Indeed the opposite is true today, when dumbing down of instruction is so rampant that the better a book is, often the shorter is its shelf life. There are happily a few exceptions to this in case of books like spivak and courant and apostol that have proved themselves as classics. Unfortunately, even these are sometimes attacked here by people for whom they were not intended. as one of my best teachers put it, mathematics is not democracy, where the view of the majority is always right.


no matter how much mathematics einstein understood, he did not create any to my knowledge and hence would not be considered a mathematician. I am not a mathematician because sometimes I can explain to somebody (or fail to) what a tensor is, or why some path integrals are not homotopy invariant, or do (or not do) some elementary calculus problem for them. I am a research mathematician because I have discovered and proved some new results in the theory of abelian varieties (and attempt to continue to do so). I never talk in detail about my own mathematics here because the discussions here are not that specialized.

in another way however, i consider myself a mathematician because, even in the area of elementary calculus, i work out my own view of things, and rediscover things that are well known, rather than just read and parrot them. for me this happened before getting my PhD, but after entering graduate school. I began to try to discover and elaborate results for myself, instead of just assuming that what was written in some textbook was holy writ.

in that sense many people here are also mathematicians. I.e. if you discover for yourself any mathematics at all, even elementary or "well known" results, you have done some mathematics. it does not matter that someone has done it before, even thousands of years before you.

there is some tension here between reading and doing. reading the great mathematicians is so valuable that one will learn things there that one would never do ones self, so it is very useful in deepening ones knowledge. but trying to do things oneself is essential to building ones creative muscles, in a way reading can never do.


thus, one encounters very smart people who know amazing amounts of mathematics, but who surprizingly do not do much interesting research, perhaps because all their education has been by reading, even in well chosen texts by the best people.

anyway, this is an enjoyable discussion, and many people have been mentioned who are interesting to think about.

hausdorff, whom someone brought up is one of my favorites, because for me he clarified why Russell is not a mathematician. I was reading Russell's huge and tedious tome with Whitehead, and some essays of Russell on "what is a number?", when i came upon Hausdorff's great book, Set theory. In the first couple of pages he just said essentially, that one can belabor definitions of nuumbers as one wants, such as by saying that a cardinal number is by definiton the class of all sets of that same cardinality (Russell does this) but that for him, "it does not matter much to us what a number is, just what properties it has". So let us get on with studying them.

It was then I knew I had the sensibilities of a mathematician, and , although as a teenager i had been entertained by his logical puzzles, i put Russell's works down for all time since, and got on with the business and fun of studying mathematics.

[jcsd]

According to A History of Mathematics by Carl Boyer it is generally presumed that at least some of Euclid's surviving work was original, but you can't ignore the man who literally wrote the book on mathematics.

[fourier jr]

the smirnov-nagata metrization theorem is considered the "definitive" metrization theorem though, as far as I know, and a very important theorem in general topology. I think urysohn has one too but it doesn't give necessary & sufficient conditions (he only gives one of the other i think). now that i think about it, what mathwonk said about russell sounds right. let's not fuss over what a number is; let's get in there & do stuff with them!


how about some 20th-century algebraists: artin, wedderburn, burnside, frobenius & lie & cayley (part of 20th century anyway), schur, van der waerden, sauders maclane, gelfand (banach algebras)

[mathwonk]

those are some good names. i was tickled to learn that cayley is in my mathematical genealogy according to that website. van der waerden's famous book is apparently based on lectures of artin and noether, but he did some fundamental work on putting algebraic geometry on a firm foundation. Of course it is not his foundations that took hold, or persisted.

I don't know quite what to make of saunders maclane. I like his book Homolgy, and one could get into a whole endless discussion of how important category theory is, called by Miles Reid "surely one of the most sterile of intellectual pursuits". But some very bright people work in it. Everyone finds it interesting when they first see it, and the language is universally used. But most people get bored of it rather soon.

[Janitor]

... florence nightingale...

Checking to see if we are awake? :tongue2:

[Janitor]

Are people here impressed with Stephen Wolfram? Is computer science considered a branch of mathematics?

[Dr Transport]

As a physicist, I look at the more applied people:

Gauss, Dirichlet, Neumann, Liebnitz, Newton.

Of course, guys like von Neumann, Weyl, Wigner come to mind. Now I have seen Feynman listed, but who here has mentioned Schwinger, another of the mathematically inclined theoretical physicists who developed QED, Dyson can be considered in this group.

Nash comes to mind for Game theory, Godel for pure Logic, Hilbert for axiom"izing" math and his 20(5)?? problems for 20th century mathematics.

Erdos for 20th century mathematicians was the most prolific, has anyone here mentioned Feigenbaum for his development of Chaos theory and Mandelbrot for Fractals????

Who are we to judge, I am a mere mortal in comaprison to these giants.

[mathwonk]

I forgot two of the most outstanding figures of the latter part of the last century, Deligne and Faltings.

(Deligne solved the last of the Weil conjectures, and Faltings solved Mordell's conjecture, both more interesting to me than Fermat's conjecture.)

Hilbert of course had 23 problems. his remarks on problem solving may be of interest:

"If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems. After finding this standpoint, not only is this problem frequently more accessible to our investigation, but at the same time we come into possession of a method which is applicable also to related problems. The introduction of complex paths of integration by Cauchy and of the notion of the IDEALS in number theory by Kummer may serve as examples. This way for finding general methods is certainly the most practicable and the most certain; for he who seeks for methods without having a definite problem in mind seeks for the most part in vain.

In dealing with mathematical problems, specialization plays, as I believe, a still more important part than generalization. Perhaps in most cases where we seek in vain the answer to a question, the cause of the failure lies in the fact that problems simpler and easier than the one in hand have been either not at all or incompletely solved. All depends, then, on finding out these easier problems, and on solving them by means of devices as perfect as possible and of concepts capable of generalization. This rule is one of the most important levers for overcoming mathematical difficulties and it seems to me that it is used almost always, though perhaps unconsciously.

Occasionally it happens that we seek the solution under insufficient hypotheses or in an incorrect sense, and for this reason do not succeed. The problem then arises: to show the impossibility of the solution under the given hypotheses, or in the sense contemplated. Such proofs of impossibility were effected by the ancients, for instance when they showed that the ratio of the hypotenuse to the side of an isosceles right triangle is irrational. In later mathematics, the question as to the impossibility of certain solutions plays a preeminent part, and we perceive in this way that old and difficult problems, such as the proof of the axiom of parallels, the squaring of the circle, or the solution of equations of the fifth degree by radicals have finally found fully satisfactory and rigorous solutions, although in another sense than that originally intended. It is probably this important fact along with other philosophical reasons that gives rise to the conviction (which every mathematician shares, but which no one has as yet supported by a proof) that every definite mathematical problem must necessarily be susceptible of an exact settlement, either in the form of an actual answer to the question asked, or by the proof of the impossibility of its solution and therewith the necessary failure of all attempts. Take any definite unsolved problem, such as the question as to the irrationality of the Euler-Mascheroni constant C, or the existence of an infinite number of prime numbers of the form 2n + 1. However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes."

[Gokul43201]

No one's mentioned Selberg...he's not that big a deal then ?

[fourier jr]

No one's mentioned Selberg...he's not that big a deal then ?

that was the guy who shafted Erdos, so I don't like him much even though I don't really know anything about him except for that

[mathwonk]

i have only heard of selberg's trace formula, but he is famous, much more as a mathematician than erdos, who is known primarily for being eccentric, and for writing a huge number of papers.

in fact there is an invariant known as the "erdos number" which is one less than the smallest number of people say A,B,C,D.....,X, such that A = you, X = erdos, and A has written a paper with B, and B has written a paper with C and so on.

so it is the smallest link between you and erdos in terms of writing papers. I.e. if you have written a paper with erdos, then your erdos number is 1. If you have not, but you have written a paper with someone who has writen a paper with erdos, then your erdos number is 2, and so on. Erdos wrote so many papers that most people have a fairly small erdos number. It may be conjectured that everyone in the world who has written a paper has a finite erdos number.

I for example who have very little interest in or admiration for erdos, and work in a different area, nonetheless have an erdos number of about 3.

erdos has perhaps the record for the largest number of papers, about 1,000 or so.
but to me this is almost a joke, as no one can write that many good papers. or it would be except that i know from personal experience that erdos has had a very good influence on young people in interesting them in mathematics with his many problems. so he is doing this (or was) for a good unselfish reason. i.e. he was not just publishing papers to make money or become famous. still the quality of the output is highly questionable in many cases.

for example riemann wrote far, far, fewer papers, his collected works list 31, of which i am personnaly familiar only with 5.

These 5, the only ones by riemann that are famous (to me) are his thesis on riemann surfaces where he introduces concepts of topology to study plane curves and complex functions, his followup paper on abelian functions including his analysis of analytic functions on a riemann surface and the first part of the famous riemann - roch theorem, his beautiful paper on the vanishing of theta functions containing his (partial) proof of the famous riemann singularities theorem, his great paper (habilitationschrift) on differential geometry in which he defined n dimensional manifolds and curvature (translated in spivak's book on diff geom, volume 2) , and his famous paper on prime numbers.

yet each of these 5 is absolutely earth shattering, and his prime number conjecture, the so called "riemann hypothesis", is perhaps the most famous unsolved problem in mathematics today.

ironically, although one can readily buy a translation of almost any piece of trivial #%**&* written in any language, I do not know of a translation into english of any other of the great papers of riemann except that in spivak's book. (nor of galois' famous letter. perhaps that is why so few people know it anticipated some of riemann's works, and in particular that it contains more than the theory of groups.)

the only mathematics i know of that erdos is famous for is his "elementary" proof of the prime number theorem. "elementary" means that someone else proved it first (hadamard?) using more sophisticated mathematics and erdos proved it afterward using fewer tools. this does not in itself impress me, as often the real insight into a theorem comes from using more sophisticated and more natural tools suited to the problem. It is often easy to analyze someone else's proof and then remove the sophisticated techniques in an unnatural way, so that they become disguised, and claim to have an elementary proof, but a proof no one would ever have thought of without the original proof to guide them.

a friend of mine once explained to me a small modification of a problem of erdos on the other hand which I solved in 5 minutes, and everyone else i have told about it solved it in a few seconds. so i know some of his problems are rather easy.

to be fair, erdos also posed some extremely non trivial problems that lasted for years, and some of my most respected colleagues are proud to have solved them, but i am still not moved too much, perhaps because of that first experience.

even his hard problems do not seem super interesting to me, because the ones i have seen are somewhat narrow in scope and application.

i will admit however that i know some fine mathematicians who have the highest possible regard for erdos, but not huge numbers of them. almost everyone on the other hand reveres the names of riemann, gauss, euler, hilbert, and archimedes. i see on looking back that my list overlaps considerably with the first post on this thread, especially since i omit physicists, so einstein is not eligible for my list. i would also admit newton but do not want to give up any of mine, so i have 6.

in the 20th century i still like grothendieck, serre, deligne, weil, weyl, poincare, hilbert, chern, kodaira, milnor, mumford, faltings, witten (a physicist who definitely impacts mathematics) and others.

I do not know if these are comparable to the ancients, with less than 100 years of perspective. If so, then the 20th century may be the richest source of great math scientists, and it probably is. my personal favorite century for rich math though is the 19th, led by riemann and gauss.

the early 21st century may lag somewhat behind the 2oth, since today's NY Times records that congress decided to cut the budget of the national science foundation, partly in order to have money to fund the rock and roll hall of fame in cleveland and the country music hall of fame in nashville. Is it any wonder why the US lags the world in math/science, but not in football or rock and roll?

[shmoe]

The "elementary" in the Erdos/Selberg proof of the prime number theorem refers to the absense of complex analysis. It's not at all a disguised version of the (independant) proofs supplied by Hadamard and de la Vallee Poussin but a creature of it's own design. While the elementary version was not earth shattering-indeed it's much more difficult and produces an inferior error term than complex methods-it was interesting from a view of what tools were "necessary" in prime number theory. Many believed that a proof outside complex variables was impossible-Hadamard said, "The shortest path between two truths in the real domain passes through the complex domain. " It was now clear that 'only' could not be substituted for 'shortest'.

Another quite interesting thing about the elementary proof is it results in a non-trivial zero free region of the Riemann Zeta function. It's been said "The longest path between two complex truths lies on the real line," but not by anyone important (just me I think).

About the "shafting"-I've only read second hand versions of the elementary proof (mathwonk is thinking it already-shame on me!), but my understanding is that the crux of the proof relies on a non-obvious identity that Selberg has sole ownership of. I'd put Erdos near the top of the list of "problem solvers/posers" and certainly one of the top collaboraters. On my list of "doers of deep mathematics," Selberg's higher up.

mathwonk-Edward's "Riemann's Zeta Function" has a translation of Riemann's "On the Number of Primes Less Than A Given Magnitude" in it. You'd like Edwards, the last line in his preface reads "If you read this book without reading the primary sources you are like a man who brings a sack lunch to banquet."

[mathwonk]

thanks for the enlightenment on erdos proof even if second hand, and the reference to edwards. if you know of any reference for the papers on abelian functions and vanishing of theta functions i'd really enjoy those.

[fourier jr]

what was published in erdos' times of london obituary was this: "Selberg and Erdös agreed to publish their work in back-to-back papers in the same journal, explaining the work each had done and sharing the credit. But at the last minute Selberg ... raced ahead with his proof and published first. The following year Selberg won the Fields Medal for this work", which is why i said shafted. i read that in 'the man who loved only numbers' also. that's all i know; i haven't tried to read the proof though, or anything original relating to it.

[mathwonk]

that appraisal of the fields medal in erdos obituary sounded wrong, or at least misleading to me, and it seems in conflict with the following account on the web. i could look it up mrore authoritatively later in the official account of the ICM of 1950.

"In 1950 Selberg was awarded a Fields Medal at the International Congress of Mathematicians at Harvard. The Fields Medal was awarded for his work on generalisations of the sieve methods of Viggo Brun, and for his major work on the zeros of the Riemann zeta function where he proved that a positive proportion of its zeros satisfy the Riemann hypothesis.

Selberg is also well known for his elementary proof of the prime number theorem, with a generalisation to prime numbers in an arbitrary arithmetic progression."

so perhaps selberg did not in fact receive the fields medal for his proof of the prime number theorem. he may however have won for results which were needed for his proof. I am not speaking here from personal knowledge of the mathematics.

here may be the problem Fourier jr: you seem to have misquoted the London Times obituary by one letter: "this work" in place of "his work". That has a different connotation and was my conjecture as to what it should have said.

"Selberg and Erdos agreed to publish their work in back-to-back papers in the same journal, explaining the work each had done and sharing the credit. But at the last minute Selberg (who, it was said, had overheard himself being slighted by colleagues) raced ahead with his proof and published first. The following year Selberg won the Fields Medal for his work"



if you consider fields medalists to be candidates for best mathematicians of the latter 20th century, and they are at least candidates for the mathematicians who looked best by the age of 35, up to 1998 they are:

1936 L V Ahlfors
1936 J Douglas
1950 L Schwartz
1950 A Selberg
1954 K Kodaira
1954 J-P Serre
1958 K F Roth
1958 R Thom
1962 L V Hörmander
1962 J W Milnor
1966 M F Atiyah
1966 P J Cohen
1966 A Grothendieck
1966 S Smale
1970 A Baker
1970 H Hironaka
1970 S P Novikov
1970 J G Thompson
1974 E Bombieri
1974 D B Mumford
1978 P R Deligne
1978 C L Fefferman
1978 G A Margulis
1978 D G Quillen
1982 A Connes
1982 W P Thurston
1982 S-T Yau
1986 S Donaldson
1986 G Faltings
1986 M Freedman
1990 V Drinfeld
1990 V Jones
1990 S Mori
1990 E Witten
1994 P-L Lions
1994 J-C Yoccoz
1994 J Bourgain
1994 E Zelmanov
1998 R Borcherds
1998 T Gowers
1998 Maxim Kontsevich
1998 C McMullen


ohmigosh, i never mentioned atiyah or novikov!

[Trigger]

What about Hamilton?
Surely he deserves a mention.

[dextercioby]

Let's settle some scores:
1.I'd bet my money on mathematicians who provided useful results for theoretical physics:(chronologically).I wpuld have to chose from the following 2 lists:
1.Isaac Newton+Gottfied Wilhelm Leibniz.
2.Leonhard Euler.
3.Carl Gauss.
4.William Rowan Hamilton.
5.Bernhard Riemann.
6.DAvid Hilbert.
7.Tulio Levi-Civita.
8.Hermann Weyl.
9.Elie Cartan.
10.Eugene Paul Wigner.
11.John von Neumann.


Physicists (theorists,of course):Chronological order:
0.Carl Gauss.
1.James Clerk Mawell.
2.Ludwig Boiltzmann.
3.Rudolf Clausius.
4.Max Planck.
5.Henri Poincaré.
6.Henrik Antoon Lorentz.
7.Niels Bohr.
7'.Erwin Sommerfeld.
8.Albert Einstein.
9.Louis de Broglie.
10.Erwin Schroedinger.
11.Werner Heisenberg.
12.Max Born.
13.Pascual Jordan.
14.Paul Adrien Maurice Dirac.
15.Enrico Fermi.
16.Wolfgang Pauli.
17.Julian Schwinger.
18.Shinjiro Tomonaga.
19.Richard Feynman.
20.Murray GellMann.
21.Seldon Glashow.
22.Steven Weinberg.
23.Abdus Salam.
24.Gerardus'tHooft.

I'd go for all mathematicians.Without,let's say,one of them,many of the guys from the second group would not have accomplished too much.Einstein would have done s*** without Hilbert and Weyl guiding him through tensor analysis.
For the second,i ended my list once with the completion of the SM,as theorists working after 1971(1974 exactly) have not received any Nobel Prize so far and their theories' predictions have not been tested experimentally.
Usually Dirac and Feynman (as u can see,neither is German :tongue2: ) get the credit for "the greatest",Dirac through his prolific theoretical results and Feynman for his QM&QED path-integral appraches.
It should be fair to put along one German as well (historically,GR is a German theory and QM a German theory based on a Frenchman's enlightning idea).I would go for Albert Einstein.

Daniel.

PS.Many mathematicians have had tremendous contribution to theoretical physics as well.I only chose Gauss of them,though Newton,Cartan,von Neumann & Hilbert to the say the least,should have been put in the second list.

[shmoe]

so perhaps selberg did not in fact receive the fields medal for his proof of the prime number theorem. he may however have won for results which were needed for his proof. I am not speaking here from personal knowledge of the mathematics.

They are unrelated. I would have my doubts that the elementary prime number theorem proof was a major source for the Fields medal, considering just how deep his other work was. I've now read both Erdos and Selberg's '49 papers on the prime number theorem (they live in jstor if you have access to it). Here's my brief synopsis to maybe clear a few things up:

1)The heart of the method is a formula I mentioned of Selberg's. In the usual number theory way, it has a bunch of sums over log's of primes. I'm not sure if this formula was actually new at the time-it's actually pretty trivial to prove with the Prime Number Theorem. What was definitely new is that Selberg managed to prove this with elementary methods (of course independant of the PNT).
2)Erdos, using Selberg's formula, proved a little result relating to the number of primes in certain intervals. This depended on Selberg's result, though was done without Erdos knowing Selberg's proof.
3)Selberg then used the Erdos result (and it's proof) on his own to prove the prime number theorem. Yay. This was pretty terrific, since it was not at all an obvious thing that Selberg's formula could be used to deduce the PNT.
4)Selberg simplified the proof of the Erdos result.
5)Together they simplified the proof of the prime number theorem.
6)Selberg came up with a new way to get the PNT from his formula from 1, bypassing the need for the Erdos' result (and it's methods). This is what Selberg published, and it was entirely his own work and ideas. In Selberg's paper, he mentions that the Erdos result was used in his first proof of the PNT, and he devotes some time to sketching the argument involved.

In short- Selberg fully acknowledged that his first proof (and it was his) relied on the Erdos result. He (and he's convinced me) felt that his method was superior in it's simplicity. There appears to be absolutely no theft of any ideas, and credit seems to be laid out where credit is due. The only possible slight I can see is Selberg doesn't mention 5 above- though simplifying the proof really wasn't worth much. Erdos paper essentially gives his original proof (of his result in 2 above) and sketches all the simplified versions of things above.

mathwonk-I ran across http://www.maths.tcd.ie/pub/HistMath/People/Riemann/
which has most (maybe all) of Riemann's works in German. That's not so useful for the German impaired, but there is a translation of his foundations of geometry (the one in Spivak) and of his number theory paper. I thought you might find the latter interesting (though Edward's book is a cheapie Dover one).

[fourier jr]

^^ coo, i didn't know about any of that. it sounds like that erdos obituary in that london newspaper was a bit one-sided & misleading. it made selberg sound like just an 'also-ran' & who stole some ideas (etc) from erdos

[Janitor]

Nobody mentioned Felix Klein, who is of importance because he initiated the explicit use of group theory methods in geometry.

[Lyuokdea]

Most of us here have nothing near the qualifications for doing things in terms of of "best" because I will at least speak for myself in saying that I don't know near as much as any of these guys did, even hundreds of years ago, give my 5 years, until I finally move past some of the really old ones like Newton, and then maybe I can make a decision. However, for my five favorite, and then a list of people I think were somewhat left out:

Einstein
Euler
Leibniz
Feynman
Gauss

Others who have been left out:
Dirac - he almost made my top 5
Calibi
Yau
Witten
Heisenburg
Schrodinger
Pauli
insert almost any other great physicist of the 20's

[quasar987]

Which Bernoulli?
There were scores of them, hating each other.

They hated each others?! Haha..

Do you have any anecdotes about that?

[Janitor]

A name I run into every few years is John Horton Conway. I know he made important contributions to group theory, cellular automata, and knot theory. He clearly doesn't restrict himself to one narrow branch of mathematics. He is still alive, as far as I know.

[^_^]

More people should be talking about Dirac...I feel sad.

[mathwonk]

we can only talk knowledgably about what we know about. of all the famous classical people mentioned I have only read riemann in the original, a few pages of newton and gauss, and one page of bernoulli. in modern times i still have read only einstein, serre, mumford, atiyah, mori, weyl, grothendieck, and some expositiory stuff by planck, poincare and hilbert, among the names above. i can spend 10 or 20 years reading one good paper by a top mathematician, and i still may not be done with it.

[Gokul43201]

Speaking of mathematicians who've most helped physics move along, Sophus Lie and Hermann Minkowski probably deserve mention.

[mathwonk]

I don't know what lie did but his name is on some of the most important and basic objects in math and physics, linear ("lie")groups and their associated ("lie") algebras. minkowski of course is famous to me as being credited with conceiving of 4 dimensional space time, and also for his work in geometrical number theory.

[Gokul43201]

Yeah, I don't believe its common knowledge that Minkowski did a lot of work on Number Theory. The only piece I'm aware of is the theorem named after him - an illusively obvious sounding statement about symmetric convex regions in the integral lattice.

[Gonzolo]

Did anyone mention Euclid?

[FulhamFan3]

Einstein, Newton, Archimedes, Euler, Maxwell, Gibbs, Schrodinger, Godel

To me Gibbs is the greatest american scientist of all time.

[afton]

There is no such thing as the best mathematicians/physicists imho. There
are some great ones like Newton and Einstein but we are all standing
on the shoulder of the giants.

[Curious3141]

If you're including mathematicians and physicists, then 5 is probably not enough. :) But let me try (in no particular order, really):

1. Gauss (math)
2. Newton (math and physics)
3. Einstein (physics)
4. Euler (math)
5. Wiles (math)

Yeah, I know, the last one is going to be controversial but who among us has solved an age old vexing mathematical question in his/her lifetime ? ;)

If we're talking about greatest philosophers, I'd have to consider people like Gödel and Kant. If the criterion were greatest genius level accomplishments in a lifetime, Da Vinci would be right up there, but Newton would almost certainly be up there too. If sheer cognitive power were to decide the ranking, I'd need to include William James Sidis, who didn't accomplish all that much, but could've.

[tornpie]

Just browsing through here quickly, no one seems to mention von Neumann. Man, was he brilliant. Not to mention Poincare. He almost had relativity before Einstein.

I got a couple of females to add that held their own too

Olga Ladyzhenskaya
Emmy Noether
Sofia Kovalevskaya

I think I'd have to break up my list into math and physics. My list for math would probably look something like this though:

Gauss
Riemann
Euler
Hilbert
von Neumann

Doh, no room for Archimedes.

For physics:

Newton
Einstein
Dirac
Feynman
Maxwell

[learningphysics]

I haven't seen these two mentioned yet (I didn't go through the entire thread tho):

Laplace
Fourier

[X-43D]

I think that the best mathematical physicists (of today) are:

1. Edward Witten
2. Michio Kaku
3. Robert M. Wald (see link (http://physics.uchicago.edu/t_rel.html))
4. John Baez

[Chrono]

I think that the best mathematical physicists (of today) are:

1. Edward Witten
2. Michio Kaku
3. Robert M. Wald (see link (http://physics.uchicago.edu/t_rel.html))
4. John Baez

Michio Kaku is probably the best one of today, I think. His first apperance on TechTV basically changed my life. Even more so after I read Hyperspace.

[mathwonk]

an english translation of riemanns works just came out and i am blown away by it. after spending my entire scientific career studying "riemann surfaces" i am learning things from his original papers i never understood before.

he dismisses things in 2 sentences that I thought were difficult. I recommend this work extremely highly, although I admit that even as an "expert" on this material it is taking me up to a week sometimes to read one page.

It is worth it though, since a week to understand something is less than 25 years not to.

It is now clear that much of the modern "sheaf theoretic" treatments of riemann roch theorems are nothing but an abstract reformulation of riemann's original conception of the topic.

what a visionary.

for example the riemann roch theorem, i.e. the problem of computing the number of independent meromorphic functions with pole divisor dominated by a given divisor D, is merely that of computing the rank of a certain matrix

from C^d to C^g, where d is the degree of the given divisor.

Riemann shows the kernel of the map has dimension one less than the dimension of the space of functions.

Hence the riemann inequality says; l(D)-1 = one less than the dimension of the space of meromorphic functiuons witrh pole divisor supported in D,

lies between d and d-g, i.e. l(D) -1 is at least d-g and at most d.

i.e. l(D) is at least d-g+1 and at most d+1.

this is riemanns famous inequality.

then the so called riemann roch theorem, computes this matrix more precisely as the g by d matrix with (i,j) entry wi(pj) where wi is the ith basic holomorphic differential, and pj is the jth point of the divisor D.

hence the rank of the matrix equals g - l(K-D) where K-D is the space of holomorphic differentials vanishing on D.

thus l(D)-1 + g-l(K-D) = d, i.e. l(D) = d+1-g + l(K-D), the full clasical RRT.

thats all. how simple is that? try getting that from any modern book, in that succint a form.

[wisredz]

Well, to be frank, I worship Sir Isaac Newton. An arrogant man or not, he was the greatest scientist the world has ever seen. He was a great man because, he invented what he needed and what he invented revolutionized the world. He invented optics. He did a great deal for science in England, while he was the headmaster of the Royal Society.

Anyway, my list for mathematicians would include Isaac Newton, Leibniz, Euler, Riemann and Gauss.
The list for phsyicists consists of Isaac Newton, Prof. Feynman, Albert Einstein.

[latyph]

YOU have just said what i was about to,to me newton is the greatest i know of,being arrogant is no reason to deprive him of his glory,while the greatest problem solver happens to be john nash.The rest were good too,really good.But the best is newton, you take a look at his works well and see the dexterity,the wide horizons related to his works, you professors shoukld give this a try

[quasar987]

I sometimes hear that Gauss is considered by many as the best matematician of all time.. But I don't really see why. It seems to me that some others were more prolific, and some discovered more interesting things than him. What is it that makes Gauss the best or one of the best matematician of all times?

[Sleazy Saint]

I'm noticing a distinct lack of love for Mandelbrot and Julia. They may not be the "best", but they're still pretty important. Plus, even laymen (such as myself) can appreciate fractals.

Cantor also belongs on the list. His brilliant ideas of the different cardinalities of infinite sets netted him huge amounts of flak from contemporary mathematicians. So much so, he had a nervous breakdown. But guess who ended up getting the last laugh?

I'm surprised that Godel wasn't mentioned more. I'm also surprised Descartes has't been mentioned.

Finally, not one person has mentioned Edward Lorenz, discoverer of the so-called "butterfly effect". He essentially jump-started interest in chaos theory, single-handedly

[mathwonk]

i'm not qualified to compare all those outstanding people, not even to evaluate one of them. I'm having real trouble even reading a few pages of riemann at sometimes a week per page.

but i am very impressed with his work, and (although i am guessing here, not having read but a tiny amount of gauss), i suspect gauss excelled at proving things rigorously.

riemann on the other hand apparently excelled at seeing true phenomena which lie deep, even when he could not completely prove them, due to lack of sufficiently sophisticated mathematics. he seems to have been inspired also by physical insight, to have faith in the correctness of his results.

so there are many different qualities which can make someone seem great. we are probably on shaky ground comparing them until we have read and understood them however, and this seems to be a job for more than one lifetime.

so far I am only through riemann's thesis, and about half of his abelian functions paper.

i admire newton for his concept of limit, as basic to derivatives. It seems to me that the previous understanding of derivatives, due to fermat, and descartes, is insufficient to achieve the fundamental theorem of caculus in the generality of newtons point of view. I also like newton's proof of the integrability of monotone functions.

unfortunately i have read extremely little of newton as well.

[IsotropicSpinManifol]

why einstein is better than newton

mc^2<mc^2

therefor

newton < einstein

[bomba923]

Personally, my top two are
Riemann (1st) &
Euler (2nd)

[mathwonk]

i like that list. interesting remark: riemann only published 9 papers, so he might not even get tenure at a state university these days. and he probably had no grant support. the paper in which he described the intrinsic curvature tensor did not even win the award he submitted it for. his story is really unbelievable. the idea that metric notions derived from observations of phenomena in the large may not hold in physics of the immeasurably small is due to him. he pointed out that if we assume rigid bodies mjy be transformed anywhere in space without changing their shape it only implies space has constant curvature. and that if this curvature happens to be positive, no matter how small, then space is necessarily finite. all this is decades before einstein. his development of necessary and sufficient conditions for functions to be represented by fourier series resembles the standard treatment by zygmund studied today. his formulation of the concept of fractional differentiation via gamma functions and fractional integrals, relating it to abels equation is still the form used today. he basically invented topology. his theory of complex variables revolutionized the subject, and brought algebraic geometry out of the elementary stages into a flourishing deep theory. he invented differentiable manifolds, and generalized gauss's theory of curvature of surfaces to arbnitrary dimensions. he initiated the study of "moduli" spaces of geometric objects, primarily complex curves, and line bundles on them, and computed their dimensions. his riemann roch theorem serves as the model for generalizations up until the present time, by enriques-severi, hirzebruch, grotyhendieck, atiyah-singer, baum - fulton - macpherson,....


his clear precise definition fo the riemann integral takes about 5 lines, and is immediately followed by a characterization of riemann integrable functions that is immediately shown to be equivalent to saying the set of dicscontinuties has "measure" zero. this theory which is what most people asociate with his name, is merely a brief remark on his way to studying fourier series.

it goes on and on... i dont really see how any one person could have done all this.

oh i completely forgot his classic 8 page paper on prime numbers which posed the still unresolved riemann hypothesis, stated in hilbert's famous lecture, and worth a million dollars today to any solver.

and there are hundreds more pages I am not familiar with at all, propagation of waves, .....

[Icebreaker]

Looking at these giants, I feel like a point. Look at Gauss: Disquisitiones Arithmeticae completed by 24... I'm an eyelash away from that age and haven't done jack.

Must catch up...

[cronxeh]

Take a look at this list http://www.sali.freeservers.com/engineering/maths.html

The last 100 years we've had quite a few great mathematicians, as good as any of the heavy hitter mathematicians like Euler, Gauss, and Riemann

[LeBrad]

My favorite 3 are Euler, Gauss, and Ramanujan

[quasar987]

In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

it goes on and on... i dont really see how any one person could have done all this.
And he died at 39 !!!

Your precious grotindiek isn't even on that list wonk :wink:

[MalleusScientiarum]

I have to like Lev Landau in physics. The dude's work was so ahead of its time that it took a while before everyone else caught up to him, and he did it in the Soviet Union.

[cragwolf]

My first 3 in each list are in order, the rest are not.

Mathematicians:
Euler
Riemann
Gauss
Fermat
Lagrange
Hilbert
Poincaré
Cantor
Kolmogorov
Grothendieck

Physicists:
Einstein
Newton
Maxwell
Bohr
Schrödinger
Rutherford
Dirac
Heisenberg
Pauli
Feynman

I suppose there are too many theoreticians and not enough experimentalists in the physicists list, but that's my bias. Physics goes nowhere without the work of experimentalists.

I find it difficult to properly judge the works of ancient Greeks, Arabs and Hindus, so I didn't include them, although Archimedes must surely rank as one of the greatest minds in history.

[cragwolf]

an english translation of riemanns works just came out and i am blown away by it.

Can you provide more details? I couldn't find it on Amazon or the web.

[fourier jr]

i still like fourier, but after reading just a bit i found that andre weil & norb weiner probably did the most significant work in fourier series since the 1800s. edwin hewitt was good too (at least in the 20th century) he's kind of a wedge antilles of math. he made up a regular T_1 space where every continuous real-valued function is constant!

[cronxeh]

In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?


I'm pretty sure its what you study in multivariable calculus in college

http://en.wikipedia.org/wiki/Analytical_geometry

[selfAdjoint]

In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

I'm pretty sure its what you study in multivariable calculus in college

No, it's the study of geometry, and especially the conic sections, through their coordinate properties, getting their equations in various coordinate systems and deriving geometric properties from that. It was a pre-calculus course and gave students a deep feel for how coordinates behave, rotation matrices and such. I took it, a three hour course as a freshman in college, along with an advanced trig course. That meant we didn't get to calculus until the sophmore year, but I've never regretted it. I don't think the modern pre-calculus courses go deep enough.

[EnumaElish]

How about Georg Cantor? "No one shall expel us from the Paradise that Cantor has created." -- David Hilbert

[Added later:] Oh, I see, cragwolf has already mentioned him.

[Even later:] and how about a cheer or two, for whomever invented zero?

[fourier jr]

yes cantor should definitely be listed here. i think we (me anyway) sometimes take for granted that, to paraphrase kepler, the laws of math are written in the language of set theory. it's a bit hard to imagine how math could be done without even a rudimentary knowledge of sets.

[TenaliRaman]

Please go through analytic geometry, its one of those really beautiful subjects. It also holds the record of "nearly" killing geometry as it was known during the post-Euclidean period. Not that i appreciate this, but analytic geometry shows that one can study behaviour of a particular entity without even visualising it.

If you enjoyed analytic geometry, then have a look at projective geometry (http://www.anth.org.uk/NCT/basics.htm). I am sure it can put you in awe of the raw power it with-holds.

-- AI(a happy geometry nut)

[quasar987]

No, it's the study of geometry, and especially the conic sections, through their coordinate properties, getting their equations in various coordinate systems and deriving geometric properties from that. It was a pre-calculus course and gave students a deep feel for how coordinates behave, rotation matrices and such. I took it, a three hour course as a freshman in college, along with an advanced trig course. That meant we didn't get to calculus until the sophmore year, but I've never regretted it. I don't think the modern pre-calculus courses go deep enough.
What book would you recommend on analytical geometry Mr. Adjoint?

[Pyrrhus]

I don't know about Adjoint's taste, but i like Analytic Geometry by Charles H. Lehmann

[TenaliRaman]

I did most of my Analytic Geometry from Thomas and Finney. (Yes i am an engineer)

-- AI

[tcamps]

Why has nobody mentioned Boltzmann? He unified thermodynamics and classical dynamics by pushing out into two then-conceptually untested realms simultaneously: 1. atoms and 2. stochasticity.

[mathwonk]

here is the site for riemann's works in english. i was the official reviewer for math reviews.

http://kendrickpress.com/Riemann.htm

i will post my review somewhere if i have not done so.

[mathwonk]

Review of Bernhard Riemann, Collected Papers,
translated by Roger Baker, Charles Christenson, and Henry Orde, published by Kendrick Press, copyright 2004, 555 pages.

My father's childhood copy of Count of Monte Cristo is inscribed: “this the best book I ever read,” exactly my opinion of this translation of Riemann's works. After the shock of how good and extensive these works are, by a man who died at 39, one is overwhelmed by his succinct, deep insights. It is amazing no English version of these works has appeared before, and this event should be celebrated by all mathematicians and students who read primarily English.

This translation contains all but one of the papers I-XXXI from the 1892 edition of Riemann’s works, but not the “Nachtrage”. The translation seems faithful, misprints are few, it reads smoothly, and the translators do not edit or revise Riemann's words, in contrast to the selections in "A source book in classical analysis", Harvard University Press.

I feared Riemann was obscure, and inconsistent with modern terminology, but once one starts reading, the beauty of his ideas begins to flow immediately. There is no wasted motion, computational results are written down with no visible calculation, and their significant consequences simply announced. This is a real treat. Mysterious statements become a pleasant challenge to interpret, in light of what they must mean. Even outmoded language is clear in context.

This is a concise and understandable source for subjects that paradoxically are harder to learn from books which expend more effort explaining them. That Riemann omits details, and knows just what to emphasize, make it a wonderful introduction to many topics. Even those I thought I understood, are stripped of superfluous facts and shine forth as simple principles.

Some highlights for me:
"Riemann's theorem" and the "Brill - Noether" number, are both derived on page 99. If L(D) = {meromorphic functions f with div(f)+D ≥ 0}, on a curve of genus g, then dimL(D) - 1 = dim ker[S(D)], where S(D) is a (2g) by (g+deg(D)) “period matrix”. Hence (Riemann's theorem) deg(D)-g ≤ dimL(D) -1 ≤ deg(D), and C(r,d) = {divisors D with deg(D) = d and dimL(D) > r} has a determinantal description = {D: rank(S(D)) ≤ (d-r+g)}.

Hence a generic curve should have a non constant meromorphic function with ≤ d poles only if d ≥ (g/2) + 1, by the intersection inequality (d-1) ≥ (g+1-d) (= codimension of the rank (d-1+g) locus, in (2g) by (g+d) matrices). The similar estimate (d-r) ≥ r(g+r-d) gives the “Brill - Noether” criterion for C(r,d) to be non empty for all curves of genus g, 16 years before Brill and Noether.

Eventually one realizes Roch's version of Riemann's matrix represents the map H^0(O(D))-->H^1(O), induced by the sheaf sequence:
0-->O-->O(D)-->O(D)|D-->0. In particular the ancients understood and used the sheaf cohomology group H^1(O) = H^1(C)/H^0(K).

The proof of Riemann's theorem for plane curves, although not algebraic, seems not to depend on Dirichlet's principle, since the relevant existence proof follows by writing down rational differentials. Hence later contributions of Brill - Noether and Dedekind - Weber apparently algebraicize, rather than substantiate, his results.

Riemann's philosophy that a meromorphic function is a global object, associated with its maximal domain, and determined in any subregion, "explains" why the analytic continuation of the zeta function and the Riemann hypothesis help understand primes. I.e. Euler's product formula shows the sequence of primes determines the zeta function, and such functions are understood by their zeroes and poles, so the location of zeroes must be intimately connected with the distribution of primes!

More precisely, in VII Riemann says Gauss's logarithmic integral Li(x) actually approximates the number π(x) of primes less than x, plus 1/2 the number of prime squares, plus 1/3 the number of prime cubes, etc..., hence over - estimates π(x). He inverts this relation, obtaining a series of terms Li(x^[1/n]) as a better approximation to π(x), whose proof apparently requires settling the famous "hypothesis".

In XII, Riemann both defines integrable functions, and characterizes them as functions whose points of oscillation at least e > 0, have content zero. I thought this fact depended on measure theory, but it appears rather that measure theory started here, [cf. Watson in Baker’s bilbiography].

In XIII, Riemann observes that in physics one should not expect large scale metric relations to hold in the infinitesimally small, a lesson I thought taught by physicists writing 50 years later. Elsewhere he hypothesizes that electrical impulses move at the speed of light, another assumption often credited to early 20th century physicists.

In VI, he proves a maximal set of non bounding curves has constant cardinality by the “Steinitz' exchange” method, 14 years before Steinitz' birth.

The translator apologizes for Weber’s inclusion of paper XIX on differentiation of order v where v is any real or complex number, written when Riemann was only 21, but I found it interesting: i.e. Cauchy’s theorem shows that differentiation of order v can be expressed as an integral of a (v+1)th power, which makes sense for any v, once one has the Gamma function to provide the appropriate constant multiple.


I hope this sampling from this wonderful book persuades you to read it for your own pleasure.

[mathwonk]

by the way in the official published version of my review, the editor changed my father's book inscription to include the word "is", losing the more accurate flavor of the 19th century farm child's grammar. Actually the inscription was written by my less literate uncle, and my very precise father would probably have done it correctly.

[zhentil]

Riemann and Cauchy.

[epenguin]

I am wondering how much some people posting here understand of the maths of the people they are rating?:tongue: It’s quite fun though, but especially to hear from the obviously more qualified people. I think it would be good to state more the criteria for ratings.

Some random thoughts.

Are mathematicians divided or continuously distributed between problem-solvers and new-path-breakers? Or is that an unreal distinction?

For new paths sometimes the virtue is just that? When you have had the initial idea it is not too hard to then make a lot of progress without being brilliant? Chaos theory is quite recent, but they could easily have made the same discoveries 3 centuries earlier if they had asked the same questions?

One asks, could I have done something like that? For the various familiar things, maybe they are so familiar that it is false, but I get the feeling I might have done something the sort of things as Newton, Euclid, D’Alembert, Fermat and a few others. Not so much not so fast. I am a bit lazy anyway. A few little things I have.

Some things are simple, become obvious once you know them. E.g. Euler’s relationship between pi and the prime numbers. I looked at it and thought how ever did he get that? Unimaginable! Then I read how it was done and – it becomes obvious! So one is convinced one could have done it. I think I would have got that if I had worried at it for five or ten years.

So some of the logical and systematic things I think I might have got somewhere with. But others are more mysterious. To actually guess the thing that you then prove is sometimes the inspiration. By report Ramanujan’s theorems have this weird quality of mysterious unguessability and even he couldn’t say where they came from. Maybe it is the problem-solvers who are the most admirable. Or this superhuman non-logical faculty to be celebrated. Ramanujan. Eordos? GC Rota? Reimann just for his hypothesis?

(I am nor a professional mathematician by the way and have only used math applications which means occasionally finding little theorems. :mad:Oh why can't I be superhumanly brilliant?)

[mongoose]

euler

[mathwonk]

in the spirit of the last comment by epenguin, people who brag on various candidates could at least read those luminaries' works.

gauss, riemann, archimedes, euclid, euler, all are available in english.

if these people are on your list and you have not read their works, why not? you are not listening even to yourself.

[delta_moment]

Michael Faraday and Charles Coulomb influenced some of my aspects of studies. Many of the others I've seen readily mentioned have also.

The Farad is such a fun quantitative unit.

[Bosonichadron]

Aristarchus...Copernicus basically took over his ideas on planetary motion and the heliocentric modell.

I would name Ptolemaeus as the worst physicist ever...
Gauss is the best mathematician...

regards
marlon

What!? Gauss the best!?

While I have to admit that Gauss was good, Euler was far better; As he is indisputably the most prolific mathematician of all time.

Not to mention that when he became blind from cataracts everyone thought that he was at the end of his rope--they could not have been more wrong, as he only became more productive and efficient because he stopped taking the extra time to write his ideas down!!!

That, and I think Euler's Identity (e^(pi)i+1=0) is the most beautiful equation in all of mathematics.

Oh, and as far as physicists go:

1.) Newton (Single most important mathematical contribution to physics of all time)
2.) Kepler (got all the confusion out of what was Copernicus's theory of planetary motion)
3.) Dirac (Creativity and beauty of the delta function)
4.) Richard Feynman (Independent path method in Quantum Mechanics)
5.) Einstein (Photoelectric effect, Special and General Relativity, Brownian Motion)

Runners up (no particular order)
Boltzmann, Lorentz (the last classical physicist), Heisenberg, Schrödinger, Neils Bohr, Marie Curie...

This, of course, is just my opinion.

BH

[Gib Z]

And of course, you are entitled to your own opinion. What a shame you thought Marlon didn't.

If we are going to ridicule each others opinions, I might as well state that it is foolish to put Heisenberg and Schrödinger and Einstein second to Richard Feynman, who was a genius who came up with the path integration formulation, QED and Feynman diagrams, yes, but is far better known for his problem solving skills and fresh personality. I would put Special/General Relativity, Matrix and Wave Mechanics (Foundations of Quantum Mechanics) as better contributions.

Not to mention, Neils Bohr may be the most overrated physicist in history, and Marie Curie receives far more acclaim than she deserves, most likely because she was one of the few female physicists of the time. She, along with her husband who never seems to receive anywhere near as much credit, discovered two radioactive elements. She didn't make any discoveries about radioactivity, she isolated two elements. I don't even know the persons name who first isolated Oxygen!

In my opinion, which Im sure many will disagree with, Marie Curie did not deserve two Nobel prizes, one for studying the previous discovered phenomenon of Radioactivity (which I don't believe she actually got any groundbreaking results from, what do they give Nobel prizes out for...) and another for Isolating Radium and Polonium.

[Bosonichadron]

Aristarchus...Copernicus basically took over his ideas on planetary motion and the heliocentric modell.

I would name Ptolemaeus as the worst physicist ever...
Gauss is the best mathematician...

regards
marlon

Marlon,

I appologize if I offended you in any way. It was not my intention to ridicule your opinion, as I may have come off. Gauss was a great mathematician, and a fine choice.

BH

[Bosonichadron]

And of course, you are entitled to your own opinion. What a shame you thought Marlon didn't.

If we are going to ridicule each others opinions, I might as well state that it is foolish to put Heisenberg and Schrödinger and Einstein second to Richard Feynman, who was a genius who came up with the path integration formulation, QED and Feynman diagrams, yes, but is far better known for his problem solving skills and fresh personality. I would put Special/General Relativity, Matrix and Wave Mechanics (Foundations of Quantum Mechanics) as better contributions.

Not to mention, Neils Bohr may be the most overrated physicist in history, and Marie Curie receives far more acclaim than she deserves, most likely because she was one of the few female physicists of the time. She, along with her husband who never seems to receive anywhere near as much credit, discovered two radioactive elements. She didn't make any discoveries about radioactivity, she isolated two elements. I don't even know the persons name who first isolated Oxygen!

In my opinion, which I'm sure many will disagree with, Marie Curie did not deserve two Nobel prizes, one for studying the previous discovered phenomenon of Radioactivity (which I don't believe she actually got any groundbreaking results from, what do they give Nobel prizes out for...) and another for Isolating Radium and Polonium.


As far as Neils Bohr and Marie Curie goes, I must admit that I agree; honestly, I just didn't want to seem sexist by leaving her off (she did, after all, receive two noble prizes in a period of history much more sexist than our own, and to leave her off may have looked bad).

And I like the path integration of Quantum Mechanics (over Feynman's other contributions) because it seems to remedy the "layers" of theory in physics (philosophically, anyway, if not practically). But I see your point.


--Bosonichadron

P.S. Thank you for point out my possible insult to Marlon.

[cragar]

1. Einstein
2. Newton
3. paul dirac
4. fermi
5.pauli

[CRGreathouse]

What!? Gauss the best!?

While I have to admit that Gauss was good, Euler was far better; As he is indisputably the most prolific mathematician of all time.

Pauca sed matura.

Euler was more prolific than Gauss, and I have always enjoyed the story of the productivity of Euler after going blind. But I must agree with Marlon: Gauss was the greatest mathematician of all time. Modular arithmetic, quadratic reciprocity (I can't remember how many proofs he had), the FFT 150+ years ahead of its time, additive number theory, the fundamental theorem of algebra, etc. As an amazing calculator, he made great strides with least squares, the normal distribution, and other statistical methods.

[csprof2000]

I always liked Lagrange. Probably not one of the best of all time, but his stuff has a nice, clean feel to it.

[maze]

Gonna throw Hermann Grassmann (http://en.wikipedia.org/wiki/Hermann_Grassmann) out there. Out of nowhere the guy singlehandedly invented linear algebra in his dissertation - the concept of a vector space, linear independence, subspace, span, dimension, projection onto a subspace, etc - things way ahead of his time. He also invented the exterior algebra and quaternions before "abstract algebra" was even a field of math.

Grassmann's work was treated with great suspicion by contemporaries. His phd advisor Mobius failed him, so he left math and spent the rest of his years studying linguistics. It wasn't until 30-40 years later that people took another look at his work, realized what he had created, and started to cite him.

[epenguin]

I don't even know the persons name who first isolated Oxygen!



He didn't even know it himself! :biggrin:

[Werg22]

Pauca sed matura.

Euler was more prolific than Gauss, and I have always enjoyed the story of the productivity of Euler after going blind. But I must agree with Marlon: Gauss was the greatest mathematician of all time. Modular arithmetic, quadratic reciprocity (I can't remember how many proofs he had), the FFT 150+ years ahead of its time, additive number theory, the fundamental theorem of algebra, etc. As an amazing calculator, he made great strides with least squares, the normal distribution, and other statistical methods.

Gauss reluctance to publish meant a huge part of his work didn't contribute to anything. Instead the results were collectively rediscovered. He was a great mathematician for sure, but not the greatest in terms of contributions.

[Ofey]

Feynman is my favourite. I still consider him being my main mentor in physics. He showed me what it's actually about. And I never got to meet him since he was dead before I was born. Pretty good considering he did it all from his grave?

[de_brook]

Gauss is usually referred to as the greatest mathematician in 17th centuries. Euler is referred to as greatest mathematical analyst up to this moment. Newton is referred to as the father of classical mechanics. From my own point of view, top three mathematician are,

1. J. Von neumann
2. David Hilbert
3. Cauchy( with over 700 articles written)

[Werg22]

Feynman is my favourite. I still consider him being my main mentor in physics. He showed me what it's actually about. And I never got to meet him since he was dead before I was born. Pretty good considering he did it all from his grave?

Feynman did not show you what physics is all about, he showed you his idea of what physics is all about. You then decided to adopt it. Just saying.

[Ofey]

Feynman did not show you what physics is all about, he showed you his idea of what physics is all about. You then decided to adopt it. Just saying.

Point taken. :shy:

[Freddy_Turnip]

Paul Dirac
Alan Turing

[CRGreathouse]

Gauss reluctance to publish meant a huge part of his work didn't contribute to anything. Instead the results were collectively rediscovered. He was a great mathematician for sure, but not the greatest in terms of contributions.

I have no argument there -- I even quoted his 'reluctance' quotation in my post (usually given as 'few, but ripe').

[ObHassell]

My favorite physicists are:
1. Newton-arrogant? yes. But he invented calculus and basically invented classical mechanics (not that it wasn't around before him, it's just he recognized it as "not-philosophy")
2. Richard Feynman- he's a brilliant man and I think he's hilarious
3. Galileo Galilei- I like him, he's a good guy
4. Maxwell- he's actually a mathematician, but he's more remembered for his physics contributions, he seemed to be a great guy too
5. Enrico Fermi- hilarious guy, brilliant too

My least favorite physicists are:
5. Copernicus- very intelligent, but he was a wimp...yeah they'd kill him if he had published his stuff earlier, but he stalled science by not putting it out there, not the most manly move.
4. Albert Einstein- sure he was great and his discoveries revolutionized physics, but he actually wasn't all that smart, I mean, I recognized the relativity of simultaneity halfway through high school after seeing a guy smack a sign and not hearing it for a second (I didn't give it a name, I just thought it was an interesting thought I had). I don't really have much of a rational reason why I don't like him, he just strikes me as a guy I wouldn't like I guess...
3. Michio Kaku- total idiot, he's a good writer and is good at explaining things, but he's a moron, he does junk science, like he's "looking for an equation about an inch long". YOU DON'T LOOK FOR AN EQUATION!!! YOU LOOK FOR THE REASON THAT SOMETHING HAPPENS OR AN IMPLICATION OF SOMETHING ELSE AND THEN YOU FIND AN EQUATION OR A SET OF EQUATIONS THAT DESCRIBE IT!!! Totally against what Feynman believed in, and Feynman has a Nobel and Michio Kaku has a following of science-buffs, you can't argue with that, well you can...just Feynman's belief in how to do science is much more rational.
2. Keppler- not because I think he's stupid or he did anything wrong, but because all of those educational videos my high school showed made him look like a creep.

.
.
.
.
.
and my least favorite physicist of ALL time is...
.
.
.
.
.
1. Aristotle- he believed that theories did not have to be proven or experimented with, he thought that if someone makes a claim and it is logically sound then it MUST be true...he gets Oden's Stamp of Stupidity.

okay...now that I've shook it up a bit, let's hear the controversy flow

[CRGreathouse]

Some of the top mathematicians:
Gauss
Euler
Euclid
Cauchy
Hilbert
Gödel

Runners-up (died young):
Ramanujan
Riemann
Eisenstein
Galois
Abel

[KnowPhysics]

In my list
Einstein
Euler
I added Einstein as first because no one would have ever imagined that some invisible atom is going to carry such a big energy but he revealed it. when ever i think this, i give big salute for the great physicists. I like Leonhard Euler for his best maths.

[Gib Z]

My favorite physicists are:
1. Newton-arrogant? yes. But he invented calculus and basically invented classical mechanics (not that it wasn't around before him, it's just he recognized it as "not-philosophy")
2. Richard Feynman- he's a brilliant man and I think he's hilarious
3. Galileo Galilei- I like him, he's a good guy
4. Maxwell- he's actually a mathematician, but he's more remembered for his physics contributions, he seemed to be a great guy too
5. Enrico Fermi- hilarious guy, brilliant too

My least favorite physicists are:
5. Copernicus- very intelligent, but he was a wimp...yeah they'd kill him if he had published his stuff earlier, but he stalled science by not putting it out there, not the most manly move.
4. Albert Einstein- sure he was great and his discoveries revolutionized physics, but he actually wasn't all that smart, I mean, I recognized the relativity of simultaneity halfway through high school after seeing a guy smack a sign and not hearing it for a second (I didn't give it a name, I just thought it was an interesting thought I had). I don't really have much of a rational reason why I don't like him, he just strikes me as a guy I wouldn't like I guess...
3. Michio Kaku- total idiot, he's a good writer and is good at explaining things, but he's a moron, he does junk science, like he's "looking for an equation about an inch long". YOU DON'T LOOK FOR AN EQUATION!!! YOU LOOK FOR THE REASON THAT SOMETHING HAPPENS OR AN IMPLICATION OF SOMETHING ELSE AND THEN YOU FIND AN EQUATION OR A SET OF EQUATIONS THAT DESCRIBE IT!!! Totally against what Feynman believed in, and Feynman has a Nobel and Michio Kaku has a following of science-buffs, you can't argue with that, well you can...just Feynman's belief in how to do science is much more rational.
2. Keppler- not because I think he's stupid or he did anything wrong, but because all of those educational videos my high school showed made him look like a creep.

.
.
.
.
.
and my least favorite physicist of ALL time is...
.
.
.
.
.
1. Aristotle- he believed that theories did not have to be proven or experimented with, he thought that if someone makes a claim and it is logically sound then it MUST be true...he gets Oden's Stamp of Stupidity.

okay...now that I've shook it up a bit, let's hear the controversy flow

Well, i'll take the lead. No objections to the favorites list, but some of your reasoning for the least favorites list leads me to think you are a layman of physics, amateur in many ways. If you think Einstein was not all that smart for recognizing something at an older age than you say you did, how about every physicist before him who did not formulate it at all? Or perhaps every single one of them felt it was intrinsically obvious as you say you do, and just never bothered to mention it? And on Michio Kaku. You are a fool to think that the "inch long" quote is his entire philosophy of physics. Obviouslly he merely said that to engage the target audience, which was definitely amateur physicists such as yourself.

The others are so obvious as to why your reasoning is odd, I will leave them.

[disregardthat]

And aristotle is probably one of the cleverest persons in history.

[cragar]

A couple more good mathematicians are Brooke taylor and Colin Maclaurin

[John Creighto]

I'm wondering where philosophy fits in here. Contributions to science and marth aren't always about solving problems sometimes it is about shifting paradigms be it putting the sun in the center of the solar-system (Copernicus), basing science on measurable properties instead of subjective descriptions (Galileo in The Assayer), representing motion on the Cartesian plane (Descartes), removing the absoluteness of time (Einstein), quantifying infinities (Cantor), exposing the naivety of set theory (Burchant Russell).

There is an inter-play here of both philosophers making important contributions to math and science and mathematicians\scientists proposing axioms with striking philosophical implications.

[Sycatech]

Al-Khwarizmi, father of algebra

[jonjacson]

In physics I have three favourites:

newton, if you read his biography and his works (in both math and physics) carefully, and you are conscient of the date he wrote all this works, you realise that he had one of the most powerful minds all over the history.


Behind him, Maxwell made an incredibly job. Everithing was under the ideas of Newton, and he made a revolution introducing the concept of field , the main idea of a lot of theories of the XX century, he broke the tendency of using force to solve everything and made a very beautiful theory.

And I don't forget his works on statistics, and other subjects, so for me one of the bests of the history for sure.

Finally Einstein, his general theory of relativity and the way he found it is absolute incredible for his time.

And in mathematics, I agree that Riemann achievements are impressive, his originality is wonderful.

Perhaps you have not talked so much about cantor, but he made for the first time in the history something clear with the infinite(a slippery concept for everybody during centuries), so I would put him in the list.

[trambolin]

So where is this list anyway? It has been 9 pages there must be one!

[lubuntu]

In physics( I don't know much about mathematians) in no particular order here are the ones I am most inspired by:

Feynman
Newton
Einstein
Dirac
Maxwell
Faraday
Hawking

Not necessarily the greatest in terms of contributions just the ones I happen to look at with a good deal of pure awe.

Honorable mention for:
Copernicus
Kepler
Tycho Brahe
Galileo

For there work in getting the ball rolling as it were.

[epenguin]

I could say there is something that awes me that distinguishes Dirac from the others mentioned.

I would have said so even if I were not reading as I am at the moment The Strangest Man, the biography of this brilliant scientist and miserable git.

Scientists are mostly ‘constitutionalists’: they discover the constitution of the universe, its structures and components, what it is made of and how that stuff behaves. Galaxies, stars, solar system, earth, rocks, atoms, particles. Then some of them are (or also are) dynamicists, starting with those structures in a certain state, retrodict or predict what they will do (including evolve into something else). Newton, Laplace, Einstein, Schrodinger, Pauling… But these dynamicists had to predict starting with what there is (or what there can be thought to be). They had to take the constituents of the world for granted.

Whereas Dirac was the first to predict a constituent of the world. Not because of some missing mass (Lavoisier) or energy (Pauli) or there was a gap in what there is, so fill it (Mendeleev). But what there had to be. An experimentally unknown particle, the positron, only because otherwise his equations were not nice. Something of a different nature from all the others it seems to me, that raised the game of understanding Nature.

(Summarised in the books as 'he predicted and a few years later that was found experimentally', the biog. cited gives the somewhat more tortuous real historical story.) Then he did it again for the magnetic monopole, jury still out. Then his theory showing electrons not just had, but had to have, spin is perhaps at nearly the same level.

Since then other particles constituting the world have been predicted to exist and found, maybe another soon. And I read that String Theories are at the same time dynamics and constitution inseparably – but Dirac was the first of the kind.

[disregardthat]

What about Abel?

[robert Ihnot]

Underestimated Mathematicians:

Well, since no one I've read has mentioned Cardan/Cardano--who confessed to cheating on the solution of the cubic, making him a difficult person to celebrate these touchy classroom days; I have to say he was as Ore has written, "The Gambling Scholar."

He published 130 works and his Ars Magna gave solutions to the cubic and quartic equations. (The quartic was solved by his student Ferrari.) He was aware of imaginary numbers, but was unable to develope a successful theory about them.

It can be argued that he deserves credit for the cubic, since he was the first to publish. (In those days there was considerble secrecy about methods, but such is a hinderence to mathematical progress.)

Furthermore his abjuct confessions were a method of gaining favor with the Vatican, and he was restored to favor by Pope Gregory X111, and received a lifetime pension.

Ore insists that Cardano was the first to intelligently expound on the theory of probability, a century ahead of Pascal and Fermat.

[robert Ihnot]

I think it somewhat rediculous that Newton, because he was considered a Physicst, is generally ignored as a mathematician, when he was at the very top.

"Gottfried Wilhelm Leibniz, Newton's contemporary and a philosopher/mathematician in his own right who found himself at odds with Newton, told the Queen of Prussia that "In mathematics there was all previous history, from the beginning of the world, and then there was Newton; and that Newton's was the better half."

Newton did hold the Lucaisian chair of Mathematics, and deserved the title of "Mathematican." He worked out the binominal theorem for small fractions, and found the Taylor series for sins and cosigns among his other acievements. Also, today noted by students for his method of root location, sometimes called "Newton's iteration".

[MikeyW]

I really don't know enough maths to comment on the level that some others have (read pages 1-4 and there is a lot of knowledge on those pages!), but my personal favourite came from Archimedes, his work to find pi without any tools that we have today was very impressive to me.

From physics I like Feynmann's totally conceptual approach.


For top people, I have always thought Gauss and Euler simply because in almost every module I took there would be some link to one of these people.

[God's Pen]

for me,there is no "best mathematicians" or "best physicians" i think they all make the best.

[robert Ihnot]

Gib Z I don't even know the persons name who first isolated Oxygen!

Priestly in 1774 extracted oxygen from mercuric oxide. He discovered that it caused a flame to burned very brightly, and a mouse could be kept alive 4 times as long in "dephlogisticated air" as in regular air.

Priestly traveled to France and met Lavaisier, who named the gas, "oxygen."

[wisvuze]

Faraday is one of the most interesting ones, I've heard that his mathematical knowledge went only up to trigonometry and algebra (and I don't mean linear/abstract)

[epenguin]

Gib Z I don't even know the persons name who first isolated Oxygen!

Priestly in 1774 extracted oxygen from mercuric oxide. He discovered that it caused a flame to burned very brightly, and a mouse could be kept alive 4 times as long in "dephlogisticated air" as in regular air.

Priestly traveled to France and met Lavaisier, who named the gas, "oxygen."

Priestly made those observations but is debated whether you should call him the 'discoverer' or rather Lavoisier who conceptualised them and others as 'oxygen'. If you don't know what you have discovered have you discovered it?

Remind me whether Columbus knew he had discovered America?

[robert Ihnot]

wisvuze: Faraday is one of the most interesting ones, I've heard that his mathematical knowledge went only up to trigonometry and algebra (and I don't mean linear/abstract)

If you want a name of someone who had very little understanding, and even contempt of math, it is Edison. Edison put it very simply,

"I hire mathematicians, they don't hire me."

PS: Edison had a detactor in Tesla who said, "His method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calcuation would have saved him 90% of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor's instinct and practical American sense." Wikipedia.org/wiki/Thomas_Edison.

[AakashR]

Ramanujan, Gauss, Newton, Riemann, Einstein

[JustGaussing]

Physics: Maxwell
Math: Euler, Gauss
But then again, I am not particularly good at either, so how would I really know? There are so many, and each stands on the shoulders of giants who came before.

[ilikemaths]

I have to second Lagrange, if for no other reason than he fits the bill so well having approached mechanics as a purely mathematical field. I read somewhere that he took enormous pride in not including a single diagram in his Méchanique analytique.

[lavster]

apparently there was a poll and Maxwell came out on top. in physicsworld or new scientist or something like that. I like Newton. he was one of the founders of calculus and he did his three laws of motion etc.etc. :)

[RoughRoad]

Ramanujan! This guy, with no formal education of any sort, did so much in this field in just 32 years!

[henglin]

best mathematician or physician? Thats comparing a top fuel dragster with a formula 1 race car.

But id say Newton (maths and physics)
Einstein(physics along with maths)
gauss
archimedes
liu hui
leibnitz

[Clu2.0]

feynmann, einstein, john nash and neumann

[micromass]

I'd like to add Euler, Hilbert, Godel, Grothendieck.

[Outlined]

in no particular order, here are some that come to mind off the top of my head:
- Hilbert
- Euler
- Erdos
- Gauss
- Archimedes
- Galois

i don't think i know enough physics to have an opinion about physicists. i guess you could go through the list of nobel prize winners to find a bunch of the best ever.

Erdos? No, would say von Neumann or Newton.

[snipez90]

Euler and Lebesgue, mainly because I'm partial towards analysts.

[ejnorman]

Saunders Mac Lane for discovering general abstract nonsense.

Haskell Curry for discovering why equals can be substituted for equals.

[HallsofIvy]

What?? 166 posts and no one has listed me yet??

[mathwonk]

We live and learn. Earlier in this thread I dissed Euclid but praised Newton for his limit definition of a derivative. Then in Fall 2009 I actually read Euclid and discovered that his description of a tangent line uses the limit definition (if you think about it, that is precisely what Proposition 16, Book III, Elements, says, in the epsilon delta version) and thus anticipates newton by over thousand years. I then learned that Newton read Euclid shortly before coming up with his own definition. Newton has not gone down, but Euclid has gone up in my estimation. I now consider his geometry book the best available even today.

[camilus]

Newton
Archimedes
Riemann
Gauss
Euler
Ramanujan
Grothendieck

What do you guys think of Grisha Perelman? I think he's absolutely brilliant.

[epenguin]

We live and learn. Earlier in this thread I dissed Euclid but praised Newton for his limit definition of a derivative. Then in Fall 2009 I actually read Euclid and discovered that his description of a tangent line uses the limit definition (if you think about it, that is precisely what Proposition 16, Book III, Elements, says, in the epsilon delta version) and thus anticipates newton by over thousand years. I then learned that Newton read Euclid shortly before coming up with his own definition. Newton has not gone down, but Euclid has gone up in my estimation. I now consider his geometry book the best available even today.

That is a motivation.

Sorry, but I find this thread irritating and pointless when people just give names or lists without reasons or motivations, criteria.

[mathwonk]

Yes, this is like a video game break from real work. But try not to be irritated when you are not required to look at it. Life is stressful if you go out of your way to be irritated.

[Outlined]

Newton
Archimedes
Riemann
Gauss
Euler
Ramanujan
Grothendieck

What do you guys think of Grisha Perelman? I think he's absolutely brilliant.

only dead ones would count I think :wink:

[widderjoos]

I think the people who had the greatest impact on physics are:

Galileo
Maxwell
Weyl
Einstein

For math:

Gauss
Hamilton
Riemann
(Emmy) Noether

for having important contributions (imo).

Personally, I admire Kitchen and Feynman who got me into math and physics through their writings.

[JonF]

IMHO George Cantor.

[mxbob468]

neumann for all that he contributed to and the lore surrounding him

[G037H3]

mathematics:

* Gauss
* Riemann
* Archimedes
* Euclid
* Euler
* Pascal


Physics:

* Newton
* Maxwell
* Poincare
* Faraday

[mathwonk]

just to be annoying, i will suggest that if you mention someone, you should have actually read at least some of their own writings. if not, then perhaps, just perhaps, you do not know what you are talking about.

[Abdul Quadeer]

My favourite Mathematicians/Physicists-
1) Einstein
2) Muhammad ibn Musa al-Khwarizmi
3) Euclid
4) Omar Al-Khayyam
5) Alhazen
6) Sir Isaac Newton
7) Abu Rayhan Biruni
9) Ibn Sina

[cragar]

1. HallsofIvy

[P-Jay1]

I would say Leibniz! Galois is my favourite though. Check out these podcasts on the BBC radio 4 site, really good listening:

http://www.bbc.co.uk/podcasts/series/maths

[camilus]

just to be annoying, i will suggest that if you mention someone, you should have actually read at least some of their own writings. if not, then perhaps, just perhaps, you do not know what you are talking about.

thanks mathwonk, you have been an inspiration throughout this entire thread. I honestly read through practically the entire thread several times and at disperse instances just because of the quality of your posts.

and to Outlined, only dead ones count in the debate of greatest of all time, I just wanted to incite a dicussion about Perelman and the current developments in topology. This is not yet my area of focus, but I plan on getting around to it, currently studying prime numbers and set theory. I need to study the geometrization conjecture a bit more, although I believe I understand the fundamental principles of topology.

Mathwonk, speaking of reading the masters in their own words, I was reading Riemann's 1859 paper (calling it that for lack of will to recall the German name), and I was wondering if you could recommend a good book in complex analysis specific for understanding the jump he made in end of page 2 and page 3 to derive the functional equation. Thanks

[Fil7]

Newton, Einstein, Gauss, Euler, Neumann, Feynman, Kelvin, Turing, Maxwell, Galilei, Hilbert, Poincaré, Majorana, Landau, Dirac, Faraday, Pedro Nunes (I'm portuguese), etc.

[cragar]

some more that I thought should be mentioned.
Gibbs, Boltzmann, Tesla, Wheeler, Hugh Everett,Eugene Wigner

[engphy2]

Pythagoras and Descartes