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 don't 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

 

[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 wouldn't 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...

no one included Muhammed bin Musa Al-Khawarizmi in their 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...

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

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

peace

Welcome to the forums.

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.

 

[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.