Best all time mathematicians/physicists.

[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.

 

[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 written 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?