Best all time mathematicians/physicists.

[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 ) 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 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 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.