Best all time mathematicians/physicists.

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  • #71
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.
  • #72
More people should be talking about Dirac...I feel sad.
  • #73
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.
  • #74
Speaking of mathematicians who've most helped physics move along, Sophus Lie and Hermann Minkowski probably deserve mention.
  • #75
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.
  • #76
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.
  • #77
Did anyone mention Euclid?
  • #78
Einstein, Newton, Archimedes, Euler, Maxwell, Gibbs, Schrodinger, Godel

To me Gibbs is the greatest american scientist of all time.
  • #79
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.
  • #80
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.
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  • #81
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:

von Neumann

Doh, no room for Archimedes.

For physics:

  • #82
I haven't seen these two mentioned yet (I didn't go through the entire thread tho):

  • #83
I think that the best mathematical physicists (of today) are:

1. Edward Witten
2. Michio Kaku
3. Robert M. Wald (see [Broken])
4. John Baez
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  • #84
X-43D said:
I think that the best mathematical physicists (of today) are:

1. Edward Witten
2. Michio Kaku
3. Robert M. Wald (see [Broken])
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.
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  • #85
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.
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  • #86
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.
  • #87
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
  • #88
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?
  • #89
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
  • #90
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.
  • #91
why einstein is better than Newton



Newton < einstein
  • #92
Personally, my top two are
Riemann (1st) &
Euler (2nd)
  • #93
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 don't really see how anyone 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, ...
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  • #94
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...
  • #95
Take a look at this list [Broken]

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
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  • #96
My favorite 3 are Euler, Gauss, and Ramanujan
  • #97
In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

mathwonk said:
it goes on and on... i don't really see how anyone person could have done all this.
And he died at 39 !

Your precious grotindiek isn't even on that list wonk :wink:
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  • #98
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.
  • #99
My first 3 in each list are in order, the rest are not.



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.
  • #100
mathwonk said:
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.
  • #101
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!
  • #102
quasar987 said:
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
  • #103
quasar987 said:
In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

cronxeh said:
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.
  • #104
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?
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  • #105
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.

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