Best all time mathematicians/physicists.

[TenaliRaman]

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

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

-- AI(a happy geometry nut)

 

[quasar987]

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

What book would you recommend on analytical geometry Mr. Adjoint?

 

[Pyrrhus]

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

 

[TenaliRaman]

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

-- AI

 

[tcamps]

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

 

[mathwonk]

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

http://kendrickpress.com/Riemann.htm

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

 

[mathwonk]

review of riemann's works

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

 

[mathwonk]

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

 

[zhentil]

Riemann and Cauchy.

 

[epenguin]

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

Some random thoughts.

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

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

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

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

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

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

 

[mongoose]

euler

 

[mathwonk]

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

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

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

 

[delta_moment]

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

The Farad is such a fun quantitative unit.

 

[Bosonichadron]

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

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

regards
marlon

What!? Gauss the best!?

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

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

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

Oh, and as far as physicists go:

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

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

This, of course, is just my opinion.

BH

 

[Gib Z]

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

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

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

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

 

[Bosonichadron]

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

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

regards
marlon

Marlon,

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

BH

 

[Bosonichadron]

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

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

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

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

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

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


--Bosonichadron

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

 

[cragar]

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

 

[CRGreathouse]

What!? Gauss the best!?

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

Pauca sed matura.

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

 

[csprof2000]

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

 

[maze]

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

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

 

[epenguin]

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

He didn't even know it himself!

 

[Werg22]

Pauca sed matura.

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

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

 

[Ofey]

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

 

[de_brook]

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

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

 

[Werg22]

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

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

 

[Ofey]

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

Point taken. :shy:

 

[Freddy_Turnip]

Paul Dirac
Alan Turing

 

[CRGreathouse]

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

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

 

[ObHassell]

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

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

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

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

 

[CRGreathouse]

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

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

 

[KnowPhysics]

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

 

[Gib Z]

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

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

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

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

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

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

 

[disregardthat]

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

 

[cragar]

A couple more good mathematicians are Brooke taylor and Colin Maclaurin