Best all time mathematicians/physicists.

[IsotropicSpinManifol]

why einstein is better than Newton

mc^2<mc^2

therefor

Newton < einstein

 

[bomba923]

Personally, my top two are
Riemann (1st) &
Euler (2nd)

 

[mathwonk]

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, ...

 

[Icebreaker]

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...

 

[cronxeh]

Take a look at this list http://www.sali.freeservers.com/engineering/maths.html

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

 

[LeBrad]

My favorite 3 are Euler, Gauss, and Ramanujan

 

[quasar987]

In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

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

 

[MalleusScientiarum]

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.

 

[cragwolf]

My first 3 in each list are in order, the rest are not.

Mathematicians:
Euler
Riemann
Gauss
Fermat
Lagrange
Hilbert
Poincaré
Cantor
Kolmogorov
Grothendieck

Physicists:
Einstein
Newton
Maxwell
Bohr
Schrödinger
Rutherford
Dirac
Heisenberg
Pauli
Feynman

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.

 

[cragwolf]

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.

 

[fourier jr]

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!

 

[cronxeh]

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

http://en.wikipedia.org/wiki/Analytical_geometry

 

[selfAdjoint]

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

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.

 

[EnumaElish]

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?

 

[fourier jr]

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.

 

[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.