The World's Greatest Mathematician?

[Albertus Magnus]

Who was the world's greatest mathematician? Why?

[Savant]

Your list is screwey. Cantor isn't even on the list, and he's easily in the top 10, probably 5.

[Universe-Hun]

Why is Pythagoras not in the poll?

[Impérialiste]

Why is Kepler on the list? He was not a good mathematician even if he was an admirable one.

Where are Grigori Perelman, Alexander Grothendieck, and Andrew Wiles? They're more recent.

But where is David Hilbert? Hilbert demanded a rigor to mathematics that hadn't been there since the Ancient Greeks. For retards who think applied mathematics is better than pure mathematics, how are the former justified to use anything without the latter first proving the theorem?

If Newton is on the list, then where is Leibniz?

Where is Cauchy? Bernoulli is very important in Differential Equations and more. John von Neumann isn't on your list. Why ignore Pythagoras? Granted, no one really knows of Pythagoras and what he actually discovered, but you could cluster Pythagoras under one whole school just like the Bourbaki School could be clustered as one mathematician (if for no reason other than the fact that those schools tend to have one principle discoverer with many small contributions done by the rest).

How did you ignore Ramanujan? G. H. Hardy thinks he could have been on par with Gauss and Riemann had he lived longer. G. H. Hardy also thinks critics like you are total losers and create nothing worth considering.

[Delmac]

how are the former justified to use anything without the latter first proving the theorem?

IIRC your man Hardy believed that directly perceiving the truth of the theorem was the real thing, the proof being in a sense only so much handwaving.

I do agree with most of your complaints about omissions, but honestly do you consider any one of them the equal of Gauss?

[Baron_Corvo]

IIRC your man Hardy believed that directly perceiving the truth of the theorem was the real thing, the proof being in a sense only so much handwaving.

Interesting that, because he believed in bringing continental rigour to mathematics and thought most of his students (at least in the early days) were very deficient at providing rigorous proofs of theorems.

If we can have Hardy, I'd add John E Littlewood, who collaborated with Hardy extensively, as one of the greatest British mathematicians in recent times. Hardy looked up to him if I remember rightly.

Ramanujan was incredible, I agree. I don't think he created any ground-breaking new theories though, his main gift (and it was huge) was for formulae. There are a couple of other people whom I know of who died young and could have gone on to make even bigger contributions than they did; F P Ramsey and Evariste Galois.

I'd add Euler to the poll list, he was extremely prolific in his time.

[Impérialiste]

Interesting that, because he believed in bringing continental rigour to mathematics and thought most of his students (at least in the early days) were very deficient at providing rigorous proofs of theorems.

If we can have Hardy, I'd add John E Littlewood, who collaborated with Hardy extensively, as one of the greatest British mathematicians in recent times. Hardy looked up to him if I remember rightly.

Ramanujan was incredible, I agree. I don't think he created any ground-breaking new theories though, his main gift (and it was huge) was for formulae. There are a couple of other people whom I know of who died young and could have gone on to make even bigger contributions than they did; F P Ramsey and Evariste Galois.

I'd add Euler to the poll list, he was extremely prolific in his time.

For some odd reason, I assumed Euler was already included simply because Euler is one of the top greats.

"e" is really a convergence point such that the derivative of its sequence is equal to itself.

Taylor's Theorem F(Xo) / 0! + F'(Xo)*(X - Xo)/1! + F''(Xo)*(X - Xo)^2/2! + . . . + F^n(Xo)*(X - Xo)^n/n!).

Let F(x) = e^x and Xo = 0.

F(x) = e^x; F'(x) = e^x; F^n(x) = e^x.

e^x = 1 + x / 1! + X^2 / 2! + X^3 / 3! + . . . + X^n / n!.

That's a bound such that 1 is greater than the rest of the areas.

d/dx [e^x] = d/dx [1] + 1/1!*d/dx [x] + 1/2!*d/dx [x^2] + . . . + 1/n!*d/dx [x^n] = 0 + 1/1! + 2x / 2! + . . . + n*x^(n - 1) / n! = 1 + x / 1! + x^2 / 2! + . . . + x^n / n! = e^x.

Euler = Excellent.

[Impérialiste]

IIRC your man Hardy believed that directly perceiving the truth of the theorem was the real thing, the proof being in a sense only so much handwaving.

I do agree with most of your complaints about omissions, but honestly do you consider any one of them the equal of Gauss?

Depending on the standard, one can argue a case for a number of people, including Newton or Leibniz. Calculus made that break for algebra and geometry that non-Euclidean geometry would do for the fifth postulate. Honestly, I think ranking mathematicians is silly. I tried that with pro-wrestling, and it doesn't work. Different eras, different standards, different relativity values, and a divergence between primary sources and secondary sources. Even Hardy hated critics.

Speaking of which, Hardy was part of a different school of thought then. At least Hardy brought analysis back into the English school of thought, given that Newton's defenders went against analysis to protect him by spiting Leibniz.

Gauss at least was a strong mathematical physicist, but I would not argue his contributions were greater than Euler's even. Euler even founded topology.

[Impérialiste]

On Hardy's intuitive standard, as unscientific as that standard sounds, it makes sense to one who does a lot of proof writing.

[Gedanken]

Mathematics these days is so fragmented, that it takes eons for a really important result to spread around, unless it's in a trendy area like AG or whatnot.

Groebner bases (actually first discovered by Shirshov) is one good example, but another would be the recent introduction of gauge integrals, a vast generalization of the Riemann integral (the latter only valid for a small class of functions, & convergent sequences of R-integrable functions do not always converge to an R-integrable function). This is comparable in importance to the introduction of the Lebesgue integral, but I see only one good book on it in the press. Not even Mathoverflow (the ONLY good place to seriously discuss problems) is very helful here.

My own research is in lattice theory, but I would nominate Jean Leray as the most interesting modern mathematician - for his introduction of sheaves, spectral sequences and stuff. And Gel'fand for Banach space theory and automorphic forms. Shelah is the leading light in model theory and AST.

[Kodos]

Despite having an engineering degree I don't feel im qualified to comment. Imperialiste knows far more on this subject then I...

[Impérialiste]

Despite having an engineering degree I don't feel im qualified to comment. Imperialiste knows far more on this subject then I...

It's not that serious of a thread, clearly because the options are so poor. Moreover, I'm not a mathematical historian. I just have problems with who were excluded - people who obviously are more important than 90% of the people listed.

[Savant]

Precisely...

It's not that serious of a thread, clearly because the options are so poor. Moreover, I'm not a mathematical historian. I just have problems with who were excluded - people who obviously are more important than 90% of the people listed.