Greatest mathematician ever?

Being said there are several "types" of mathematicians, the greatest (at least in Logic) could be Kurt Gödel. With his Incompleteness Theorems, he had the same revolutionary impact in Maths as Einstein (with whom he was friend) had in Physics with his Theory of Relativity.
By the way, his life could be interesting enough to be transposed into a movie, such happened with John Nash. He was a bit "schizophrenic", as well.

I always say too much Maths hurts. ... 


I'm Winston Wolf. I solve problems.

...And no dream is ever... just a dream...

reply share

add reply

formatting help

Can you really be the greatest mathematician ever known if you can't prove your own work?

I suppose yes.

In mathematics the art of proposing a question must be held of higher value than solving it.
- Georg Cantor

Sounds rather counter productive I know 

To see how this could be true, one needs to actually do math, or physics, or philosophy,... or other sciences, or literature or art, etc.

However, only a very gifted individual actually experiences the truth of the statement (i.e. to ask something so profound that it creates a (or a few) new branch of mathematics).

Usually the greatest mathematicians (or physicists) are known for solving unsolved problems by creating new abstract structures or using old ones in a fundamentally new way (Planck with quantum energy, Einstein with the Lorentz group, Grothendieck with Scheme, Wiles with Elliptic curves, Perelman with Ricci flow etc. and recently Mochizuki with Frobenioids and his theory that about 5 people in the world can understand and none can explain it well enough for others). In any case, at the end of these theories (just flip to the final pages of the thesis) you often see a summary of results, references to other work, for the sake of completeness they don't usually include unsolved question(s). First of all, these questions always exist. Sometimes these questions are not much of a logical leap away for people at this level, i.e. it doesn't take long (months, years) for experts at the frontier of human knowledge to see them. HOWEVER, sometimes, especially in mathematics, the profound questions in a theory don't arrive until a generation later when humans are used to its abstractness (which is right now the case with Mochizuki's theory).
I suppose the one who asked an unsolved question of this latter category is great indeed. Ramanujan's conjecture doesn't quite belong to this class, but then again he also solved many difficult problems - all of which are great achievements in mathematics so it's safe to say he proved most of his work and didn't prove some of his conjectures - like any great mathematician...so, rather moot point

I can tell you the reason why he is ridiculously influential and also the favorite of many working mathematicians in this generation: Ramanujan has unparalleled intuition, unseen before in history.

He is not an infallible oracle, Hardy knew this, Littlewood knew this, but he was eerily close to one, in fact, too close for comfort in the culture of early twentieth century Cambridge mathematics (which has always been a timeless rigorous monument of definitions - axioms - theorems - proofs, in that order). I don't follow the legend of Ramanujan, and he isn't my favorite mathematician but I am aware of his quite disproportionately big influence (given the very brief period they knew each other) on Hardy and Littlewood's work, even up to modern analysis! That is incredible for a guy who is almost entirely self taught.

One thing I quite like about this movie is that it doesn't glorify a special snowflake figure in the typical Hollywood way, in my interpretation anyway. Ramanujan claimed, in his letters to Hardy, that he had found a more or less exact formula for the prime counting function (the number of primes less than or equal to n). Upon closer inspection by Hardy and Littlewood, this formula was later shown to be incorrect. Hardy even commented

Ramanujan’s theory of primes was vitiated by his ignorance of the theory of functions of a complex variable. It was (so to say) what the theory might be if the Zeta-function had no complex zeros. His method depended upon a wholesale use of divergent series… That his proofs should have been invalid was only to be expected. But the mistakes went deeper than that, and many of the actual results were false. He had obtained the dominant terms of the classical formulae, although by invalid methods; but none of them are such close approximations as he supposed.



This is part of the ongoing tension in the movie between the transcendental intuition, as exemplified by Ramanujan, and the classical deductive-analytical rigor, as exemplified by Hardy; however it explores the conflict between these two aspects in a way that did them both justice, I honestly don't see the hero and the villain. There is no final victory or defeat, there's only the usual development of mathematics, with drama! I believe the massage of this juxtaposition is that pure mathematicians do what they do not because of applications to physics or anything else, but simply because they feel compelled to: for the devout Ramanujan, math was literally about writing down “the thoughts of God,” while for the atheist Hardy, math was a religion-substitute.

reply share

add reply

formatting help

All you have to do is count up the number of theorems and fundamental results and discoveries that a mathematician made in his entire career. And if you go by that measure, which is the only reasonable measure, then no one compares to Gauss, no one even deserves to be mentioned in the same sentence as Gauss.

Do you actually have a number for the total amount of theorems, fundamental results and discoveries by Gauss? If not, then your opinion is subjective.

reply share

add reply

formatting help