Any candidates?
Way too early to tell. You might have better luck asking who the greatest mathematician of the second half of the twentieth century is.
After doing a little research, I think that it would be possible to list several dozen mathematicians who might be contenders for being the greatest mathematician of the second half of the twentieth century. Do you really want to see that list? What would it prove? It’s not like being considered the greatest player of a given sport for that time period. Within a given sport there are semi-objective measurements for accomplishments. Within mathematics, it’s hard to compare the relative importance of various achievements.
A camel?
Practicing for Jeopardy!, astro?
Count me in with the reluctance of the former posters, but if you must have an answer, many consider Terrence Tao (Terence Tao - Wikipedia) to be one of the brightest guys around. I remember reading somewhere that one strategy of current mathematicians is to get Terrence interested in a problem they’re working on.
The guy who figured out how to beat the house at poker in Vegas.
Not an answer to your question, but Paul Erdos has one of the more fascinating life stories I’ve read.
Joe
Smart.
(That’s what you get for asking “what” rather than “who.”)
:eek:
Math is such a large field, I’m not sure if it would make sense to try to give a definitive answer, the same way it would be odd to ask the more general “Who is the greatest academic in the world today?”. Do there exist mathematicians with their fingers in every pie anymore? (Did there ever, or is that just historical illusion?)
Any name I could think of as one I admire, I would have to say “Yes, they are a towering name in subfield X. But that’s still only such a small part of math; the average mathematician knows little of their work.”
Though, for me, the name Terrence Tao came to mind first, as well. But, honestly, I know nothing of his actual work, at least not to any significant detail; I am just aware of his reputation, basically.
astro, please return to this thread. Why do want to know the answer to this question? Give us some more information about what you want to know and maybe we’ll be able to give you an answer to some more limited question that’s more easily answered.
Tao is very interesting. I wonder if the character of Charlie Epps in Numbers was based on him.
StG
I’m far from a mathematician, but I have read the fascinating story of Grigori Perelmen, a Russian who solved the Poincare Conjecture (among other less famous achievements), which had been a long-standing problem that eluded other mathematicians.
What strikes me as unusual is that his proof seems to have come out of left field. From that wiki article:
And Terence Tao himself said:
IOW, other genius mathematicians are kind of in awe of him.
Interestingly, he appears to fit the stereotype of the eccentric, reclusive genius compeltely. He refused the Fields Medal (the only one to do so), and appears to have withdrawn from the field.
He doesn’t appear to have been as precocious as Tao, however. I’ll let those who work in the field comment further.
Clifford Pickover’s 2001 book Wonders of Numbers includes a list of the 10 most influential mathematicians alive today, “based on surveys and interviews with mathematicians.” The list:
- Andrew Wiles
- Harold Coxeter
- Roger Penrose
- Edward Witten
- William Thurston
- Stephen Smale
- Robert P. Langlands
- Michael Freedman
- John Horton Conway
- Alexander Grothendieck
The Count.
He loves to count… ah, ah, ah, aaaaaahh!
Just going off of my experience with mathematicians, I don’t think the first word of the OP’s title is used incorrectly. 
Someone who is still alive but who did his work long enough ago that its impact can be meaningfully assessed is John Nash (of A Beautiful Mind fame).
Terrence Tao seems to be the consensus. I was recently at a talk covering some extensions of his work. Tao’s work (which he did for “fun”, apparently) caused distinguished mathematicians to shake their head in disbelief (some extension of Goedel’s dialectica translation to ergodic Ramsey theory, or something).
Let me start by saying that that list is fatuous. Let me take them one by one:
For the second half of the 20th century, most mathematicians would agree on Grothendieck. Wiles is a fine mathematician, but if he is in the top ten he is near the bottom of the list. Langlands has certainly been among the most influential, mostly for his global vision and could be second, though I doubt. Conway should be higher on the list. Coxeter is no longer alive, though he was in 2001. A fine mathematician but very limited range and does not belong on the list. Witten is more of a physicist, but even as a mathematician he blongs well up on the list. Smale was influential (and a colleague of mine) for a time, but he stopped early. I’ve heard him talk on real (as in real numbers) computation and it makes no sense to me. Freedman did some outstanding work, then sold out to the dark side. I have no idea what he has done for Microsoft. Thurston may be in the top 5, but I would have trouble putting him there. That leaves only Penrose. I consider him an ass. Not only did he utterly misunderstand the meaning of the undecidability of the halting problem, after it was explained to him carefully (by me, among others) he just ignored and compounded his error. This is not a mark of greatness. Yes he did some fine work early on, but his later stuff is either trivial or plain wrong.
Someone earlier suggested Perelman. Had he not dropped out completely, that would be an interesting thought. But I concur with an earlier post that it is virtually impossible to know who is doing the best contemporary work. However, Grothendieck was different. Even at the beginning of his career he was widely described as the best mathematician around and his work amply justified that claim. However, he also dropped out early.