These men are routinely cited as the class of their respective fields.

But, for some fun and a little spirited debate, tell which you think is actually the GREATER genius.

Perhaps not in terms of accomplishments (unfair since Witten is 20+ years older)...

But maybe in terms of setting them back to the age of 20 and having them switch disciplines...which would be better at the other's game?

Or, maybe if both were first-rate experts on the same issue (let's say they've spent an ENORMOUS amount of time thinking about it), but had differing opinions (let's say vastly different), which one would you choose to believe?

even the switch disciplines is unfair, witten is a physicist but he also won a fields medal. while they'd both probably succeed i feel witten i many ways has done both.

on the one hand tao proved a major result about prime numbers, this sort of thing has been the white whale of number theory for as long as it has existed. i wish i understood witten's work more to appreciate it, but from the way physicists like max raker in SMP talk about him i know he should by no means be taken lightly.

who'd win in a fight, batman or spiderman?

I've met them both and Ed Witten is the correct answer. I think Tao would agree with me.

My sister dated Terry Tao's brother Nigel for a number of years. The family still lives in our home town Adelaide.

MaxRaker,

Would you mind elaborating a bit on why you pick Witten?

You may be more qualified than anyone who will post on this thread.

I should point out that I might not be objective here. Witten has had a pretty tremendous impact on the fields of math that i am interested in. I also should mention that outside of Tao's work in representation theory, I can't really follow much. He is pretty remarkable in that just his work that I can understand would make him a very good mathematician and that only scratches the surface of what he has done. I'll give some details on why Witten is so important later.

I'm all ears!

Also, if you don't mind, what makes you think Tao would agree that Witten is smarter than him?

Sorry, I totally forgot about this. That was just a guess and I think Tao would admit that he hasn't revolutionized a field to the level that Witten has. He's still young of course, but I don't think Tao is clearly the hands down best mathematician under 40.

Ok, I'm not really going to explain why Witten is important. It just ends up being alot about topological quantum field theory or twisted K theory and won't mean a whole lot to most people. I'll instead give some evidence that he is a genius.

So unlike most other peopel at his level, Witten didn't really have scientific interests as an undergrad. The first time in which he officially had anything related to math/physics on his resume was when he started as a grad student at Princeton. I'm not even sure exactly how he got in, but i think within a few months he was working for David Gross. Gross was at this time likely the best physicist in the world. Just before Witten joined his group, he had just finished some very important work on asymptotic freedom SU(3) and the strong interaction. This was work that he and his student , Frank Wilczek later received a Nobel prize for.

So Gross was at the top of his game and also had good experience will gifted and Nobel prize worthy students. Witten had a BS in History and had worked in politics. There are many stories you hear around Princeton about how frustrating Witten was to mentor. David would come up with a problem that he thought would take anybody a few weeks to solve and require a ton of calculations, which a person sort of needs to go through to be educated as a theoretical physicist. Witten would instead come back in a day or 2 with a one page proof that required no calculations and was based on some deep symmetry or other hidden but mathematically sophisticated technique.

You can talk to some profs who were at Princeton at the time and as a school its produced its share of talent (including Tao) but I don't think the faculty has ever been blown away like they were with Witten. He must have had one of the quickest journeys from "I want to be a physicist" to "I am the most important person in the field" in history. Since then he has a ton of important discoveries on his own, and also has done an amazing job of explaining and realizing the significance of other peoples work like his first paper on the Maldacena Conjecture. The latter imo is very unique.

i know max raker said he didn't know, but does anyone know how the hell he got into the grad program in applied math at princeton? did he teach himself all the prerequisite math? did he just blow away the interviewers to the point where they figured he'd teach himself? i just cannot imagine what had to occur for the admissions staff to let in a guy with a BA in history. obviously they made the right choice but he must have done something incredible to impress someone so much to ignore the fact that he had no formal background in the sciences

Witten for sure.

I'm way smarter than virtually everyone I run into in daily life, and smarter than prominent figures in some areas, but I'm not smart enough to even "get" the intelligence of people this smart. I don't really care to even think about which is "smarter," because at this level I will probably never be close enough to even appreciate their accomplishments, much less try to evaluate and compare them. I could take the word of people like Max Raker, but eh. People one "tier" smarter than me I can try to arrange in these superhero contests, people one tier above them I can maybe say something about, people one tier higher probably don't even live in the same world that I do. I'm happy that they're gracious when speaking to us mere mortals, but these guys are the only ones who really inspire star-struck awe in me and it does seem a bit silly to compare them.

I doubt Witten could do exactly what Tao has done, and certainly Tao couldn't do exactly what Witten has done. I think Witten's biography is surreal, and he has more of the "polymath" elements that we tend to value highly. Does that make him "smarter?" No idea.

Yeah, smarter sort of doesn't make sense. But I think Witten's biography is more unbelievable and Tao's is almost "standard" for a genius. Granted it is sort of silly to go by that, but its fine for random speculation

And way more modest too!

I think this is probably a pretty reasonable statement, as Tao's career progression is what one expects of a 'typical' prodigy. The thing that makes Tao unique is that he's done everything incredibly quickly -- near perfect SAT scores at the age of 8, IMO gold medal at the age of 13 (still youngest ever). Big awards for PDE/harmonic analysis research at 25. The biggest component of his Fields medal work was done before he was 30 (although in fairness, his co-author, Ben Green, was even younger). The number of fields he's currently active in is almost unrivalled.

I also think that he is clearly the best mathematician in the world under the age of 40 (he's only 34 now), and that this is definitely an opinion held by a plurality of mathematicians (likely a majority).

Witten is pretty amazing as well. It seems that they have different strengths, Tao being unbelievably technically strong, and Witten being unbelievably conceptually strong. Of course Tao is conceptually stronger and Witten is technically stronger than any of us could ever hope to be.

blah_blah -

Can you give a comparative anatomy of 'technical' vs. 'conceptual' strength?

Not really, I may just be speaking out my ass here but it makes sense to me at least. I'm not particularly familiar with any of Witten's work, but it seems to be conceptually very deep to me. I am somewhat familiar with Tao's work, and a dominant theme is use of hard (quantitative) analysis methods over soft (qualitative) analysis methods. This often requires estimates which are very difficult to derive, but which I generally think of as being 'technical' in nature.

I thought gene beat him (confirm/deny?).

I spent a lot of time with terry and im convinced hes ******ed.

either way his reign of terror isn't for long. Hes overseeing Gene Kim who will quickly over take both of these peoples accomplishments, Which is why Im surprised Gene is as terrible at poker as he is, but whatever.



Then after gene will be 吴剑秋 (Luke Wu) undergrad at UCD, 16 years old, transferring to MIT. hes solid, prolly fields medal material.

But as for the question, Terry is smarter, and im not just saying that b/c of my relationship with him

Are people really saying Tao belongs in the Groethendiek/Atiyah class of living mathematicians? If you twist my arm, I can put Witten in that class, I don't think Atiyah would mind atleast.

I would think that Witten got himself into Princeton's applied math/physics programs because he likely performed very well in some undergrad (perhaps higher level) math/physics courses, killed the GRE and probably had some VERY good letters of recommendation. He worked on McGovern's campaign, so he may have gotten a letter from him.

Tao seems to me more conceptual than technical.
I think math research is very conceptual. You have an idea then you find the tools to make the technical part work. But a lot of the time you can explain the idea of the proof in concepts (which I think Tao does a very good job of doing in his talks) instead of explaining in the nitty gritty details.

I didn't know of Ed Witten's background. That seems amazing.

Grothendiek and Atiyah are not the sort of mathematicians I strive for. I think Tao might not be good to compare against them because Tao seems to me more of a problem solver than a theory builder. I would compare Tao against someone like Erdos in terms of how good he is. Erdos was a problem solver and that is the sort of mathematician I strive to be.

I have never heard of either hence I assume they are both carp.
Certainly no good at publicity.
What are the 'famous' for? (or rather not famous for?).

you should probably stop posting in this section of 2p2.

Who have you heard of? Einstein and that's it?