Lubos Motl has a posting announcing that Terence Tao will be one of the 2006 Fields Medalists. The announcement of the Fields medals is officially made at the time of the International Congress of Mathematicians, which this year will be in Madrid in August. A few months before the Congress generally there are solid rumors circulating in the math community about who the winners will be. If Lubos is right (and while I don’t know his source, this agrees with earlier speculation), the blogosphere will be responsible for a much earlier spread of rumors about this than usual.

**Update**: Lubos’s posting just disappeared. So, maybe this rumor is not right, or maybe it is, but whoever he got it from didn’t want it spread so publicly. His posting has been replaced with the comment “I removed information about a certain medal that was far too preliminary.”

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Not surprising. I guess Yau would definitely be the first one to know who wins, if he is not one of those who decides. And Lubos would learn that quickly due to proximity to Yau’s office.

His Fields winning proof can be found here. I can only understand the first few pages. What interests me is conjecture 2.2, which is awesomely simple and is a much more general statement that can automatically lead to what he is trying to prove. He did not attempt to prove that conjecture. Has any one attempted at that conjecture?

It’s simply stated as that as long as an infinite sequence of integers {ai} satisfy sum(1/ai) = infinity, then it follows that within {ai} you can always find infinite collections of progressive sequences of any arbitrary length, i.e., sequences where all elements bi can be found within {ai}, and bi = p + q*i, 0

I followed Quantoken’s link above to the Field’s medal paper on arxiv.org, and it is 56 pages of beautifully written text and maths. I like the historical introduction, and the way that the various components are described in detail first, instead of referring the reader somewhere else. It’s the kind of helpful paper that encourages people who find pure maths a real headache (like me).

Congratulations to Terence Tao, whether he has won or not! To me what is even more interesting than his childhood story is where he discusses his way of working in an understandable way. See

http://www.college.ucla.edu/news/05/terencetaomath.html –

How does Tao describe his success?

“I don’t have any magical ability,” he said. “I look at a problem, and it looks something like one I’ve already done; I think maybe the idea that worked before will work here. When nothing’s working out; then I think of a small trick that makes it a little better, but still is not quite right. I play with the problem, and after a while, I figure out what’s going on.

“Most mathematicians faced with a problem, will try to solve the problem directly. Even if they get it, they might not understand exactly what they did. Before I work out any details, I work on the strategy. Once I have a strategy, a very complicated problem can split up into a lot of mini-problems. I’ve never really been satisfied with just solving the problem; I want to see what happens if I make some changes.

“If I experiment enough, I get a deeper understanding,” said Tao, whose work is supported by the David and Lucille Packard Foundation. “After a while, when something similar comes along, I get an idea of what works and what doesn’t work.

“It’s not about being smart or even fast,” Tao added. “It’s like climbing a cliff; if you’re very strong and quick and have a lot of rope, it helps, but you need to devise a good route to get up there. Doing calculations quickly and knowing a lot of facts are like a rock climber with strength, quickness and good tools; you still need a plan – that’s the hard part – and you have to see the bigger picture.”

His views about mathematics have changed over the years.

“When I was a kid, I had a romanticized notion of mathematics — that hard problems were solved in Eureka moments of inspiration,” he said. “With me, it’s always, ‘let’s try this that gets me part of the way. Or, that doesn’t work, so now let’s try this. Oh, there’s a little shortcut here.’

“You work on it long enough and you happen to make progress towards a hard problem by a back door at some point. At the end, it’s usually, ‘oh, I’ve solved the problem.'”

Tao concentrates on one math problem at a time, but keeps a couple of dozen others in the back of his mind, “hoping one day I’ll figure out a way to solve them. If there’s a problem that looks like I should be able to solve it but I can’t, that gnaws at me.”

Glad to know that Tao, a Chinese mathematician (correct me if I am wrong), has got a very good chance to win the Fields medal. He will be the second Chinese winning the Fields medal after Yau if he will make it. Tao is modest about his math ability in his speaking. But why are his works important? Somtimes, I don’t know why mathematicians like to solve mathematical problems that seem to have little relevance/applications to our daily life.

Tao is Australian, probably of Chinese descent, but Australian. I doubt if he finds all this talk about his future Fields medal entertaining.

mathjunkie, I’d suggest that relevance or applications to our lives isn’t really a good metric to use for mathematical problems. Or indeed most problems in academia. I mean, suppose tomorrow some bright spark has an ‘ah ha!’ moment and formulates a complete and consistent theory of everything. Will this help me build a better mousetrap?

Sure, in twenty, thirty year’s time the theory might lead to the invention of the quantum frambotzulator, revolutionising the frambotz industry and profoundly changing all our lives. But is that really why we want a theory of everything? Wouldn’t it be just as interesting without the frambotzulator?

Of course it would. We don’t want a theory of everything because of the technology it might lead to, we want a theory of everything because it’s cool and interesting.

You can justify physics by applications to engineering, and mathematics by applications to physics, other practical subjects, etc. but frankly doing so is missing the point. Tao’s work will probably never see a useful application, but this doesn’t make it any less cool and important.

There’s a great quote which is attributed to Feynmann: “Physics is like sex. Sure it has a useful purpose, but that’s not why we do it.” The same is true of mathematics.

I know of at least one sequence that satisfies this relationship, namely the integers. The harmonic sequence of 1/1 + 1/2 + 1/3….. has no upper bound. And of course in the integers, you can find an infiite amount of progressive sequences if you play with the p’s and q’s.

Lubos had a post reporting a rumor. Later the post was deleted. The post here is a reference to a (now deleted) post of a rumor.

“So, maybe this rumor is not right, or maybe it is, …”

Ugh. The post here should be deleted in its entirety.

If there are “reliable sources” (~ earlier speculations), then cite the credible sources.

sunderpeeche, I don’t agree, for this reason. The comments on the post have occasioneed some very interesting mathematical discussions. This is quite diffferent from just retailing rumors that “Enquiring Minds Want to Know”. 🙂

I wasn’t sure whether to leave this post up or not, but don’t see a good reason not to. It’s true that Terry Tao might not be amused by all this, but if so, I fear that’s the price of fame. If and when he does get a Fields medal, he’ll have to learn to contend with the massive media attention and the women throwing themselves at him. The Fields medal committee may not be happy if this is a genuine leak, but then it’s their own fault for having members who blab to Lubos.

In general I feel that rumor-mongering (when done with scrupulous accuracy), is a fine thing to do on a blog like this. Unfortunately I normally feel constrained not to repeat interesting rumors here, because it almost always would be too obvious to many people who my source was, and said source would not be pleased (and would stop repeating juicy rumors to me). This case is kind of different, Lubos did make a public announcement….

Hi,

Slightly off topic.

The proceedings for ICM 1998 is availiable on the website for download. But, I have never been able to find the proceedings for ICM 2002!

I was wondering if anyone knows if the proceedings for ICM 2006 will be availiable for download direct from the site!

An amateur mathematician.

In reference to David MacIver’s comment that “Tao’s work will probably never see a useful application, but this doesn’t make it any less cool and important.” I would like to say that this prediction is entirely incorrect. Indeed, please look at Notices of AMS (February 2001) pages 175-186 where you will find a paper by Tao and Knutson for which they both got a mathematics prize already. But, in addition what they are saying this this paper is immediately useful in theory of quantum computation, e.g. see Ann. Phys. 315 (2005) 80-122, and soon will find its rightful place in string theory…

Ark said:

“, and will find its rightful place in string theory”

Ark, you should write for John Stewart, or The Onion

Annon, can you be a bit more specific: who are these people and why do you think that I have to write to them…? especially in connection with string theory?

TV Comedian Jon Stewart and spoof website The Onion though I’ve never seen Stewart’s show and only saw The Onion during a web design course. Apparently anon is not a string theory fan though even in that context one has to keep in mind that parts of string theory could stay around and be useful even if string theory is ultimately changed to look a lot like say LQG.

I sort of had the impression that Tao’s work has a lot of ingenuity, but doesn’t have depth at a level comparable that ingenuity (not counting his work with Knutson).

I tend to think similar things about Mozart’s music, too, so the comparison doesn’t bother me :). Calling him the Beethoven of math would, though.

(I am willing to be corrected, as I am no authority here.)

John,

thank you for clarifications…I am not fan of the existing string theory formulations as well…Nevertheless, I happen to know how Tao’s results can be used in string theory. Normally, good mathematics always find its place in physics.. In fact, I can also see some bioinformatics-type applications of Tao’s results as well in near future…Just read the references I’ve provided…!

I knew I should have qualified that statement. 🙂

Ark, I didn’t mean Tao’s work in general. While I wasn’t aware of any specific applications, given what I know about what he does it would seem very unlikely that none of it was applicable (after all, he does harmonic analysis and this is a very useful subject in general). I was referring specifically to the result about arithmetic progressions in the primes, and similar stuff he’s done.

Ok, the best thing in the world to discriminate the question is to ask Professor Tao. It was what I do with my gmail account my mail was

Dear professor Tao,

Today the blog Not even wrong ( http://www.math.columbia.edu/~woit/wordpress/?p=350 ) has rumored that you won the Fields Medal 2006,

I don’t know if you can reply me sincerly but is this notice true?

Thanks for you attention

—

Dr. Piero Giacomelli

His answer arrived this morning:

It’s certainly news to me. I actually have no clue who is going to win

the Fields this year.

Terence

—

Terence Tao, Department of Mathematics, UCLA

http://www.math.ucla.edu/~tao

Email: teorth@gmail.com / tao@math.ucla.edu

I belive this closes the question.

zerocold

zerocold:I belive this closes the question.Not really. He could be, you know, lying.

Well, let’s not forget that sometimes the committee awarding the fields medal makes some “political” choices as well; Deligne did his award-winning work in the early seventies, but didn’t recieve the fields medal until 1978. The 1974 fields medal went to Bombieri, who would have been over 40 in 1978.

I don’t know how old Terence Tao is, but Ben Green is probably not even 30, so he might last another ICM or two…

In the last post, substitute “Bombieri” by “Mumford”.

Terence Tao grew up in my home town of Adelaide, Australia. He was a famous child prodigy, but is equally famous for being rather shy and retiring. I’m sure there are many in Australia who wish that he had stayed in the country to enhance the country’s mathematics. But he left and we are all rather proud of him. (BTW the level of maths education seems to be slightly higher in Adelaide than in Sydney or Melbourne, and perhaps that contributed to his success in some small way.)

Yes he could lying but I cannot see the eventual reason

“I sort of had the impression that Tao’s work has a lot of ingenuity, but doesn’t have depth at a level comparable that ingenuity (not counting his work with Knutson”.

An amazing thing for someone who is anonymous to post!

The only mathematician of the twenty century who work was truly abstract and yet got results was Grothendieck! Everyone else, had to ‘localize’ as it were!

An amateur mathematician

Some of his work has found applications in theoretical computer science. The paper “Gowers Uniformity, Influence of Variables, and PCPs” (Samorodnitsky, Trevisan, http://www.cs.huji.ac.il/~salex/papers/gowers.pdf) at least partially builds up on two papers of Green and Tao. The question of course is whether thereotical computer science itself is an application. 🙂

Somebody asked about the ICM 2002 proceedings. All the papers are available on the arxiv. One way to find them is to search for “ICM” in the “Journal-ref” entry, or follow the link

http://front.math.ucdavis.edu/search/jr:icm-beijing

At least ten ICM 2006 papers (including Tao’s) have also been posted on the arxiv by the authors.

Wow!

This is an amazing resource!

An amateur mathematician

I have had now a good look now at what Mr Terence Tao has acheived, and he is the surest bet for the Field Medal I have come across!

An amateur mathematician

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