Earlier today, Fields Medals were awarded. This is often called the “Nobel prize of math” but it’s an imperfect analogy — they are awarded only to mathematicians who are 40 or under, they are given out once every four years, and at most four people can get them in a given International Congress (the conference at which they are awarded, which is held every four years). This means they’re a bit rarer than Nobels in, say, physics, where the award is given out every year and often shared among two or more researchers; also a bit more capricious, since a lot of the best work nowadays is done by people over 40 and because the age requirement means the work has to be judged in a bit of a hurry.
This year, four were given, and one went to a Vietnamese man who was born in Hanoi in 1972. If some kid born in Vietnam during the war can go onto win one of the most prestigious and competitive intellectual prizes that there is, then maybe anything is possible.
Can you explain to us non-mathematicians, the work for which he got the award?
Yes, it’s an important result related to the Langlands program. This is one of the most difficult programs in all of math to describe, but here goes:
Suppose you’re given a polynomial, e.g.
Since sqrt(5) and -sqrt(5) are both solutions to this equation, there’s a natural notion of symmetry associated to the equation — that is, you can flip sqrt(5) and – sqrt(5). This symmetry turns out be quite powerful and can actually be viewed as a sort of symmetry of the Cartesian plane.
If you take all polynomials (with integer coefficients) you get a gigantic set of symmetries, sometimes called the absolute Galois group (of the rational numbers). This is an extremely important object in mathematics and one that is notoriously difficult to say much about.
The Langlands program seeks to describe this object by describing all the ways that it can act as a symmetry of any Euclidean space (sort of, I’m simplifying a lot).
As a Vietnamese person, I wish I could understand what Ngô Bau Châu did. But I’ll still take pride in his accomplishment anyway.
His bio states that after high school he moved to France to go to university. This means that he had to pass the entrance exams first before he could even go, and French university exams at the time were not nearly as simple as the SATs (for better or worse). That’s an accomplishment he should be very proud of, but the other side of the story is that at the time, his family probably viewed the university as the ultimate sine qua non of life. After all, the only alternative to going to college at the time was the military draft. You’d better believe he understood the value of education.
I don’t advocate such a system for the US, but sometimes I think about what such a system would do for global warming deniers, birthers, and creationists in our society.
Man, reading this make me feel as dumb as a Palin.
edit: DougJ’s description makes it somewhat less opaque.
in the way that saying much about bathroom habits is difficult for newly-dating couples ?
@DougJ: Thanks! I had never heard of Langlands program before, but I am a physics cat not a math cat.
Maybe hiring him makes up for the collected works of the Chicago School?. Still, good on the alma mater. And the Dean they quote in the article, Bob Fefferman, taught my honors calculus class when I was there 20ish years ago. He was a spectacular teacher who had a droll sense of humor and used to joke that he was the family failure because despite being tenured at U of C at 24 or 25 as this guy was his brother.
@DougJ: Thanks for the explanation. At least I have a vague idea of what it is about now.
This is at least the third Fields Medal that has been given in connection with the Langlands program, after Drinfel’d (1990) and Lafforgue (2002).
I was also an undergraduate at U. Chicago (in math), although for me it was more like 30 years ago. Bob Fefferman was a great mentor to me and many of my classmates.
My colleague Parimala is giving one of the plenary talks at the ICM (International Congress of Mathematicians, where the Fields medals are given), I think she talks on Saturday. We (my department) are so proud of her. DougJ, you did a great job explaining the work of Chau to non-matematicians. Now you can try to explain Parimala’s work in linear algebraic groups. :)
dare I say, Yes We Can!
Unless you’re muslim, of course.
I don’t know what the fuck you just said, but you’re special.
anyone here ever see “Good Will Hunting”?
I get the feeling bloggers don’t see many movies.
Off Topic, and bad of me since I have made fun of DougJ reading Politico, but Mike Allen of Politico has been included in blogger meetings at the Treasury. And it looks like he either does not understand what people are saying, or using it as an opportunity to editorialize about the virtues of cutting Social Security.
The Tapped Blog says:
Mike Allen’s Mind-Mis-Meld.
A few folks e-mailed me about this item from Mike Allen’s win-the-morning Playbook:
” ADMINISTRATION MINDMELD: The virtue of action on Social Security is that it demonstrates the ability to begin to affect the long-run deficits. Social Security isn’t the biggest contributor to the problem — that’s still health-care costs. But ti could help a little bit, buy time, and strengthens the odds of a political consensus behind other spending cuts or tax increases. Most importantly, it would establish more CREDIBILITY with the MARKETS. The mood of the world at the moment (slightly excessive, from the administration’s point of view) is that if you don’t do anything with spending cuts, it doesn’t get you credibility. ”
Sure makes it seem like the administration wants to cut Social Security, doesn’t it? By chance, I was at the same deep-background briefing where Allen had his “mindmeld,” and I have to say, I don’t think he’s got it right. After reviewing my notes and a recording of the conversation, here’s my take. (The rules for this conversation were no direct quotes and no identifying the senior administration official in question.)
Allen references a part of the conversation that concerned the Deficit Commission and what the official might know about its agenda…
found via Brad DeLong’s blog. And I made some edits to distinguish what Allen said in the Politico piece from Tim Fernholz says at Tapped blog (’cause I am scared of trying to block quote).
Edit: I actually went to Politico to see the whole thing, but cannot find anything on social security. There is something else under the same title. Did Allen change it?
I’m hoping this powerful symmetry can help balance the force between futures trading and subsidies in the wheat market. Then Sarah Palin can tweet about it.
slow ball over the plate– http://www.youtube.com/watch?v=MZ70hbvaPdU
Jay & Silent Bob – Good Will Hunting 2
@jl: since when do facts have anything to do with mike allen’s reporting?
Left Coast Tom
Oh, sure…they give all the awards to people whose calculators work into the billions. But what about our Native Pakistani Rock Salt Lovers who can’t find their local Fry’s and buy such devices? Huh?!
(Not sure how to get this thing to display an open XML tag, /, then theatlantic, then a close XML tag…)
thanks for the clip.
nice to see they can laugh at themselves.
Thanks for the post and thanks for the clear explanation. But what’s the big deal if we are able to explain this symmetry? Is it just because so much other work depended on it being true? If so, are there are any serious implications from that other work for us non-mathematicians that we should be concerned about? If not, then what’s the answer to the “so what” question?
Still struggling to understand.
those aren’t mutually exclusive
This is one of those posts I wish I could write something intelligent about, but being a language as opposed to a math or physics or engineering type, I will just simply add that I have been amazed over the years at my students from Vietnam.
They are not the refugees, but rather people who have been able, over the years to come here to the states and study English. They are not all the same, of course, but I have always admired them for the courage it must take for a 20-something today to choose to come here and learn.
For the most part, they are full of histories of how their families have either survived the bad years or just gotten here by strength of will.
I admire them all. This post reminded me of why I love my job and how it is in universities much of the bigotry displayed in everyday life is broken down, little by little.
You’re at Emory? Very up and coming place in number theory, that is for sure.
I don’t know of any serious applications outside of mathematics, but it is number theory, so there is always the potential for applications in coding theory and encryption.
This basic symmetry is perhaps the cornerstone of algebraic number theory. It was invented in the early 1800s by a Frenchman named Galois (probably the most romantic mathematician of all time, he died in his early 20s in a duel) and was a revolution in the solution of algebraic equations.
For example, you have probably heard of the the quadratic formula. Well, there are similar formulas for cubic and fourth degree degree equations. Galois showed (it was shown earlier by Abel, but Galois’s proof is superior) that there are no such formulas in degree 5. This is truly a landmark theorem in mathematical history.
But the underlying subject of these symmetries is incredibly deep and we are just scratching the surface of truly understanding them.
@Left Coast Tom:
Fry’s Electronics is one of the biggest supporters of research math in the entire world, btw. Not kidding.
You math guys are just showing off. And a damn fine job. Thanks very much for the explanation.
The first time I read this, I passed over the fact that Ngo was born in Hanoi, the former capital of North Vietnam, and the former capital of French Indochina. It is also a blast to learn that his family had moved to France and that he had studied at the University of Paris.
So, not just someone born during a terrible war, but also perhaps someone who also kicks to the curb the remnants of French imperialism.
I guess agent orange has it’s good side effects too.
Dai Viet, son!
@DougJ: Thanks for the further explanation; it does help. And thanks again for the post of this news item as I would have totally missed it; amazing how balloon-juice can be such a wonderfully efficient news aggregator.
Fields Medal! Pshaw! Everyone knows the only math medal that counts is Andy Schlafly’s ConservaMath Medal! The only math medal to stand against the notorious liberal bias of numbers!