2010 Fields Medal Awarded(icm2010.in)
icm2010.in
2010 Fields Medal Awarded
http://www.icm2010.in/imu-prizes/prize-winners-2010
4 comments
Ergodic theory is a theory that comes from Statistical Mechanics. Imagine you have a handful of atoms and a box, now let's say that you line the atoms up along one side of the box and give them all a push perfectly perpendicular to the side (oh, and the sides are perfectly flat). What happens? The atoms keep just bouncing back and forth between those two sides, and large regions of the box never have any atoms in them. If this situation could happen in real life, then Statistical Mechanics would have serious problems! So Ergodic Theory is basically the study of making sure that the atoms in a box bounce all over equally...
Covered a bit in Cybernetics:
http://books.google.com/books?id=NnM-uISyywAC&lpg=PP1...
http://books.google.com/books?id=NnM-uISyywAC&lpg=PP1...
I'm about to graduate with my PhD in math and I don't have any idea what that research summary means.
Does that mean the landscape of human math knowledge is so large that one specialist does not usually have a chance to visit other areas apart from one's own?
Yes.
When I was a kid I wanted to get a PhD in math and physics and comp sci and etc etc etc. I was really disappointed when I got older and realized I would only have time for one. So I chose math because I wanted to study mathematical logic, differential equations, numerics and etc etc etc. Then I got to grad school and realized I would only have time for one. So I chose numerics because I wanted to study molecular dynamics, computational neuroscience, fluid dynamics, etc etc. Then I had to choose an advisor, and I realized I'd only get in an education in one sub discipline. So I chose fluid mechanics, because I wanted to study polymeric fluids, multiscale dynamics, fluid-structure interactions, etc etc. Then I finally started doing real research and realized I'd be lucky just to make a noticeable contribution to one of those.
There are exceptions, of course.
(I don't mean to sound pessimistic, just realistic. Research has been good to me, and I love doing it)
When I was a kid I wanted to get a PhD in math and physics and comp sci and etc etc etc. I was really disappointed when I got older and realized I would only have time for one. So I chose math because I wanted to study mathematical logic, differential equations, numerics and etc etc etc. Then I got to grad school and realized I would only have time for one. So I chose numerics because I wanted to study molecular dynamics, computational neuroscience, fluid dynamics, etc etc. Then I had to choose an advisor, and I realized I'd only get in an education in one sub discipline. So I chose fluid mechanics, because I wanted to study polymeric fluids, multiscale dynamics, fluid-structure interactions, etc etc. Then I finally started doing real research and realized I'd be lucky just to make a noticeable contribution to one of those.
There are exceptions, of course.
(I don't mean to sound pessimistic, just realistic. Research has been good to me, and I love doing it)
How often are you exposed, even minimally, to other disciplines inside mathematics?
For example, I'm no researcher, but I tend to try and read a few good books about maths, and sometimes even actual mathematical books, just for the fun. Do you tend to do the same?
For example, I'm no researcher, but I tend to try and read a few good books about maths, and sometimes even actual mathematical books, just for the fun. Do you tend to do the same?
It's really a big gap though between having an understanding of the basics in an area and really knowing enough to follow the current research. It wouldn't surprise me at all if this guy actually had looked at things in basically the same direction as some of this research and still isn't able to really follow what they have done.
Absolutely. I read up on a lot of science, and even chug through text books. As robryan says above though, reading a book on chemistry or functional analysis is long way from being ready to do research in the field.
One of the reasons I chose applied math was because I thought it was the best centralized position in all of science. It would take me years to switch to another branch of math, but in applied math I can at least switch the focus of application, possibly in under a year or two.
One of the reasons I chose applied math was because I thought it was the best centralized position in all of science. It would take me years to switch to another branch of math, but in applied math I can at least switch the focus of application, possibly in under a year or two.
Oh, hell yes.
The work summaries are actually quite good. I've only an undergraduate degree in math and physics, and I can at least get some idea of what the accomplishments are. Julie Rehmeyer is to be commended.
It sounds like the editors of Social Text are still butthurt over the Sokal paper and are back for revenge.
I'm from Vietnam, and Ngo Bao Chau made us proud
Honest question to the HN audience:
Do you think that being proud of someone just because he's your compatriot is rational or irrational?
After all, you just share the same nationality by random chance, therefore isn't it the same as being proud that you were born on the same day of the week as Einstein or that your hair is the same colour as George Washington's?
Do you think that being proud of someone just because he's your compatriot is rational or irrational?
After all, you just share the same nationality by random chance, therefore isn't it the same as being proud that you were born on the same day of the week as Einstein or that your hair is the same colour as George Washington's?
It's unclear if its rational to be "proud",but I do think it might be rational to be happy about it.
To the extent that people make snap judgments about other people based on race or nationality, it would seem that you'd want people that share your ethnicity or nationality to do well. This likely has a minor increase in people's perception of you.
Likewise, you probably feel shame or unhappiness when the opposite happens. Just look at what being Muslim is like in the US now.
To the extent that people make snap judgments about other people based on race or nationality, it would seem that you'd want people that share your ethnicity or nationality to do well. This likely has a minor increase in people's perception of you.
Likewise, you probably feel shame or unhappiness when the opposite happens. Just look at what being Muslim is like in the US now.
You inspired a related question: is it irrational that I feel proud of the two French people although I'm not French, I just live in France ? Plus, the Vietnamese mathematician has studied and worked in France.
I somehow feel proud that I made a good choice of place to live for now, if that makes any sense.
PS: I noticed they are almost all "outsiders", foreigners that immigrated to Western countries, or locals outside the traditional elite of the Western countries. The point, which is a depressing one, is that mathematics and, more generally, pure science, is an "outsider" activity nowadays.
I somehow feel proud that I made a good choice of place to live for now, if that makes any sense.
PS: I noticed they are almost all "outsiders", foreigners that immigrated to Western countries, or locals outside the traditional elite of the Western countries. The point, which is a depressing one, is that mathematics and, more generally, pure science, is an "outsider" activity nowadays.
I'm with you; it makes no sense to me to be proud of an unknown stranger's achievements just because s/he happened to be born within the same borders as you.
I've never understood the swellings of national pride that occur within a country when (for example) one of their citizens wins an Olympic medal; only a handful of people played any part in that achievement, to insinuate yourself amongst them by virtue of these random relationships is almost parasitic.
Likewise, though less on-topic, I have no time for patriotism either. George Bernard Shaw put it best: "Patriotism is your conviction that this country is superior to all others because you were born in it."
I've never understood the swellings of national pride that occur within a country when (for example) one of their citizens wins an Olympic medal; only a handful of people played any part in that achievement, to insinuate yourself amongst them by virtue of these random relationships is almost parasitic.
Likewise, though less on-topic, I have no time for patriotism either. George Bernard Shaw put it best: "Patriotism is your conviction that this country is superior to all others because you were born in it."
Is it rational to feel happiness?
If someone feels proud, he/she naturally just got a good moment in life. I guess your question was: Is it rational to identify yourself with an external entity in order to feel good/bad when something happens to this entity. The answer is: In many cases it is perfectly rational. E.g. when people start supporting an old soccer sclub that got a breakout success, old supporters refer to new ones as "gloryhunters".
By the way, I am a gloryhunter here as well. One of the four Fields medalists this year (Stas Smirnov) graduated from the same high school and college as I did.
If someone feels proud, he/she naturally just got a good moment in life. I guess your question was: Is it rational to identify yourself with an external entity in order to feel good/bad when something happens to this entity. The answer is: In many cases it is perfectly rational. E.g. when people start supporting an old soccer sclub that got a breakout success, old supporters refer to new ones as "gloryhunters".
By the way, I am a gloryhunter here as well. One of the four Fields medalists this year (Stas Smirnov) graduated from the same high school and college as I did.
I've argued with people that this is not only irrational, but wrong. I feel it is exploiting the successes of others to justify your own lack thereof. For another curious perspective on national pride, there's evidence that people use it to offset their horror of their own mortality. (Even if I die, my nation/culture will survive, and being part of it, a part of me will survive)
It's not just sharing the same nationality. It's the sharing of the same culture and and heritage. It's like the town people feeling proud about the Olympic gold medalist from the same town. Just human emotion. Rational or irrational is irrelevant.
I think it is rational to be happy about it for reasons stated in other comments (perception of your country, etc.)
There is another reason though: it shows that your country/culture is a good one in terms of innovation or whatever. This directly reflects on the culture that your are a part of, both in the sense that you're affected by it, and also that you are part of shaping it. So in a way, a win for your culture is a win for you.
There is another reason though: it shows that your country/culture is a good one in terms of innovation or whatever. This directly reflects on the culture that your are a part of, both in the sense that you're affected by it, and also that you are part of shaping it. So in a way, a win for your culture is a win for you.
I don't really want to defend nationalism, but to play devil's advocate: is it rational to be proud if the company you work for is successful?
In the widest sense, a nation is like a company. You could argue all it's members contribute to making it the place it is. If it brings forth a field medal winner, it might be a result of the favourable conditions you helped creating.
In the widest sense, a nation is like a company. You could argue all it's members contribute to making it the place it is. If it brings forth a field medal winner, it might be a result of the favourable conditions you helped creating.
I agree, we all share the same nationalities by random chance. but why spending too much time thinking about the root of the fact that we all feel proud when some people in our country achieve sth phenomenal, it happens everywhere. It's nothing too complicated or rational or irrational, it's just the emotional conenction that everyone has
It is hard not to derive pride from your identity, whatever you think it to be.
There's probably genes in common, so there's a biological side to it too.
I'm proud for you, too. Great work from Mr. Chau.
yes! definitely! Go go Prof. Ngô Bảo Châu!
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Read Harry Kesten's laudation of Stas Smirnov, you can skip over the "details" and it's still a fun read: http://www.icm2010.in/wp-content/icmfiles/laudaions/fields3....
Tao has a nice post describing some of the accomplishments of the Fields medal winners here:
http://terrytao.wordpress.com/2010/08/19/lindenstrauss-ngo-s...
http://terrytao.wordpress.com/2010/08/19/lindenstrauss-ngo-s...
Elon Lindenstrauss is being awarded the 2010 Fields Medal for his results on measure rigidity in ergodic theory, and their applications to number theory.
Fields Medal - Elon Lindenstrauss, Princeton University Lindenstrauss has made far-reaching advances in ergodic theory, the study of measure preserving transformations. His work on a conjecture of Furstenberg and Margulis concerning the measure rigidity of higher rank diagonal actions in homogeneous spaces has led to striking applications. Specifically, jointly with Einsiedler and Katok, he established the conjecture under a further hypothesis of positive entropy. It has impressive applications to the classical Littlewood Conjecture in the theory of diophantine approximation. Developing these as well other powerful ergodic theoretic and arithmetical ideas, Lindenstrauss resolved the arithmetic quantum unique ergodicity conjecture of Rudnick and Sarnak in the theory of modular forms. He and his collaborators have found many other unexpected applications of these ergodic theoretic techniques in problems in classical number theory. His work is exceptionally deep and its impact goes far beyond ergodic theory.