Friday, August 22, 2014

Two Russians Named Grigory

This is a bit peripheral to our primary interest here at the Music Salon, but so very interesting I wanted to put it up anyway. There is a very interesting fellow, a Russian mathematician, who may be the smartest person in the world. His name is Grigory Perelman.

Grigory Perelman

I recommend reading the whole Wikipedia article as it is fascinating. Some highlights:
In 1994, Perelman proved the Soul conjecture. In 2003, he proved Thurston's geometrization conjecture. This consequently solved in the affirmative the Poincaré conjecture, posed in 1904, which before its solution was viewed as one of the most important and difficult open problems in topology.
In August 2006, Perelman was awarded the Fields Medal[1] for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow." Perelman declined to accept the award or to appear at the congress, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."[2] On 22 December 2006, the scientific journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.[3]
On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize[4] for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars.[5][6] He additionally turned down the prestigious prize of the European Mathematical Society.[7]
Apparently he is working on another one of the problems that the Millennium Prize people have designated as deserving of an award. If he solves that one, that will be another embarassing moment for them if he turns it down as well.

I like this guy! He seems to have the crazy idea that higher mathematics really has nothing to do with either money or fame.

So who is the other Grigory? That would be Grigory Sokolov who is possibly the finest pianist alive, but who refuses to do commercial recordings (all the CDs available are from live concerts) and, when the US and the UK put in onerous new visa requirements for touring musicians, simply canceled his concerts in those countries. He seems to share Perelman's stance. The fine arts, like classical music, really have nothing to do with how many records you sell or how many concerts you give.

Here is Grigory Sokolov, showing us how it's done:

What is it with these Russians?


Rickard Dahl said...

There are very few mysteries (new things to be found) left in mathematics I think. I can be wrong though (someone could come up with a new theorem or problem that none thought about before, who knows, maybe in the future a new branch of mathematics will be created). Most of the current focus in mathematics, as far as I know, is finding methods to efficiently solve mathematic problems (such as differential equations, using computers. Basically: finding optimal mathematical/programming algorithms. The core principles on the other hand are very solid (as far as I know) and I have no idea what theoretical mathematicians are working on. Obviously there are the Millenium Prize Problems (I think I've read about those in a National Geographic magazine many years ago) which remain to be solved. On the other hand there are certain specific smaller problems that have no known analytical solution. For instance, there are many types of integrals ( that can only be calculated numerically using computers. I suppose it's a bit redundant to spend too much effort trying to find analytical solutions to these when computers can give numerical solutions when application is needed. Anyways, thanks for bringing attention to this. I had no idea one of the Millenium Prize Problems has been solved and I've never heard about Grigory Perelman before.

Bryan Townsend said...

I've always found mathematics fascinating, but as soon as they get to a certain level of abstraction, I just seem to bounce off. I think this is the way my mind works. With music theory as well, I always want to tie it to specific, concrete musical events. Reading about the Poincaré conjecture and slicing up the Ricci flow or something, it sounds as if they are talking about something concrete, but of course they aren't. My knowledge of math is so rudimentary that I don't understand the simple meaning of the words. Something like this: "Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere" might as well be written in ancient Greek!