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So, is there any way for someone with no theoretical math background to even grasp a poor analogy of what her work is? With prizes like chemistry and biology, I

by qq66 12y ago

So, is there any way for someone with no theoretical math background to even grasp a poor analogy of what her work is? With prizes like chemistry and biology, I can usually sit down with Google and slowly figure out what exactly the person did. With theoretical math and physics, I can't even decipher what I'm reading. Wikipedia: "... this led her to obtain a new proof for the celebrated conjecture of Edward Witten on the intersection numbers of tautology classes on moduli space as well as an asymptotic formula for the length of simple closed geodesics on a compact hyperbolic surface."

Mz 12y ago
I did some digging yesterday and this seems to be the best explanation in layman's terms I could find: http://www.simonsfoundation.org/quanta/20140812-a-tenacious-explorer-of-abstract-surfaces/ http://www.simonsfoundation.org/quanta/20140812-a-tenacious-... Mirzakhani became fascinated with hyperbolic surfaces — doughnut-shaped surfaces with two or more holes that have a non-standard geometry which, roughly speaking, gives each point on the surface a saddle shape. Hyperbolic doughnuts can’t be constructed in ordinary space; they exist in an abstract sense, in which distances and angles are measured according to a particular set of equations. An imaginary creature living on a surface governed by such equations would experience each point as a saddle point. It turns out that each many-holed doughnut can be given a hyperbolic structure in infinitely many ways — with fat doughnut rings, narrow ones, or any combination of the two. In the century and a half since such hyperbolic surfaces were discovered, they have become some of the central objects in geometry, with connections to many branches of mathematics and even physics.
- qq66 12y ago
  Well, this is probably as good as it get for someone of my mathematical maturity. Thanks.

by qq66 12y ago

Mz 12y ago

I did some digging yesterday and this seems to be the best explanation in layman's terms I could find: http://www.simonsfoundation.org/quanta/20140812-a-tenacious-explorer-of-abstract-surfaces/ http://www.simonsfoundation.org/quanta/20140812-a-tenacious-... Mirzakhani became fascinated with hyperbolic surfaces — doughnut-shaped surfaces with two or more holes that have a non-standard geometry which, roughly speaking, gives each point on the surface a saddle shape. Hyperbolic doughnuts can’t be constructed in ordinary space; they exist in an abstract sense, in which distances and angles are measured according to a particular set of equations. An imaginary creature living on a surface governed by such equations would experience each point as a saddle point. It turns out that each many-holed doughnut can be given a hyperbolic structure in infinitely many ways — with fat doughnut rings, narrow ones, or any combination of the two. In the century and a half since such hyperbolic surfaces were discovered, they have become some of the central objects in geometry, with connections to many branches of mathematics and even physics.

qq66 12y ago
Well, this is probably as good as it get for someone of my mathematical maturity. Thanks.