First female winner for Fields maths medal(bbc.co.uk)
bbc.co.uk
First female winner for Fields maths medal
http://www.bbc.co.uk/news/science-environment-28739373
8 comments
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."
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."
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-...
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.
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.
Well, this is probably as good as it get for someone of my mathematical maturity. Thanks.
Great to see that someone who grew up in a country which many in the west believe is backward and opposed to women's education and scientific progress in general win such an award.
Despite popular beliefs women outnumber men in Iran universities. Sadly government is trying to "fix" this but academic community always resisted.
She isn't from Saudi Arabia. Apart from having a few nutty leaders Iran is closer to countries like Turkey than it is to Saudi Arabia.
Anyway, academia is generally one of the few "liberal" institutions in Islamic countries. The issue is usually of female graduates finding work outside academia (eg Saudi Arabia graduated its first batch of female law students in 2008 and still hasn't let them practice law).
Anyway, academia is generally one of the few "liberal" institutions in Islamic countries. The issue is usually of female graduates finding work outside academia (eg Saudi Arabia graduated its first batch of female law students in 2008 and still hasn't let them practice law).
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Statement from IMU (PDF) http://www.mathunion.org/fileadmin/IMU/Prizes/2014/news_rele...
Her Wikipedia page: http://en.wikipedia.org/wiki/Maryam_Mirzakhani
I like to think I'm fairly learned in math and science, and i don't know what any of those words mean.
Hyperbolic geometry is the geometry of surfaces and spaces that aren't flat. Think of a 2D surface which is curved like a saddle. A triangle drawn on this surface will have angles that add up to less than 180 degrees.
Ergodic theory is the study of dynamical systems (things that change over time) that are allowed to run for a long time. They are "ergodic" if the state after the system has run for a long time is like picking a state randomly from the set of all possible states. Pouring cream into coffee and then mixing it is ergodic - after a sufficiently long time, you might as well have just arranged all the molecules at random.
Symplectic geometry is a bit more abstract. It's the study of dynamical systems that look similar to Newtonian mechanics, i.e. there are analogues of position and momentum. It encompasses all of Newtonian mechanics (i.e. mechanics without friction) but also a large set of other possible dynamics, like electrodynamics.
Riemann surfaces are surfaces that look like the complex plane "up close" but might look more complicated "from a distance". For example, an infinitely tall spiral staircases (which extends to infinity in the x and y directions) is a Riemann surface. It's interesting to study functions on Riemann surfaces, because the limitation of behaving like the complex plane at small distances is quite restrictive.
Ergodic theory is the study of dynamical systems (things that change over time) that are allowed to run for a long time. They are "ergodic" if the state after the system has run for a long time is like picking a state randomly from the set of all possible states. Pouring cream into coffee and then mixing it is ergodic - after a sufficiently long time, you might as well have just arranged all the molecules at random.
Symplectic geometry is a bit more abstract. It's the study of dynamical systems that look similar to Newtonian mechanics, i.e. there are analogues of position and momentum. It encompasses all of Newtonian mechanics (i.e. mechanics without friction) but also a large set of other possible dynamics, like electrodynamics.
Riemann surfaces are surfaces that look like the complex plane "up close" but might look more complicated "from a distance". For example, an infinitely tall spiral staircases (which extends to infinity in the x and y directions) is a Riemann surface. It's interesting to study functions on Riemann surfaces, because the limitation of behaving like the complex plane at small distances is quite restrictive.
Modern math can be fairly removed from anything a lay person hears in pop science. (And even as a mathematician, I don't know what most of the things on the wikipedia page are about. I'm into a different subfield.)
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Someone posted a video of part of a Mirzakhani lecture a few hours ago https://www.youtube.com/watch?v=XMWJW-AVVCI
First of many.
[Larry Summers' head explodes.]
A female present at the top level of math achievement is not inconsistent with the 3 reasons Summers gave for the (average) lack of females there. It will still be overwhelmingly male at the top and the higher male variance in math ability is not going to magically go away.
Might not "magically" go away but if you actually look at the data it vanishes.
Im really, honestly, interested in what data you're talking about. Please paste a link.
The AMS commissioned a study a few years ago, and it was in the Notices in early 2011 or 2012.
It's funny though, that some political blowhard can pull a self-contradictory self-serving hypothesis halfway out of an orifice, and everyone bends over backwards to imagine a circumstance in which it possibly could be partially true. Anyone who disagrees with the blowhard had better bring some actual research.
Welcome to the Patriarchy.
It's pretty sad that my most salient recent exposure to that (as a white dude myself) takes the form of apologists for a particular stupid old white man who has personally annoyed me for years. Sorry!
So apparently it's impossible for the academy to have this problem that we all agree tech has? Please. Summers' comments were barely a sketch of a hypothesis. He blustered until some percentage of people just assumed he had a real point. (Basically his career in a nutshell.) A critical part of his hypothesis is "there is no Pareto-efficient change to current educational practice that would reduce sex differences in variability". That claim is ridiculous on its face. Nothing to see here! Move along people!
http://media.swarthmore.edu/bulletin/?p=145 (read past the first three paragraphs; why is the sex variability inverted for Asians? perhaps Nature doesn't so completely dominate Nurture after all...)
http://media.swarthmore.edu/bulletin/?p=145 (read past the first three paragraphs; why is the sex variability inverted for Asians? perhaps Nature doesn't so completely dominate Nurture after all...)
And it includes links to additional info about her and the other winners, like this link to a profile of her: http://www.simonsfoundation.org/quanta/20140812-a-tenacious-...