4 ms·

Mirzakhani will always have a special place in my heart. I was an undergraduate mathematics student when I discovered her work. It was a paper on closed geodes

Mirzakhani will always have a special place in my heart. I was an undergraduate mathematics student when I discovered her work. It was a paper on closed geodesics and there was something special about her writing. Her approaches were simple an elegant -the kind that made you, as a reader, feel accomplished for understanding such a complex subject. It wasn't long until she was placed among other grand mathematicians that I looked up to. A year later she died. I wasn't even aware of her health. It sucked to see an idol go so young. But it's incredible what she accomplished within her lifetime. She'll always be one of the greatest.

benrbray 7y ago
For the curious, do you have a link to the paper?
- united893 7y ago
  Here's her two most cited papers on Geodesics. First one is her most cited work. https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/T... https://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf https://annals.math.princeton.edu/wp-content/uploads/annals-...
- fermenflo 7y ago
  I don't remember if this is the exact paper but as united893 already posted, the paper was probably: https://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf https://annals.math.princeton.edu/wp-content/uploads/annals-... Long story short: Imagine you have an object, place an ant on the surface of the object, and then instruct the ant to walk in a straight line forever. Will the ant ever end up in the same place it started (with the same initial direction)? If so, then it has formed a closed geodesic. For some objects, the answer is obvious. For a perfect sphere, the answer is always yes. In fact, any sphere-like object (imagine warping/contorting a sphere without tearing or poking holes in it) will always have at least 3 such closed geodesics: https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics. Miriam managed to construct an amazing formula that, when given the number of holes in an object, can give you the probability of forming a closed geodesic when starting from a random point in a random direction. This: https://www.youtube.com/watch?v=Sx-kAlEpiZk https://www.youtube.com/watch?v=Sx-kAlEpiZk is a great video that goes over what I explained and a couple other great achievements of hers. Worth a watch.

benrbray 7y ago

For the curious, do you have a link to the paper?

united893 7y ago
Here's her two most cited papers on Geodesics. First one is her most cited work. https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/T... https://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf https://annals.math.princeton.edu/wp-content/uploads/annals-...
fermenflo 7y ago
I don't remember if this is the exact paper but as united893 already posted, the paper was probably: https://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf https://annals.math.princeton.edu/wp-content/uploads/annals-... Long story short: Imagine you have an object, place an ant on the surface of the object, and then instruct the ant to walk in a straight line forever. Will the ant ever end up in the same place it started (with the same initial direction)? If so, then it has formed a closed geodesic. For some objects, the answer is obvious. For a perfect sphere, the answer is always yes. In fact, any sphere-like object (imagine warping/contorting a sphere without tearing or poking holes in it) will always have at least 3 such closed geodesics: https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics https://en.wikipedia.org/wiki/Theorem_of_the_three_geodesics. Miriam managed to construct an amazing formula that, when given the number of holes in an object, can give you the probability of forming a closed geodesic when starting from a random point in a random direction. This: https://www.youtube.com/watch?v=Sx-kAlEpiZk https://www.youtube.com/watch?v=Sx-kAlEpiZk is a great video that goes over what I explained and a couple other great achievements of hers. Worth a watch.