Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Maryam Mirzakhani’s Pioneering Mathematical Legacy

newyorker.com

Post reply on HN
Print view View original

21–30 of 35 posts

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#21

Post by adrianratnapala »

So I am trying to undesrstand what her work was about. It seems fields medal was for "the dynamics and geometry of Riemann surfaces and their moduli spaces" (my emphasis).

What is dynamics to a geometer? Clearly it is important -- because it is important in physics. But I want to understand what mathematicians are getting excited about.

We can talk about a family of geometrical objects foo(t) where the parameter t is a single real value, which stands in for time. But -- other than its relation to the physical world -- why is that $t$ parametrisation important? Why not complex parameters, or multiple parameters, or something completely different?

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#22

Post by therajiv »

racl101 wrote: post #20

"this is about as good motivation as we'll ever have to keep plugging along." So, other people dying of cancer not as good motivation?

Sorry if I came off that way, that's not at all what I meant. My comment was more along the lines of putting a face to statistics; reading about the numbers of people dying is a weaker motivator than hearing the stories behind the lives that are lost to cancer.

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#23

Post by dang »

racl101 wrote: post #20

"this is about as good motivation as we'll ever have to keep plugging along." So, other people dying of cancer not as good motivation?

Please be charitable when commenting here. That means responding to the strongest plausible interpretation of what someone might mean, instead of a weaker one that's more offensive or ridiculous.

We detached this subthread from https://news.ycombinator.com/item?id=14794057 and marked it off-topic.

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#24

Post by stonesixone »

adrianratnapala wrote: post #21

So I am trying to undesrstand what her work was about. It seems fields medal was for "the dynamics and geometry of Riemann surfaces and their moduli spaces" (my emphasis). What is dynamics to a geometer? Clearly it is important -- because it is important in physics. But I want to understand what mathematicians are getting excited about. We can talk about a family of geometrical objects foo(t) where the parameter t is…

My memory may be a bit fuzzy on this. But I believe one way the term "dynamics" is used in her work is in reference to the space of Riemann surfaces (or equivalently, the space of hyperbolic geometries on a surface). This space is called moduli space. Certain topological operations on the surface (e.g. twisting a "handle") give rise to a corresponding transformation on moduli space. So one of the things mathematicians in this area can study is the dynamics of such operations on moduli space. This means, for example, studying the behavior of these operations on moduli space, in the limit.

Also, to a mathematician, "dynamics" can often simply mean studying the behavior of iterations of a single function from a space to itself. So the parameter "t" in this case is over the positive integers (or all integers if the function has an inverse).

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#25

Post by tptacek »

ckarmann wrote: post #16
wfunction wrote: post #2

Still bothers me that we didn't get a black bar. Can someone explain what the criterion is?

I'm starting to think this black bar was a bad idea. All it gives is fruitless discussions like this one on the merit of a person to be awarded the black bar upon their death, like if it was a trophy or a medal of accomplishment. I think the first implementation of the black bar was for Steve Jobs. Well, I'm not a fan of Steve Jobs, and I think that individuals like Maryam Mirzakhani are far more important in the cou…

More importantly, I think, is the connection HN's operators felt to Steve Jobs --- for whatever reason, and don't discount that for some of them that reason could be pretty personal and authentic.

I could not agree more with you about these discussions, which occur at the bottom of every thread about any recently deceased, like a sort of ghoulish, amoral Slashdot "first post" contest. It is not OK to litigate how strangers choose to relate grief, least of all in their own damn house.

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#27

Post by sn9 »

adrianratnapala wrote: post #21

So I am trying to undesrstand what her work was about. It seems fields medal was for "the dynamics and geometry of Riemann surfaces and their moduli spaces" (my emphasis). What is dynamics to a geometer? Clearly it is important -- because it is important in physics. But I want to understand what mathematicians are getting excited about. We can talk about a family of geometrical objects foo(t) where the parameter t is…

The Quanta piece linked early on in the OP gives a deeper description of her work and life. It's from the time of her Fields win.

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#29

Post by hyperbovine »

wfunction wrote: post #2

Still bothers me that we didn't get a black bar. Can someone explain what the criterion is?

I really think all but a handful of HN readers first learned about Mirzakhani upon her passing. It's a tragic event -- highly so -- but not one of particular significance to this community.

Re: Maryam Mirzakhani’s Pioneering Mathematical Legacy

#30

Post by wfunction »

hyperbovine wrote: post #29
wfunction wrote: post #2

Still bothers me that we didn't get a black bar. Can someone explain what the criterion is?

I really think all but a handful of HN readers first learned about Mirzakhani upon her passing. It's a tragic event -- highly so -- but not one of particular significance to this community.

I seem to recall feeling similarly a few times when we did have black bars. Sadly I don't remember who they were (which I suppose vaguely confirms what I'm saying?) but I do remember being surprised that I hadn't heard of them before, and didn't expect many had either.
Post reply on HN