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Riemann da 40 yaşında hayata veda etmişti...

<https://terrytao.wordpress.com/author/teorth/> Maryam Mirzakhani
<https://terrytao.wordpress.com/2017/07/15/maryam-mirzakhani/>by Terence Tao
<https://terrytao.wordpress.com/author/teorth/>

I am totally stunned to learn that Maryam Mirzakhani
<https://en.wikipedia.org/wiki/Maryam_Mirzakhani> died today
<http://www.bbc.com/news/science-environment-40617094>, aged 40, after a
severe recurrence of the cancer she has been fighting for several years.  I
had planned to email her some wishes for a speedy recovery after learning
about the relapse yesterday; I still can't fully believe that she didn't
make it.

My first encounter with Maryam was in 2010, when I was giving some lectures
at Stanford
<https://mrc.stanford.edu/events/annual-bergman-lecture-terence-tao> - one
on Perelman's proof of the Poincare conjecture, and another on random
matrix theory.  I remember a young woman sitting in the front who asked
perceptive questions at the end of both talks; it was only afterwards that
I learned that it was Mirzakhani.  (I really wish I could remember exactly
what the questions were, but I vaguely recall that she managed to put a
nice dynamical systems interpretation on both of the topics of my talks.)

After she won the Fields medal in 2014 (as I posted about previously on
this blog
<https://terrytao.wordpress.com/2014/08/12/avila-bhargava-hairer-mirzakhani/>),
we corresponded for a while.  The Fields medal is of course one of the
highest honours one can receive in mathematics, and it clearly advances
one's career enormously; but it also comes with a huge initial burst of
publicity, a marked increase in the number of responsibilities to the field
one is requested to take on, and a strong expectation to serve as a public
role model for mathematicians.  As the first female recipient of the medal,
and also the first to come from Iran, Maryam was experiencing these
pressures to a far greater extent than previous medallists, while also
raising a small daughter and fighting off cancer.  I gave her what advice I
could on these matters (mostly that it was acceptable - and in fact
necessary - to say "no" to the vast majority of requests one receives).

Given all this, it is remarkable how productive she still was
mathematically in the last few years.  Perhaps her greatest recent
achievement has been her "magic wand
<https://arxiv.org/abs/1502.05654>" theorem
with Alex Eskin <https://arxiv.org/abs/1302.3320>, which is basically the
analogue of the famous measure classification and orbit closure theorems of
Marina Ratner <https://en.wikipedia.org/wiki/Ratner%27s_theorems>, in the
context of moduli spaces instead of unipotent flows on homogeneous spaces.
 (I discussed Ratner's theorems in this previous post
<https://terrytao.wordpress.com/2007/09/29/ratners-theorems/>.  By an
unhappy coincidence, Ratner also passed away this month
<https://math.berkeley.edu/about/history/in-memoriam>, aged 78.)  Ratner's
theorems are fundamentally important to any problem to which a homogeneous
dynamical system can be associated (for instance, a special case of that
theorem shows up in my work with Ben Green and Tamar Ziegler on the inverse
conjecture for the Gowers norms, and on linear equations in primes), as it
gives a good description of the equidistribution of any orbit of that
system (if it is unipotently generated); and it seems the Eskin-Mirzakhani
result will play a similar role in problems associated instead to moduli
spaces.  The remarkable proof of this result - which now stands at over 200
pages <https://arxiv.org/abs/1302.3320>, after three years of revision and
updating - uses almost all of the latest techniques that had been developed
for homogeneous dynamics, and ingeniously adapts them to the more difficult
setting of moduli spaces, in a manner that had not been dreamed of being
possible only a few years earlier.

Maryam was an amazing mathematician and also a wonderful and humble human
being, who was at the peak of her powers.  Today was a huge loss for
Maryam's family and friends, as well as for mathematics.
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