And the Fields medal goes to

An Iranian mathematician working in the US has won the Fields medal. And the kicker? She’s a woman. Professor  Maryam Mirzakhani was recognized for her work on complex geometry.

In becoming the very first female medallist, Prof Mirzakhani – who teaches at Stanford University in California – ends what has been a long wait for the mathematics community.

Prof Dame Frances Kirwan, a member of the medal selection committee from the University of Oxford, pointed out that despite maths being viewed traditionally as “a male preserve”, women have contributed to mathematics for centuries.

She noted that around 40% of maths undergraduates in the UK are women, but that proportion declines rapidly at PhD level and beyond.

“I hope that this award will inspire lots more girls and young women, in this country and around the world, to believe in their own abilities and aim to be the Fields Medallists of the future,” Prof Kirwan said.

Including girls and young women in Iran.

Prof Mirzakhani’s seminal research concerns shapes called Riemann surfaces. These are convoluted mathematical objects that can be analysed using complex numbers – i.e. numbers with real and imaginary parts.

In particular, she has studied “moduli spaces” of these shapes, which map all of the possible geometries of a Riemann surface into their own, new space.

Prof [Caroline] Series has also known Prof Mirzakhani and her work for some time.

“I came across her a long time ago when she was a PhD student, and I was sent a preliminary draft of her thesis. And I just read it in amazement – it was beautiful.

“She took something that’s been known for a while, and she took a rather elaborate and hard to understand identity between things, and she just applied it in the most ingenious and wonderful way.”

Prof Series believes the first female Fields winner is a rare talent, who has produced unique and striking work.

“I’m quite genuine about that,” she said. “I almost never think that about bits of mathematics!”

Inspiring, innit.



  1. piero says

    Finally a bit of good news. Congratulations to Prof Mirzakhani.
    I just hope I’ll see the day when humanity will stop squandering its most neglected resource.

  2. Dan says

    Of course I’ve already heard people saying they just gave it to her for the sake of diversity. Some people think if it’s based on merit white men should always be on top.

  3. Janothar says

    Anyone who says that it’s due to diversity is just a horrible person. She’s one of the best mathematicians on the planet, and, fortunately, most of the young mathematicians that I know, male and female alike, came into this International Congress with the attitude that the only reason she might NOT get one is sexism. I admit that I might be biased, as I also work on moduli of Riemann surfaces, so I know her work in a fair amount of detail, but she’s known enough that people in other subfields are aware of her abilities.

  4. Dave Ricks says

    The simplest or most familiar Riemann surface is the the square root function of the points in the complex plane. MIT would show you but their 4-D coloring pens are broken. But seriously, that’s a good demo, because your 2-D computer display makes you visualize a 3-D surface, and the colors going back through the surface show what people mean by 4-D. If you can trace your fingertip around the surface twice (from blue to red and back to blue), then you get the demo. Of course, this is just to see what a Riemann surface is. What you do with them to win a Fields medal is beyond me.

    Janothar, thank you for your appraisal of Prof. Mirzakhani’s value in the math scene. I smiled at your disclosure of your bias toward moduli of Riemann surfaces. Biases like yours I can live with!

  5. Janothar says

    Dave, I’d say the simplest and most familiar would probably just be ghee complex plane along with infinity, which is the Riemann sphere via stereo graphic projection, but that’s quibbling.

    Generally, the tone on site at ICM is excitement and I heard a few annoyed grumbles that Mirzakhani’s talk was posoned when it was changed from an invited talk to a Field’s Medal talk. As you said, if that’s the irritation caused by her getting the medal, that people wish her talk was earlier in the week (many people leave early and she was moved to after the weekend) then that’s a complaint I think we can live with.

  6. Silentbob says

    May I put in a plug for a post by Kaveh I believe will be of interest to many B&W readers? It’s about the reaction in Iran.

    the most contentious thing was her hijab. Yes, the concept of hijab became the center of attention.

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