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posted by martyb on Sunday July 16, @02:45PM   Printer-friendly
from the much-too-soon dept.

Maryam Mirzakhani, the first woman and Iranian to win the prestigious Fields Medal, has died:

Nearly three years after she became the first woman to win math's equivalent of the Nobel Prize, Maryam Mirzakhani has died of breast cancer at age 40. Her death was confirmed Saturday by Stanford University, where Mirzakhani had been a professor since 2008.

Mirzakhani is survived by her husband, Jan Vondrák, and a daughter, Anahita — who once referred to her mother's work as "painting," because of the doodles and drawings that marked her process of working on proofs and problems, according to an obituary released by Stanford.

From Wikipedia:

Mirzakhani has made several contributions to the theory of moduli spaces of Riemann surfaces. In her early work, Mirzakhani discovered a formula expressing the volume of a moduli space with a given genus as a polynomial in the number of boundary components. This led her to obtain a new proof for the formula discovered by Edward Witten and Maxim Kontsevich on the intersection numbers of tautological classes on moduli space, as well as an asymptotic formula for the growth of the number of simple closed geodesics on a compact hyperbolic surface, generalizing the theorem of the three geodesics for spherical surfaces. Her subsequent work has focused on Teichmüller dynamics of moduli space. In particular, she was able to prove the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic.

Most recently as of 2014, with Alex Eskin and with input from Amir Mohammadi, Mirzakhani proved that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal. The closures of complex geodesics are algebraic objects defined in terms of polynomials and therefore they have certain rigidity properties, which is analogous to a celebrated result that Marina Ratner arrived at during the 1990s. The International Mathematical Union said in its press release that, "It is astounding to find that the rigidity in homogeneous spaces has an echo in the inhomogeneous world of moduli space."

Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".

Also at BBC, Stanford, Newsweek, and PressTV.


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  • (Score: 0) by Anonymous Coward on Sunday July 16, @03:02PM

    by Anonymous Coward on Sunday July 16, @03:02PM (#539902)

    *Fields medal

    Please fix and mod this down.

  • (Score: -1, Offtopic) by Ethanol-fueled on Sunday July 16, @03:44PM (3 children)

    by Ethanol-fueled (2792) Subscriber Badge on Sunday July 16, @03:44PM (#539910) Homepage Journal

    Errm...well, yes, in a way. [nature.com]

    Though she would look a lot less like a man with longer hair and could also use some lipstick and mascara.

  • (Score: 2) by unauthorized on Sunday July 16, @04:02PM (1 child)

    by unauthorized (3776) on Sunday July 16, @04:02PM (#539917)

    "Great mathematician dies, identarian politicians waste no time to whore out her identity."

    • (Score: 0) by Anonymous Coward on Sunday July 16, @06:43PM

      by Anonymous Coward on Sunday July 16, @06:43PM (#539964)

      For some of us with young daughters, she is an existence proof.

  • (Score: 0) by Anonymous Coward on Sunday July 16, @05:59PM (6 children)

    by Anonymous Coward on Sunday July 16, @05:59PM (#539953)

    how do you get breast cancer from doing math?
    you know, i kindda understand certain correlations, like ...uhm... people that drink alot (of alcohol) get problems with their livers.
    people that inhale bad stuff get problems with their lungs. people with alot of sun exposure get problems with their skin. etc.
    but i am at lose about this breast cancer stuff?

  • (Score: 3, Informative) by Yog-Yogguth on Monday July 17, @02:30AM (1 child)

    If people don't understand what she worked on they won't have any reason to respect neither the mathematics nor her.

    So I wanted to change that a little even though I don't care if she was female any more than I care that Erdōs was male or a drug addict (and I have no idea what he died of either, I do not think he overdosed on his dear amphetamines).

    Math is made harder than it actually is when it isn't actually explained. It's still plenty hard (or impossibly hard for me in most cases) even afterwards but at least it can be made understandable to just about anybody when it is explained.

    If you're like me (interested in mathematics) and you read the summary and recognized the words but perhaps not much else then this link [matific.com] is to an image explaining the general topic.

    Since what is mostly plain text is unfortunately in the form of an image I've written it up into the text below with some changes. Most of the drawings in the image were unnecessary but I've described one.

    By the time you finish reading all of the explanation below the next paragraph will make prefect sense:

    "Some of Mirzakhani's main contributions are in the field of Riemann surfaces. One of her contributions was determining a general formula for the number of closed geodesic curves in a Riemann surface that has a very large genus."

    Here we go.

    So what is a Riemann surface?

    Think of a balloon or a doughnut, now imagine an ant walking on their surface.

    From the ant's point of view it can only go left, right, forward, and backward... so although the doughnut is a 3-dimensional object its surface is 2-dimensional.

    Riemann surfaces named after German mathematician Bernhard Riemann can be thought of as curved surfaces such as the surface of a sphere, or a doughnut (mathematicians call it a torus), even the surface of a pretzel is a Riemann surface.

    These are all closed Riemann surfaces but there are also ones that stretch to infinity as if it was a huge tablecloth that goes on forever but is all crinkled and needs some serious ironing if one wanted to make it flat.

    Another property of Riemann surfaces is that when our imaginary ant walks over it then no matter where it is the nearby area in general looks roughly like either a piece of a flat plane or as a piece of a sphere or as a piece of a saddle shape.

    Image showing a ballon, a sphere, a baseball bat, and a doughnut, and asking which shape is the odd one out. The answer is the doughnut since it has a hole in it while the others do not.

    An important characteristic of Riemann surfaces is the number of holes in the surface, this number is called the genus of the surface. One can translate genus to mean the species of Riemann surfaces, a classification.

    For example the genus of a sphere is zero becasue it has no holes in it while the genus of a doughnut is one since it has one hole in it.

    The genus of a figure shaped like a 3-dimension figure 8 or an infinity sign is two since it has two holes.

    Middle school geometry tells us that straight segments are the shortest paths between every two points. In what is called planar geometry this is indeed true however as far as traveling along a surface on a curved plane it is no longer true.

    As an example think of two opposing points on a sphere: the north and south pole. The shortest path between them along the surface makes a longitude on a globe of the Earth as the straight path between two points is bent along the curvature.

    The shortest path between two points on a Riemann surface along its surface is called a geodesic curve.

    Geodesic curves play a central role in Riemann surfaces and sometimes have surprising characteristics or behavior.

    For example while in planar geometry a straight line can continue forever and never intersect with itself the same is not true on Riemann surfaces where a geodesic curve may intersect with itself in various ways and where it can also form a closed loop.

    If a geodesic curve forms a closed loop it is called a closed geometric curve.

    Let's try that paragraph again:

    "Some of Mirzakhani's main contributions are in the field of Riemann surfaces. One of her contributions was determining a general formula for the number of closed geodesic curves in a Riemann surface that has a very large genus."

    I'm sometimes in a haphazard, lackadaisical, and wasteful manner and whenever I can spare the time and effort fidgeting with an unsolved 3-dimensional geometry question (the next Szilassi polyhedron, a solid with six holes, the guy isn't even dead yet but it's interesting to me and thus fun even though I'm unlikely to ever make it work and life and the world interferes way too much), a problem which is almost directly related to the mathematical topic and I didn't even realize it before trying to find a more easy to digest explanation of the area she was working on.

    All errors are mine :)

    --
    Bite harder Ouroboros, bite! tails.boum.org/ linux USB CD secure desktop IRC *crypt tor (not endorsements (XKeyScore))
    • (Score: 2) by Yog-Yogguth on Monday July 17, @02:43AM

      One error I see now is that I mistakenly wrote
      "If a geodesic curve forms a closed loop it is called a closed geometric curve."
      which should instead be
      "If a geodesic curve forms a closed loop it is called a closed geodesic curve."

      Easy mistake to make.

      I should also point out the obvious: the little explanation above isn't an explanation of her work, it's only an explanation of the general topic of a little bit of her work.

      I could also throw in a link to the (first) Szilassi polyhedron [wikipedia.org], someone (very likely not me) will find the next one or alternatively prove that it is impossible but who knows how long it may take.

      --
      Bite harder Ouroboros, bite! tails.boum.org/ linux USB CD secure desktop IRC *crypt tor (not endorsements (XKeyScore))
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