Maryam Mirzakhani finds curves on cupcakes

Instead of describing a circle using three points, you can also characterize it by its center and radius. This greatly simplifies the unit space. In this way, it has only three dimensions (x and y coordinates for center and another number for radius). However, if you only want to consider circles of different sizes, as required at the beginning, you can design the unit area more simply. In this case, the center of the circle doesn’t matter: if two circles have the same radius at different locations in the plane, you don’t want to tell them apart. Therefore, one has only to take into account the radius – and have a one-dimensional scale space that includes all positive real numbers. Each of these points (ie, each number) corresponds to a circle of corresponding radius.

unit room | Example of a unit room

Mirzakhani did something similar: She collected the scales of the surfaces she wanted to examine in a model room. For example, the modulus space contains all two-hole figures, where a point in space defines the exact geometry in that figure. By examining the structure of these modular spaces, the mathematician was able to calculate how many simple closed geodesics the surfaces had – without taking each individual geometry into account. In contrast to the general case (where cross geodesy is also allowed), the number of curves does not grow exponentially with their length the in. Instead, Mirzakhani found outthat their number can be calculated by the polynomial, that is, the equation of the form a + M + cl2 + Del3 + …

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Indeed, Mirzakhani’s work was like that influences on other subjects: Through her methods, she found new evidence for a conjecture that originally came from physics. In 1991, string theorist Edward Witten put forward a hypothesis, which resulted from his research on a possible theory of quantum gravity: according to it, two-dimensional models should be equivalent. The models he studied dealt with so-called strings, which are one-dimensional objects like loops or threads. In the 2D version, these strings wrap around all kinds of surfaces. From a mathematical standpoint, Witten’s research concerned curves on surfaces—exactly the kind of problems Mirzakhani was working with.

The mathematician caught the attention of experts with the breakthroughs Mirzakhani made during her doctoral dissertation. Soon, voices were raised that she was deserving of the prestigious Fields Medal—the prestigious award given to mathematicians under the age of 40 at most every four years since 1936. When Mirzakhani finally received an email in early 2014 naming her that year’s winner, she believed in First it is spam. Although she was the first woman to receive the honor, she remained very humble: Mirzakhani’s parents, with whom they had a good relationship, only appeared on television. When asked why she didn’t tell anything about it, the mathematician replied that she didn’t find it important.

Her friendly and sometimes reserved nature made her popular with her classmates. She avoided the spotlight and enjoyed spending time with her family, husband, and daughter. In 2017, at the age of 40, Mirzakhani died tragically of cancer. to commemorate her The Iranian media broke taboosThey photographed Mirzakhani without a headscarf – which is not usually the case with Iranian citizens, even if they live abroad. To this day, she is a role model for women in science, both in her home country and elsewhere in the world.

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What is your favorite math theory? Feel free to write it in the comments – maybe it will be the topic of this column soon!

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