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Maryam Mirzakhani - Mathematician

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A candle in the Illumination Problem

Maryam Mirzakhani (1977-2017) was a mathematician from Iran who made history in 2014 when she became the first female winner of the Fields Medal, the highest honour in mathematics.


Maryam was born on 3 May, 1977, in Tehran, Iran. Her childhood was overshadowed by the Iran-Iraq war (1980-88) but her parents encouraged her academic talents. In spite of the challenges she won a place at a school for girls that had a strong track record of academic achievement. At first, Maryam enjoyed reading and thought she might become a novelist, but then an inspirational teacher helped her to discover a talent for mathematics.

The International Mathematics Olympiad is an event where people compete by taking part in problem-solving challenges. Although the previous Olympiad entrants from Iran had all been boys, Maryam's headteacher enabled her to join the national team in 1994. The headteacher's words, which served Maryam well as a motto in her life, were: 'You can do it, even though you'll be the first one.' Maryam went on to win a gold medal. She entered again the following year and not only won a gold medal, but also achieved a score of 42 out of 42.

University Life

Maryam went to Sharif University of Technology in Tehran and gained a Bachelor of Science degree in 1999. She was then admitted to Harvard University in the USA. Her doctoral advisor was Curtis McMullen, who had won a Fields Medal in 1998.

The Fields Medal was first awarded in 1936 in honour of the Canadian mathematician John Charles Fields (1863-1932) who had bequeathed funds to be used for awards similar to the Nobel Prize. The Fields Medal is awarded every four years to distinguished mathematicians under the age of 40. Up to four medals are awarded each time. By 2010 there had been 52 winners, all male.

Maryam had published papers on Graph Theory during her bachelor's degree, but turned to Hyperbolic Geometry for her thesis, entitled 'Simple geodesics on hyperbolic surfaces and volume of the moduli space of curves'. A hyperbolic surface disobeys Euclid's Fifth Postulate so, for example, the angles of a triangle on the surface add up to less than 180°. Coral is an example of a three dimensional object that has this kind of structure. Geodesics are curves drawn on the surfaces that are analogous to straight lines drawn on a flat piece of paper: they are the shortest routes between two points. The power of her imagination enabled Maryam to visualise and draw the mathematical concepts, which she could then describe in text form with the required rigour. Her work was awarded the 'Leonard M and Eleanor B Blumenthal Award for the Advancement of Research in Pure Mathematics'.

From 2004 to 2008, Maryam held the post of Assistant Professor at Princeton University, and was awarded a Clay Fellowship grant so she could concentrate on research rather than lecturing. This was useful to her, as she could avoid the 'low hanging fruit' and work on more challenging unsolved mathematical problems (she viewed herself as 'a slow thinker').

In 2005, Maryam married Jan Vondrak, who was originally from the Czech Republic. They had met at Princeton, as he was a mathematician and computer scientist working as a Postdoctoral Teaching Fellow there. In 2008 Maryam became Professor of Mathematics at Stanford University and Jan moved to Stanford to join her. Their daughter Anahita was born in 2011.

Making History

Maryam's enthusiasm for mathematics shone through into her presentations, so she was well regarded as a lecturer and conference speaker. Her research, too, was recognised as important. One of her most groundbreaking achievements was proving the so-called 'Magic Wand Theorem' with her colleague and fellow female mathematician Alex Eskin. Curtis McMullen had proved the theorem for one case, while Mirzakhani and Eskin proved it for all cases. The proof required concepts from geometry, topology and dynamical systems and had direct applications to the Billiards Problem (considering whether a billiard ball bouncing off the sides of a not-necessarily-rectangular table will cover every point on the table) and the Illumination Problem (considering whether a candle in a hall of mirrors will be able to light up the whole room). The 'Magic Wand' enabled a particular billiard ball or candle starting point to be selected and then the theorem would provide information about the behaviour of the ball or the light beams (previously, the only information that was available described what was most likely to happen).

Thus it was that in 2014 Prof Maryam Mirzakhani became the first female winner of the Fields Medal 'for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces'. The Medal was presented to her by Curtis McMullen at the International Congress of Mathematicians in Seoul, South Korea.

Maryam was even more in demand as a speaker thanks to this historic achievement, but sadly all was not well - she had been diagnosed with breast cancer that went on to spread to her bones and liver in spite of medical treatment. She died on 14 July, 2017, at the age of just 40. She was mourned around the world. However, her legacy lives on as she is a role model for female mathematicians everywhere, and her mathematical work and enthusiasm for the subject continue to inspire people to build on her achievements.

The beauty of mathematics only shows itself to more patient followers.
- Maryam Mirzakhani, 2008

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