Out Of The Syllabus
Maryam Mirzakhani: the person who deserves to be known
On 14th July the world lost a scholar in the field of Mathematics, Maryam Mirzakhani the first and only woman to win the prestigious Fields Medal - an award considered equivalent to Noble Prize in Mathematics.
Maryam Mirzakhani was born on 3rd May, 1977 in Tehran, Iran. In 1994 she became the first female Iranian to win the Gold Medal Level in International Mathematical Olympiad and again in 1995 she became the first Iranian to achieve a perfect score and win two gold medals in the very same event. After completing her BSc in mathematics in 1999 from the Sharif University of Technology, she then went to the United States, and earned her PhD in 2004 from Harvard University, where she worked under the supervision of the Fields Medalist Curtis T. McMullen. She was a 2004 research fellow at Clay Mathematics Institute and a professor at Princeton University, and then she became a professor at Stanford University in 2008. In 2005, Mirzakhani married Jan Vondrak, a Czech theoretical computer scientist and applied mathematician who currently is an associate professor at Stanford University.
Mirzakhani's work contained several branches of mathematics. She was intuitive and persistent. To her younger daughter, Anahita she was a sort of an artist. She would spend hours sitting on the floor, sketching out ideas, drawing diagrams and formulae on supersized canvases of paper. "What is so special about Maryam, the thing that really separates her, is the originality in how she puts together these separate pieces," said Steven Kerckhoff, a Stanford colleague. "The novelty of her [PhD thesis] made it a real tour de force."
Maryam's earliest breakthroughs solved fundamental problems of the classical origin concerning the hyperbolic geometry of individual surfaces. Her work was highly theoretical in nature, but it could have impacts related to theoretical physics of how the universe came into existence, since it could inform quantum field theory, secondary applications to engineering and material sciences. Within mathematics, it has implications for the study of prime numbers and cryptography. Her later breakthroughs were focussed on dynamical systems. Such systems describe motion. They arise throughout mathematics and physics, and through proper abstractions one can transfer knowledge gained in one setting to whole classes of problems in another. Thus a penetrating study of how a billiard ball bounces around a polygonal table can provide insights into the behaviour of many physical systems (the motion of gases for example), and equally it can be used to build bridges between different aspects of the structure of moduli spaces. An investigation into this action surprisingly led to a 200 page paper, which when published in 2013, was referred as the 'beginning of the new era' and 'titanic work'.
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Maryam always mentioned how her parents were a huge support and how she dreamt of becoming a writer but picked up a keen interest on mathematics with her brother's encouragement and then going on to make seminal contributions to algebraic geometry. According to Roya Beheshti, an algebraic geometer at Washington university in St. Louis, and a lifelong friend, Maryam's passion was evident early on. She was very humble and at the same time, ambitious and her work was driven by pure joy. When Maryam was in sixth grade in Tehran, a teacher discouraged her interest in Mathematics and noting that she was not particularly talented and certainly not at the top of her class. But fast forward a quarter century, she became the first lady and also the first Iranian to win the Fields Medal.
An interesting and hilarious event happened during the ICM meeting in Seoul where she was awarded the Fields Medal along with Manjul Bhargava, Artur Avila and Martin Hairer, the presenters hadn't realised that the name of the winners were engraved on the medals and they presented them out incorrectly. Bhargava recieved Martin's, who recieved Maryam's, who recieved Artur's, who recieved Bhargava's. The mathematicians had a real life combinatorial problem in their hands.
Despite her illness, she was producing some of her most amazing works in the last few years. On 14th July 2017, she succumbed to breast cancer at the age of 40 at a hospital in California. Iranian president Hassan Rouhani published condolence messages and praised Mirzakhani's scientific achievements. President Rouhani said in his message, "unprecedented brilliance of this creative scientist and modest human being, who made Iran's name resonate in the world's scientific forums, was a turning point in showing the great will of Iranian women and young people on the path towards reaching the peaks of glory and in various international arenas". Upon her death several Iranian newspapers along with president Rouhani broke taboo and published photos of Mirzakhani with short hair and head uncovered. This was widely widely noticed all over the press and on social media.
Maryam Mirzakhani became a heroic figure in the field of Mathematics, she serves as an inspiration for many young women - when she won the Fields Medal in 2014 she said "I will be happy if it encourages young female scientists and mathematicians".
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