The word abstract represents a fragment of one's imagination that is appreciated for its intrinsic beauty. Due to the lack of ability in projecting such a thought, the abstract often lacks a physical form or even an explanation for its existence & significance. But few minds have broken the shackles, and have pioneered in showing elegance by being different. Elegance is what we call Creativity and what’s shown is called Art. Art has many forms to it, depending on the manner it is showcased. The art of modulating your voice and breath, in a creative manner, is the art of Music. The art of moving your body with symmetry in a creative manner, is the art of Dance. The art of distribution of colours in a creative manner, is the art of Painting. The art of coding natural phenomena into a language, in a creative manner, to make it the language of the Universe and Gods, is the art of Mathematics. Due to the indictment of our modern educational form, many may not agree to that, although that’s what Anahita thought whenever she saw her mother on the floor doodling doughnuts on big white sheets. The 3 years old girl would scream, “Oh, mommy is painting again!”. This is the story of that mother and her paintings. The paintings were born from a speculative geometric intuition of one of her generation’s greatest mathematicians, Maryam Mirzakhani.
Maryam was born on 12 May 1977, in Tehran, capital of Iran, to very supportive and encouraging parents. She grew up in a family with three siblings and her elder brother got her interested in science at an early age by sharing what he had learned in school. Maryam’s parents wanted all of their children to have meaningful and satisfying professions, without caring much about any success and achievements. It was the time of the Iran-Iraq war, and there were only two schools functioning in the capital of Iran, one for boys and one for girls. After writing exams, top 90 or 100 students were qualified to go to school. In 1988, Maryam, getting through the test, entered middle school and met her best friend, Roya Beheshti Zavareh, who is currently a math professor at Washington University. Maryam and Roya did well in class and all the tests that the teachers in other schools (where all boys went) would often bring in the two girls' names and set their example as a lead for others to follow. Few assumed Maryam as a child prodigy, while others regarded her hard work, for her ingenious mind. She was selected for the National level Olympiad exam and in 1994, she became the first female student to be selected for international Math Olympiad (IMO), alongside her friend, Roya. Maryam secured 40 on 42, to win the gold medal, and Roya secured a silver medal. Though Maryam started with math for its challenges, slowly she started to enjoy the subject for its intrinsic beauty. A year later she secured 42 on 42 in IMO held in Canada. Her photo made it to local newspapers inspiring young children, especially girls, to take up Mathematics.
After School, she went to Sheriff University for her Bachelor’s, a place which allowed the students to grow at their own pace. There Maryam joined the Olympiad team and trained the young students preparing for IMO. She was tough enough and even played soccer with boys. In 1998, on 17 of March midnight, after finishing a conference held in Ahvaz, a bus with 40 students left for Tehran, bringing the students back to Tehran. Due to darkness, the bus driver drove off a cliff into a valley. Many lost their lives, leaving behind Maryam and Roya as few of its survivors. An incident that is largely considered as a National tragedy in Iran, left a deep dent in the hearts of Maryam and Roya, as they had lost their close friends. Both of them earned their degree in 1999, and were recommended to apply for different Universities, so that they could have a good chance of getting selected. Roya got into MIT and Maryam got into Harvard, both stayed nearby in Boston. You’d think that you could speak a Foreign language well, but when you do get to speak, initially your confidence might be crippled, as you would be far away from your home and culture. Similar challenges stood at each footstep for Maryam in 1999. In second year, she started working with Curtis McMullen, who had recently won the prestigious Field’s medal, which is often dubbed as the Nobel of Mathematics, although it is much more challenging than getting a Nobel. Her work, like any other research work, was agonised with frustration, but was testified by patience, as she studied Riemann surfaces, and just imagine if you had to wrap two doughnuts held together with a tight rubber band, how many such rubber bands existed. These involved understanding the hyperbolic nature of the surfaces, and eventually she had formulated not just for two doughnuts, but for any number of doughnuts. Maryam earned her PhD in 2004 (Note that a lot of mathematical details or the territories are not visited here, for general interest). Her thesis also included, giving an elegant proof for Witten’s conjecture, an original proof that had already existed, but may have lacked certain elegance that Maryam’s proof offered.
In the fall of 2003, Maryam met Jan Vondrak, who currently holds a position of associate professorship in Stanford. They got married in Princeton the next year. Earlier Maryam had turned down a fellowship at Harvard, as she planned on taking up a Research fellowship offered to her by Clay Mathematics Institute at Princeton University. She continued her work there, until she was offered a permanent professorship at Stanford University. For Maryam, covering the syllabus material in the class wasn’t as much of a fun as the discussions she had with the students outside the classroom. She enjoyed talking to younger aspirant mathematicians, as she found their optimism due to being unaware of certain potential technical difficulties, and hence their willingness to move in different directions governed by intuition, is something she shared in common with them, with only difference being, she was aware of those difficulties, with also knowing that the answers to them were mainly a virtue of patience. With the same virtue and in collaboration with Alex Eskin, she worked on the dynamics of Billiard ball, which mainly dealt with whether it is possible for a ball to move inside the board (polygon), in a such a way that the path eventually get repeated, and if so how many path exists and how do they look like? Maryam changed the perspective of the problem, by making trajectory simple (straight line) and allowing the geometry to complicate, as she imagined placing a mirror right next to the polygon's side, that the ball was incident on and letting the ball continue in a straight line without being reflected. The proof, which was a monumental work compressed to a 200 page paper, got dubbed to be the ‘magic wand’ theorem. On 13 August 2014, recognising her contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces, she was awarded the most prestigious Field’s medal at International Mathematical Union, at INC held in Seoul, South Korea. Maryam Mirzakhani became the first woman and also the first Iranian to win the Field’s medal.
Maryam in the year 2013 was diagnosed with Breast Cancer. As opposed to the belief she had recovered, the Cancer had spread and in 2016, she was diagnosed with stage 4 Cancer. At the time, her daughter, Anahita was 5 years old. Maryam spent a lot of time with her daughter during her last months, mostly playing with her at the beach or sharing her knowledge of colouring and ‘painting’. Even her husband recalls now that given the choice between any important job on a given day or doing something important with Anahita, she would pick Anahita. He further recalls that it was not all about math, they liked music, they liked sports, and even travelled together a lot and in many ways had a very normal life. On 14 July 2017, Maryam breathed her last in Stanford Hospital. Her husband recalls her as being the nicest person ever, synchronous to her colleague’s describing her as pure good. In 2014, when she received the Field’s medal, her parents got to know about this from the media. Later when asked, she told her parents that, as to do with her humbled nature, she thought it was not that big of a deal. Even the Stanford President, Marc Tessier-lavigne said that she accepted honours only with the hope that it might encourage others to follow her path. Upon her death, Iranian President vouched for the legacy that Maryam had left behind and the impact it would have on young minds. The local newspaper in Iran, broke taboo and published photographs of Maryam Mirzakhani with her hair uncovered. This was the history in making. Even policies regarding matrilineal citizenship for children of mixed-nationality parentage, were revisited with renewed debates.
As a young child, Maryam was interested in stories, novels, so much so that she thought she would be a writer in future. Her school was close to a street full of books, to which she’d often visit, along with her friend Roya. They would end up in buying a lot of books together, because the books were cheap compared to the knowledge they would gain. This was a tradition which she followed throughout her life, as her husband recalls and tells that she would lock herself up in a room full of books and with a bowl of apples, would enjoy reading hours together undisturbed. When it came to lecturing, often in the pursuit of the why’s and how’s, triggered by excitement, she would jump off to a different topic and would lose track of time, explaining about it, with full of life and energy. She had a very mysterious way of focusing on things, with an abstract sense to it, an abstract that revealed her as an artist, or it at least did, in the eyes of young Anahita.
