The Secrets of the Surface – the Mathematical Vision of Maryam Mirzakhani

Available to watch on Vimeo, The Secrets of the Surface – the Mathematical Vision of Maryam Mirzakhani is a documentary tribute to Maryam Mirzakhani, Iran’s most successful mathematician and the first woman to win the most prestigious prize in mathematics, the Fields Medal.

The documentary interviews the lecturers, her collaborators and undergraduate students in the USA, where she emigrated to. The film also goes to Iran to interview her teachers, school friends and the current pupils studying at her school back home, at Tehran Farzanegan, to get an insight into her prodigious beginnings and to help explain her contribution to maths.

Directed by George Csicsery who himself has won an award for his contributions to maths albeit for the slightly less impressive success of bringing maths to non-mathematical audiences. The story begins with a brief introduction into the importance of maths in the world around us, from general problem solving, to architecture showing intricate images of mosques, and even maths as art. It also includes recordings and footage of Maryam who goes as far as saying science and technology owe everything to maths. 

Maryam tells us about how she had no real aptitude for maths at middle school preferring books, but between the influence of her brother and her high school, she got hooked. So much so, she left a lasting mathematical legacy, shown here by the students gleefully clutching the maths book she wrote whilst at university.

The first test she had to pass was the entrance exam to Tehran’s top school, set up for gifted children. Here she would share a desk with her best friend Roya for the next 7 years. They made a formidable maths team, although Maryam was always the standout student and soon began showing signs of being the child prodigy she was.

To get the children into mathematics, competitions were organised, but there had been no female entries, that was until Maryam and Roya arrived on the scene. So began her keen interest in maths competitions and she was soon representing her country at the maths Olympiad. She won gold with 40/42 and her friend won silver. The following year she would go one better winning gold with full marks 42/42, a first for an Iranian entrant.

Of course she went on to University, Sharif University, to study maths and, although women in Iran are not considered a privileged group, with maths and science they are often on an equal footing with men and 40-50% of students are female. Here she was on the Olympiad Committee, she was a trainer, and wrote the text book that is still an essential guide for students at the university today.

After university, the top students are expected to progress further and do a PhD outside of the country. Expecting their chances to be better by applying to different universities Maryam got accepted at Harvard and her friend would go to MIT, both in Boston, USA, which meant that they could remain together on the next stage of their studies. Coming to America is a big move and getting a visa and figuring out the language was just the start of their tough cultural acclimatisation, but with the help of the Iranian study groups they were able to make a successful integration.

At Harvard she was taught by Curtis McMullen a professor who had already proved a theory of his own to be awarded the prestigious Fields Medal and Maryam would begin to take his work further. Her first thesis would be published in the top 3 mathematical journals and along with her team of collaborators the work was considered so powerful it became known as the magic wand theorem for which she won her own Fields Medal in 2014. The first Iranian and first woman to do so.

She got married to a Czech mathematician, a non-Iranian, which was considered quite unconventional, but they were happy and had a child together. Sadly when her daughter was only 2 years old she was diagnosed with breast cancer that would turn out to be terminal.

Since her passing away, she continues to inspire female students to pursue maths in her hometown in Iran and the mathematical world at large. Her image can be seen on murals and in photographs in tribute to her in Iran (not all of them with a head scarf, something unheard of for public figures, but illustrating how much Maryam is revered) and she has had a building at her university named after her, as well as a global mathematical award.

The documentary is a nice life story talking about her mathematical achievements using examples of some of the maths she worked on. It gives a great insight into how absurdly difficult maths is, without totally losing a non-Mensa audience, although further explanation would help to explain the importance of knowing ‘the trajectory of a billiard ball on a mirrored pool table.’ And whilst most of us will never understand the significance of ‘counting the simple closed curves around hyperbolic surfaces’ either, we can certainly appreciate the mathematical genius of a woman who is worshipped in her own country and has left her mark on the world of mathematics with her work continuing to be cited in the top classrooms around the world.