‘Fielding the numbers’: Maryam Mirzakhani’s Mathematical Triumph

by Stéph Kuypers

I’ve always been terrible at maths. Mostly I’d spend class adding numbers together to make funny words if you turned the calculator upside down. I was definitely more interested in history, or being a story writer. Funnily enough, so was Maryam Mirzakhani – the first and only woman to have won the prestigious Field’s Medal for Mathematics.

Beginnings

Mirzakhani was born in Iran in 1977 and wanted to be, as mentioned, a writer. She would lie in bed at night and create characters; girls who would go off and do remarkable things. Even though she spent a lot of time with her engineer father, she wasn’t hugely scientifically minded – until her brother taught her a trick to add up all the numbers from one to 100 (i.e. 1 + 2 + 3 and so on). 

Starting at both ends, he said, each two numbers add up to 101 (100 + 1, 99 + 2 etc.), so instead of labouring through all the numbers, Mirzakhani could just multiply 101 by 50 to get the answer. It was the first time she realised a mathematical solution could be a beautiful narrative all on its own. 

Mirzakhani completed her PhD at Havard. (Credit: Mott Carter – Clay Mathematics Institute)

Fields of Study

Mirzakhani attended a girls-only Farzanegan school in Tehran, which specialised in gifted pupils – although she was initially told by a teacher that she had no aptitude for maths! This changed when she was able to solve some maths Olympiad problems. After this she asked their principal whether they could have mathematical problem solving classes – usually only reserved for boys. 

Luckily, the woman agreed, and Roya Behesthi (Associate Professor at Washington University and a school friend of Mirzakhani) says both she and Mirzakhani found it motivating to compete with the boys…and surpass them. Both girls ended up joining the Iranian Mathematical Olympiad team in 1994 and 1995, where Mirzakhani won gold twice – with a perfect score in ‘95! Mirzakhani made history then too – she was the first Iranian ever to achieve this.

Further Afield

Mirzakhani graduated from Sharif University in Tehran, and went on to Harvard for her PhD, publishing papers all the while. For her 2009 thesis, she won the Blumenthal Award for the Advancement of Research in Pure Mathematics. She went on to win the Field’s Medal in 2014, (think Nobel Prize for maths, awarded every four years to a select few mathematicians aged 40 and under). This was for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces… 

In extremely basic terms this means that her interest was in structures that you can put on a surface – i.e. if you follow the trajectory of a ball on a billiard table, would it cover all of the billiard table or can you find closed billiard paths? Mirzakhani extended this to multiple billiard tables with multiple trajectories.

Mirzakhani often ‘doodled’ on sheets of paper while working on a theory. (Credit: Thomas Lin, Quanta Magazine)

In The Field

Mirzakhani described her maths as ‘slow maths’, and said “I don’t have any particular recipe [for developing new proofs]…It’s like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck, you might find a way out.” 

She even likened her work to her old love of storytelling. As she told Quanta Magazine in 2014: “There are different characters, and you are getting to know them better. Things evolve, and then you look back at a character, and it’s completely different from your first impression.” 

When working on a theory, she would always think ahead to what the shape of a theory might be that had yet to be discovered. She’d often put down sheets of paper and doodle pictures on them alongside her maths, hoping the different creative processes would spark off each other – her daughter Anahita called it ‘Mummy’s painting’.

Endings

Mirzakhani tragically died of breast cancer in 2017. She was barely 40. She was so respected that Iranian newspapers broke their own protocol and published pictures of her without a hijab in their obituaries. Humble and grounded, she cared little for the spotlight, but was always willing to listen to colleagues and friends, working on maths and sharing stories with them. 

The UN has named her among the seven women scientists who have shaped the world, and Mirzakhani’s name is attached to bursaries, scholarships and societies, thereby continuing to illuminate the path for other girls and women to follow in her footsteps. Definitely a story worth paying attention in maths class for.


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About the Author

Stéph is an editor, writer, and history tour guide working with Women of London. She in the process of starting her own editing business, and working on her steampunk fantasy novel set in London. Find her at LinkedIn.

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