# Women in maths

In a few days we’ll celebrate the International Women’s Day, so not writing a post about women in maths would be unforgivable negligence. Don’t worry, it isn’t a rant about how females in maths are treated terribly. In fact, I believe that being a mathematician is the best job if you’re a woman, want to have kids etc. Having said that, there’s one big issue with females in maths: they don’t get the fame they deserve. Let me introduce you to three ingenious female mathematicians, without whom the world wouldn’t be the same. The choice is subjective, so I hope you’ll explore the topic further, to find your favourite female mathematicians.

• Sophie Germain (1776 – 1831).

Sophie Germain (source: Wikimedia Commons)

During the French Revolution teenagers didn’t have an easy life. 13-year-old Sophie was basically stuck at home after the fall of the Bastille – you can imagine it wasn’t very safe outside. And what do bored kids do? Nothing that parent would approve of. For example, Sophie spent a lot of time in her father’s library. She was fascinated by a story of Archimedes described in J. E. Montucla’s “L’Histoire des Mathématiques”. Sophie wanted to know more about “geometry method” (this is how pure mathematics was called back then), so she basically read all maths books in her father’s library. And since the family was pretty wealthy, we might assume she read quite a few of them. This girl didn’t even skip the ones written in Latin or Greek – she just learned these languages, easy-peasy.

What a naughty child! Her parents thought mathematics was a very inappropriate subject for a young girl from a good family. Apparently they took away from her bedroom the fire and warm clothes, so she couldn’t study in the evenings. But she still did.

Sophie was 18 when the École Polytechnique opened. Of course women couldn’t attend the lectures, but she managed to get the lecture notes. To submit her homework, she started writing to one of the faculty members, Joseph-Louis Lagrange, an excellent mathematician. She signed the letters using the name of a former student, Monsieur Antoine-August Le Blanc, to pretend she was a male. However, Lagrange realised how talented the author of the letters was, so he insisted they met. Luckily, he didn’t mind her biggest flaw: being a woman.

Sophie’s main accomplishments were in number theory and theory of elasticity. Still hiding her identity, she kept using Le Blanc’s name to maintain correspondence with geniuses such as Carl Friedrich Gauss or Adrien-Marie Legendre. However, when her real name was revealed to the latter, he was delighted. Not only was she talented, but also achieved her results despite all the obstacles and prejudices she had to face because of her gender.

And the results indeed were amazing. For example, she proved that if integers x, y, z are such that  $x^5+y^5=z^5$, then neither of them can be divided by 5. This was a major step in proving Fermat’s Last Theorem. Moreover, her work in elasticity theory won the contest sponsored by the Paris Academy of Sciences. Unfortunately, even after this success, she couldn’t attend Academy’s sessions, because the only women allowed in the room were members’ wives.

55-year-old Sophie Germain lost the battle with breast cancer. She’ll never be forgotten, as she contributed significantly to development of number theory and theory of elasticity and, even more importantly, she showed us that women can be successful mathematicians.

Ada Lovelace (Alfred Edward Chalon – Science & Society Picture Library, Public Domain)

Such a disappointment! A famous English poet, Lord Byron, wanted a son, but his wife Annabella gave him a girl. Not treated properly by her husband, Ada’s mother left him, taking the baby with her.

It’s not surprising that Annabella didn’t think well of poets and other artists. This is why she made sure little Ada received a proper education in mathematics and science. Her private tutors included personages such as Mary Somerville and even Augustus De Morgan, the founder of mathematical logic.

Ada kept studying despite serious illnesses: she had obscured vision and needed crutches to walk. Maybe this is why she worked hard to make her dreams come true. As a 12-year-old, she really wanted to fly. Who doesn’t? But this girl believed it was possible. She studied different materials and examined birds’ anatomy to construct wings. She also understood that she needed a compass to not get lost above the ground. So flying wasn’t a dream as such – it was rather a plan.

Her tutor and friend, Mary Somerville, introduced her to Charles Babbage, a “father of the computer”. She was fascinated by his Difference Engine, something between a calculator and a computer.

She spent almost a year translating an Italian article on Babbage’s new idea, the Analytical Engine. More than translating, I would say. Ada also provided detailed notes and comments. Her ideas were supported even by Michael Faraday himself.

Ada’s notes included a description of calculating sequences of Bernoulli numbers using the Analytical Engine. This is considered a first algorithm ever published – thus we can call Ada Lovelace a first computer programmer.

She died aged only 36. Who knows what else she could achieve, had she lived longer… I’m grateful to her that I’m able to use my laptop to write this post and search for the information online.

• Maryam Mirzakhani (born in 1977).

You might wonder if any outstanding female mathematicians are still alive. Let me introduce you to Myryam, a first woman (and first Iranian) to ever receive the Fields Medal, the “Nobel Prize of mathematics”.

Fields Medal (By Stefan Zachow of the International Mathematical Union; retouched by King of Hearts ; Public Domain)

As a kid she wasn’t particularly fond of mathematics, she wanted to become a writer. It was her older brother who got her interested in science. He told her about the way Gauss figured out how to add numbers from 1 to 100 – and she was fascinated by the beauty of this solution.

As soon as she gave maths a chance, her life became a path of successes. In 1994 she became the first female Iranian student to win a gold medal in the International Mathematical Olympiad. In the following year, she participated in this prestigious competition again, just to get a perfect score and win a second gold medal.

After obtaining BSc in mathematics in Teheran, she started a PhD at Harvard University. Myryam was interested mostly in combinatorics and algebra. However, encouraged by an excellent seminar given by a Fields Medalist Curtis McMullen (from which she understood more or less nothing – it makes me feel so much better!), she began her research in complex analysis. Good choice, because in 2014 she received the most prestigious prize in mathematics.

I don’t think I can explain her research better than Jordan Ellenberg: “[her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables.”

We can expect she’ll achieve even more.