#### Anyone who has read my musings in these virtual pages will perhaps have discerned that I am (or at least was) a mathematician. Worse, perhaps, I am a pure mathematician. Pure mathematics is supposed to be that branch of mathematics that has no application to the real world. But the real world has a way of surprising us and many of the discoveries that pure mathematicians have made have turned out, after all, to have applications to the world around us. I wrote about the mathematician Pythagoras for The Beagle in May and I had planned to follow this by writing about a female mathematician called Sophie Germain. But then I was saddened by some news from the US.

There is no Nobel Prize for Mathematics. Nobel Prizes are awarded in Chemistry, Literature, Peace, Physics and Physiology or Medicine. A Nobel Prize, apart from the immense prestige value, is worth almost US$1 million. If there is an equivalent prize for mathematics it is the Fields Medal named after a Canadian mathematician called John Fields. This is a prize awarded every four years to up to four mathematicians under the age of 40. The Fields Medal has been awarded since 1936 and there has been a total of 56 recipients. It is worth about US$12,000.

* Above: Maryam Mirzakhani*

Only one woman has ever won the Fields Medal. She is Maryam Mirzakhani and she died at the age of 41 last weekend, on 15 July 2017. She had been diagnosed with breast cancer in 2013. It is a sad and cruel world that a woman who was a beacon for other women should die so young. Mathematics is no less a profession than any other and it faces the same or similar challenges of diversity as other professions. We hear a lot about a new acronym: STEM. This stands for science, technology, engineering and mathematics. There aren’t enough women in STEM and there aren’t enough girls doing STEM subjects at school and university.

The fact that there is only one female mathematician among the winners of the Fields Medal may be testament to a skew in the way that mathematical honours are allocated. There is another mathematics prize that has been awarded annually since its establishment by the Norwegian Government in 2001. This prize (called the Abel Prize after the Norwegian mathematician Niels Henrik Abel (1802–1829)) does not have the age restriction of the Fields Medal and was intended to be a sister prize to the Nobel Prizes. It is worth about US$750,000, so a lot more than the Fields Medal but it does not carry the prestige of the Fields. No woman has won an Abel Prize.

So, you may be asking: “what sort of mathematics did Maryam do?” I will tell you though you may wish that you hadn’t asked. Roughly speaking she did geometry. Her geometry wasn’t the geometry of Euclid that you might have learned at school. Mathematicians long ago saw the limitations of Euclidean geometry. Euclidean geometry works on a flat surface. The trouble with the world is that there are no flat surfaces. We live on a sphere (or more accurately an oblate spheroid). We know that space is curved though we don’t quite know how. Maryam’s geometry was called complex geometry, because that’s what it is. She was interested in surfaces that looked a bit like a leaf of kale. She looked at how a billiard ball might move over such a surface. You may say “what could possibly be the use of that?”

*Above:A curly kale leaf would make an interesting billiard table*
Well, perhaps you read my review of the biography of Paul Dirac, the quantum physicist. Dirac and his contemporaries realised that the atom isn’t made of stuff that we can touch, it’s a combination of waves and probabilities. Some of Maryam Mirzakhani’s work is connected to that through her contributions to something called string theory which is way of describing these waves and probabilities. When quantum computing arrives, Maryam Mirzakhani will be somewhere in the mix through her work.

Mathematics has lost a great mathematician and a great woman.