## fields medal

Martin Hairer's is being honoured for a major breakthrough that gives a way of attacking problems that had previously been impenetrable.

Maryam Mirzakhani is being honoured for her "rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity".

What's the point of the Fields Medal and other maths prizes? Who decides who gets one? And when will we have the first female medallist? Rachel talks to László Lovász, current president of the International Mathematical Union (IMU), Martin Grötschel, the IMU's secretary, and Ragni Piene, the new chair of the Abel Prize committee about all this and more.

Here's the full and uncut version of our interview with Fields Medallist Cédric Villani. We'll publish a slightly more polished version when we get the time, with more explanations, but thought you'd like the chance to listen to the whole thing.

Journey to the frontiers of maths with Plus as we cover the International Congress of Mathematics in Hyderabad, India

The work of Fields Medallist Stanislav Smirnov will take mathematics and physics into a new phase with his mathematical proof of the understanding of phase transitions.

What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.

A very tired Marianne and Rachel discuss the atmosphere at the first day of the ICM when the Fields medals were awarded...

Eron Lindenstrauss got the Fields Medal for developing tools in the area of dynamical systems and using them to crack hard problems in the seemingly unrelated area of number theory.

Results in mathematics come in several flavours — theorems are the big important results, conjectures will be important results one day when they are proved, and lemmas are small results that are just stepping stones on the way to the big stuff. Right? Then why has the Fields medal just been awarded to Ngô Bào Châu for his proof of a lemma?