At this week’s International Congress of Mathematics, in Seoul, Korea, the winners of the 2014 Fields Medal were announced. The medals, which were established in 1936, and are awarded every four years to four different mathematicians, recognise achievement in mathematics research. This year’s winners are (from the ICM website):

**Artur Avila**(CNRS, France & IMPA, Brazil) – whose profound contributions to dynamical systems theory have changed the face of the field, using the powerful idea of renormalization as a unifying principle.**Manjul Bhargava**(Princeton University, USA) – for developing powerful new methods in the geometry of numbers and applying them to count rings of small rank and to bound the average rank of elliptic curves.**Martin Hairer**(University of Warwick, UK) – for his outstanding contributions to the theory of stochastic partial differential equations, and in particular creating a theory of regularity structures for such equations.**Maryam Mirzakhani**(Stanford University, USA) – for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.

Here’s a round-up of some of the other Fields Medal coverage:

- Four winners of the 2010 Fields Medal announced, at Scientific American
- These 4 People Just Won The Most Prestigious Award In Mathematics, at Business Insider
- Awards page on the International Congress of Mathematics website
- Meet the winners of the Fields medal – the ‘Nobel prize of maths’ at The Conversation
- The Fields Medal is the greatest prize in maths, at The Telegraph (presumably why they’ve chosen to illustrate the article with a picture of a Sudoku)

One of the reasons this news story seems to be basically everywhere today (if you wake up and Sarah Montague is talking to a mathematician about something, you know there’s maths news) is that this is the first time the prize has been awarded to a woman. Given that only around 6% of mathematics professors are female (thanks, Sarah Montague), it’s not surprising it’s taken so long for a woman to achieve the award – and great news. It’s been picked up by a huge number of news outlets, some of which you may not expect to be covering a maths story…

- Fields Medal mathematics prize won by woman for first time in its history, by Ian Sample at The Guardian
- Iranian woman wins maths’ top prize, the Fields medal, by Dana Mackenzie at New Scientist
- First female winner for Fields maths medal, at BBC News
- Top Mathematics Prize Awarded to a Woman for First Time, by Alex Bellos for Time Magazine
- Maryam Mirzakhani Named the First Female Fields Medalist, at Elle Magazine
- First Woman Ever Wins a Fields Medal for Mathematics, at Jezebel

To find out more about the individual winners, here’s a great series of articles by Quanta Magazine/Simons Foundation:

- A Brazilian Wunderkind Who Calms Chaos (Artur Avila)
- The Musical, Magical Number Theorist (Manjul Bhargava)
- In Noisy Equations, One Who Heard Music (Martin Hairer)
- A Tenacious Explorer of Abstract Surfaces (Maryam Mirzakhani)

Alex Bellos, over at The Guardian, has posted an explanation of the actual maths involved in each winner’s research, from the International Mathematical Union: Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained

And if you’re interested in the Fields Medal in general:

- How to Talk About the Fields Medal at Your Next Cocktail Party, by the brilliant Evelyn Lamb at Scientific American
- How Math Got its ‘Nobel’, at the New York Times

Also, Terry Tao gave a brief high-level overview of their technical accomplishments: http://terrytao.wordpress.com/2014/08/12/avila-bhargava-hairer-mirzakhani