*You can see all our coverage from the ICM 2018 here.*

The International Congress of Mathematicians opened this morning in a packed amphitheatre, bathed in green light and the sounds of the rain forest. The ceremony celebrated the best of Brazilian talent and creativity and the emphasis of the organising committee on building a legacy for the future of mathematics in Brazil. It was particularly lovely to see the 576 gold medallists from the Brazilian Mathematics Olympiad in the crowd, perhaps some of them will take the stage at some future ICM.

We could feel the excitement in the crowd as we waited for the announcements of the prizes of some of the most prestigious prizes in mathematics. And the winners of the Fields medals are:

Caucher Birkar — Caucher Birkar has been awarded the Fields medal for his contribution to algebraic geometry.

Alessio Figalli — Alessio Figalli has been awarded the Fields medal for his contributions, among other things, to optimal transport theory.

Peter Scholze — Peter Scholze has received the Fields medal 2018 for transforming arithmetic algebraic geometry.

Akshay Venkatesh — Akshay Venkatesh has been awarded the Fields medal 2018 for his work exploring the boundaries of number theory.

You can read about the maths behind these prizes in the articles above. Also announced were:

- Constantinos Daskalakis – winner of the Rolf Nevanlinna Prize for outstanding contributions on the mathematical aspects of informational sciences.
- David Donoho – winner of the Carl Friedrich Gauss Prize for scientists whose mathematical research has had an impact outside mathematics.
- Masaki Kashiwara – winner of the Chern Medal Award, awarded to mathematicians whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics.
- Ali Nesin – winner of the Leelavati Prize for increasing public awareness of mathematics as an intellectual discipline and the crucial role it plays in diverse human endeavors.