## algebraic geometry

Fields medallist Caucher Birkar tells us about his work and his unusual mathematical journey.

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

The winner of the 2014 Chern medal tells us about beauty in maths, the twists and turns of mathematical history, and his work for the maths community.

This year's Abel Prize has been awarded to the Belgian mathematician Pierre Deligne for "seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields".

Imaginary is an interactive mathematics exhibition that inspires the imagination with beautiful images. And what is more exciting it allows anyone to step into the world of maths and play with beautiful mathematical surfaces, symmetry and much more. We went along to the Imaginary Barcelona conference, which brought together people involved in the original exhibition in Germany and its recent successful run throughout Spain.

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?

*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?