Konstantin Kakaes

These metaphorical gardens have become central objects in modern mathematics.

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.