Youth ruled the year in mathematics. The Fields Medals — awarded every four years to the top mathematicians no older than 40 — went out to four individuals who have left their marks all over the mathematical landscape. This year one of the awards went to Peter Scholze, who at 30 became one of the youngest ever to win. But at times in 2018, even 30 could feel old.

Two students, one in graduate school and the other just 18, in two separate discoveries, remapped the borders that separate quantum computers from ordinary classical computation. Another graduate student proved a decades-old conjecture about elliptic curves, a type of object that has fascinated mathematicians for centuries. And amateur mathematicians of all ages rose up to make significant contributions to long-dormant problems.

But perhaps the most significant sign of youth’s rise was when Scholze, not a month after the Fields Medal ceremony, made public (along with a collaborator) his map pointing to a hole in a purported proof of the famous abc conjecture. The proof, put forward six years ago by a mathematical luminary, has baffled most mathematicians ever since.