Algebraic geometry

Determination and effort propelled Jacob Tsimerman to the top of the math world. But now that he’s won a Fields Medal, he worries that the field is in jeopardy.

Lauren Williams tells 'The Joy of Why' how studying a fundamental object in algebraic combinatorics led to a career full of surprises.

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.

Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.

Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.

These metaphorical gardens have become central objects in modern mathematics.

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.