Joseph Howlett

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.

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.

The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major advances toward understanding it.

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

Climate science is the most significant scientific collaboration in history. This series from Quanta Magazine guides you through basic climate science — from quantum effects to ancient hothouses, from the math of tipping points to the audacity of climate models.

Earth’s climate is chaotic and volatile. Climate change is simple and predictable. How can both be true?

Earth’s radiation can send some molecules spinning or vibrating, which is what makes them greenhouse gases. This infographic explains how relatively few heat-trapping molecules can have a planetary effect.

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.