Gregory Barber

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.

Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.

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.

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?

Two new notions of infinity challenge a long-standing plan to define the mathematical universe.

An exploration of how artificial intelligence is changing what it means to do science and math, and what it means to be a scientist.

Technology has forever served as science’s toolbox. But now that AI is being used to develop questions and methods as well, some scientists wonder what their role is going to become.

A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge.