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Why Math’s Final Axiom Proved So Controversial
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.
What Can We Gain by Losing Infinity?
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.
A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots
With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots.
The AI Revolution in Math Has Arrived
AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.
In Math, Rigor Is Vital. But Are Digitized Proofs Taking It Too Far?
The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean.
How Writing Changes Mathematical Thought
David E. Dunning explores how mathematical notation is a social, world-building technology.
The Math That Explains Why Bell Curves Are Everywhere
The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day.
New Strides Made on Deceptively Simple ‘Lonely Runner’ Problem
A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem in decades.
Can the Most Abstract Math Make the World a Better Place?
Columnist Natalie Wolchover explores whether applied category theory can be “green” math.