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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.
The Man Who Stole Infinity
In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism.
How Can Infinity Come in Many Sizes?
Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.
Long-Sought Proof Tames Some of Math’s Unruliest Equations
Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.
Networks Hold the Key to a Decades-Old Problem About Waves
Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.