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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. How do mathematicians decide that something is...
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. From the tangle in your computer cord to the mess your...
The AI Revolution in Math Has Arrived
...Intelligence, Axiom Math, and Math Inc. “One reason there is so much interest in AI for mathematics in the corporate world is that people are recognizing that the key to...
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. In...
How Writing Changes Mathematical Thought
David E. Dunning explores how mathematical notation is a social, world-building technology. It’s natural to think of math as being fundamentally abstract. Whether it’s invented or discovered, its truths are...
Are Strings Still Our Best Hope for a Theory of Everything?
...mathematical equivalences, or “dualities,” between different versions of string theory, and between strings and quantum fields in different dimensions. It made things more complicated, but more mathematical miracles emerged —...
Quantum Cryptography Pioneers Win Turing Award
...any mathematical assumptions. Not even an eavesdropper who could magically solve the world’s hardest math problems would learn the secret key. Teleporting Forward Bennett and Brassard’s quantum key distribution paper...
The Math That Explains Why Bell Curves Are Everywhere
...limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is...
Can the Most Abstract Math Make the World a Better Place?
Columnist Natalie Wolchover explores whether applied category theory can be “green” math. “I’ve spent a long time exploring the crystalline beauty of traditional mathematics, but now I’m feeling an urge...