You are looking for
Advanced search
Two Researchers Are Rebuilding Mathematics From the Ground Up
...revolutions in logic and set theory that marked the boundary between 19th-century and modern mathematics. Their birth was a crucial waypoint on math’s inexorable march from the numbers and shapes...
How Alexander Grothendieck Revolutionized 20th-Century Mathematics
...were his actual mathematical contributions? What Albert Einstein was to 20th-century physics, Alexander Grothendieck was to 20th-century mathematics. He is much less well known because math gets technical even more...
What Do Gödel’s Incompleteness Theorems Truly Mean?
...mathematicians — most forcefully David Hilbert, the leading mathematician of that time — was to rid mathematics of iffy intuitions by way of formally axiomatizing mathematics into a consistent and...
How Unknowable Math Can Help Hide Secrets
A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography. Mathematicians spend most of their time thinking about what’s knowable. But the...
What Can We Gain by Losing Infinity?
Mathematicians Want to Banish Infinity. What Might They Gain? Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights...
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...