You are looking for
Advanced search
New Proofs Probe Soap-Film Singularities
Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist...
What Are Lie Groups?
By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools. In mathematics, ubiquitous objects called groups display...
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...
Researchers Reveal the Power of ‘Quantum Proofs’
...that hypothetical computers based on the laws of quantum physics would be able to rapidly solve difficult math problems. Ever since then, they’ve sought to pinpoint cases where quantum computers...
A Master of the Traveling Salesperson Problem Finds His Own Path
...seemingly unrelated subject: understanding the best way to choose randomly from a large collection of mathematical objects. For these efforts and others, Oveis Gharan has received the International Mathematical Union’s...
Is AI Reasoning Right for the Wrong Reasons?
...on cue, another “hold my beer” moment: Google DeepMind and the mathematician Terence Tao (the GOAT!) used AI to rediscover or improve the solutions to 67 problems “spanning mathematical analysis,...
How Big Data Carried Graph Theory Into New Dimensions
Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data. Graph theory isn’t enough. The mathematical language for talking about connections, which...
New Number Systems Seek Their Lost Primes
For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering. Mathematicians are digging up the root...
A Puzzle of Clever Connections Nears a Happy End
The three young friends who devised the “happy ending” problem became some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle....