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After 80 Years, Mathematicians Give Famed ‘Erdős Method’ an Upgrade
Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.
What Is the Positive Grassmannian and Why Does It Show Up Everywhere?
Lauren Williams tells 'The Joy of Why' how studying a fundamental object in algebraic combinatorics led to a career full of surprises.
Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.
How Terry Tao Became an Evangelist for AI in Math
With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research.
Two Researchers Are Rebuilding Mathematics From the Ground Up
By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.
How Alexander Grothendieck Revolutionized 20th-Century Mathematics
Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?
What Do Gödel’s Incompleteness Theorems Truly Mean?
At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications.
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.
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.