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New Proof Settles Decades-Old Bet About Connected Networks
According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong.
Where Does Meaning Live in a Sentence? Math Might Tell Us.
The mathematician Tai-Danae Bradley is using category theory to try to understand both human and AI-generated language.
A New Proof Smooths Out the Math of Melting
A powerful mathematical technique is used to model melting ice and other phenomena. But it has long been imperiled by certain “nightmare scenarios.” A new proof has removed that obstacle.
Three Hundred Years Later, a Tool from Isaac Newton Gets an Update
A simple, widely used mathematical technique can finally be applied to boundlessly complex problems.
‘Once in a Century’ Proof Settles Math’s Kakeya Conjecture
The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems.
Years After the Early Death of a Math Genius, Her Ideas Gain New Life
A new proof extends the work of the late Maryam Mirzakhani, cementing her legacy as a pioneer of alien mathematical realms.
After 20 Years, Math Couple Solves Major Group Theory Problem
Britta Späth has dedicated her career to proving a single, central conjecture. She’s finally succeeded, alongside her partner, Marc Cabanes.
The Largest Sofa You Can Move Around a Corner
A new proof reveals the answer to the decades-old “moving sofa” problem. It highlights how even the simplest optimization problems can have counterintuitive answers.
How Noether’s Theorem Revolutionized Physics
Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics.