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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.
New Proofs Probe the Limits of Mathematical Truth
By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.
The Jagged, Monstrous Function That Broke Calculus
In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.
Mathematicians Discover New Way for Spheres to ‘Kiss’
A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.
Rational or Not? This Basic Math Question Took Decades to Answer.
It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.