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Mathematics
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Two Twisty Shapes Resolve a Centuries-Old Topology Puzzle
The Bonnet problem asks when just a bit of information is enough to uniquely identify a whole surface.
Using AI, Mathematicians Find Hidden Glitches in Fluid Equations
A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.
The Year in Mathematics
Explore a shape that can’t pass through itself, a teenage prodigy, and two new kinds of infinity.
String Theory Inspires a Brilliant, Baffling New Math Proof
Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.
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.
‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard
Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.
A New Bridge Links the Strange Math of Infinity to Computer Science
Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.
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.
What Is a Manifold?
In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.