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Decoding Math’s Most Famous Fractal
Mathematicians working in the field of complex dynamical systems are patiently unraveling the Mandelbrot set’s mysteries and may be on the verge of solving a fundamental conjecture that would allow them to describe the set completely.
The New Math of How Large-Scale Order Emerges
...to what the component parts are doing. Using a mathematical formalism called computational mechanics, the researchers identified criteria for determining which systems have this kind of hierarchical structure. They tested...
Math’s ‘Bunkbed Conjecture’ Has Been Debunked
...a mathematician astray. Early evidence might not represent the bigger picture; a statement might seem obvious, only for some hidden subtlety to reveal itself. Unexpectedly, three mathematicians have now shown...
How Public Key Cryptography Really Works, Using Only Simple Math
...invisible ink: One encrypts messages, the other decrypts them. But instead of using chemicals, public key cryptography uses mathematical puzzles called trapdoor functions. These functions are easy to compute in...
2024 Biggest Breakthroughs in Math
We investigate three of 2024’s biggest breakthroughs in mathematics, including a better way to pack spheres in high dimensions, a new way to avoid forming patterns of numbers, and an 800-page proof of the so-called geometric Langlands conjecture.
One Step Closer to a ‘Grand Unified Theory of Math’: Geometric Langlands
After 30 years of effort, mathematicians finally proved a major component of the ambitious Langlands program.
A New Proof Smooths Out the Math of Melting
...to mean curvature flow. Should a singularity appear, the flow can go on — making it possible for mathematicians to assess the surface’s evolution. Over the past few decades, mathematicians...
New Math Revives Geometry’s Oldest Problems
...to understand,” said Sheldon Katz, a mathematician at the University of Illinois, Urbana-Champaign. As mathematics advanced, the objects that mathematicians wanted to count got more complicated. It became a field...
Long-Sought Proof Tames Some of Math’s Unruliest Equations
...held for this kind of PDE. Unfortunately, “the real world is nonuniformly elliptic,” said Giuseppe Mingione, a mathematician at the University of Parma in Italy. That meant mathematicians were stuck....