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2023’s Biggest Breakthroughs in Math
In 2023, mathematicians improved bounds on Ramsey numbers, a central measure of order in graphs; found a new aperiodic monotile; and discovered a new upper bound to the size of...
The Math Hiding in Plain Sight
Sarah Hart, the professor of geometry at Gresham College, sees symmetry everywhere. Video: Christopher Webb Young and Emily Buder/Quanta Magazine; Photo: Philipp Ammon for Quanta Magazine...
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...
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...
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. Christopher Webb Young/Quanta Magazine; Kelsey Houston-Edwards for Quanta Magazine...
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...