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‘A-Team’ of Math Proves a Critical Link Between Addition and Sets
...in the set and the type of structure that mathematicians should look for, thinking that would allow mathematicians to extract even more information. Marton’s conjecture has links to proof systems,...
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...
What Makes for ‘Good’ Mathematics?
...phenomenon that occurs. So it’s not just that mathematics, that [what] mathematicians find intellectually interesting end up being physically important. But even within mathematics, subjects that mathematicians find elegant also...