Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians. What does that mean for their future? Credit...Illustrations by Yoshi ...
In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...
“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...
The central technical result is a quantum error-correcting code built on the Face-Centered Cubic (FCC) lattice — the densest possible packing of spheres in three dimensions, the arrangement at the ...
A new Physical Review Letters study places constraints on the ER = EPR conjecture, showing that under the authors' assumptions, the conjecture would imply possible alterations to the hyperfine ...
OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...
You have likely seen oranges or tangerines stacked beautifully at a supermarket. Stacking them in a staggered pattern to minimize gaps—that method is, in fact, the "densest possible way to pack them." ...
Three mathematicians just proved a famous 30-year-old conjecture in geometry, with only a tiny assist from AI. The conjecture says that even within enormous, scattered and chaotic assemblages of ...
Sphere packing and crystallization involve the study of how identical particles arrange themselves in space under pairwise interactions, with sphere packing focusing on the densest arrangement of ...
The Sphere, the Las Vegas-based orb that Madison Square Garden boss James Dolan spent $2.3 billion to build, is now the world’s highest-grossing entertainment venue — defying initial doomsday ...
As the chords in “Sigma Oasis” reverberated last Saturday night, it felt to 17,600 Phish fans like they were inside an egg. The shell cracked, and they were birds hatching and taking flight. They were ...
It was during “Run Like an Antelope” when the giant guy in the Godsmack shirt behind me finally lost his shit. Those of us sitting near him at Night Three of Phish’s nine-show, three-weekend run at ...
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