How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...

Grok 4.5 constructed a counterexample proving hypercontractivity fails on the 4-sphere, closing a decades-old gap in ...

Without any manufacturing here with which to claim tariff remissions — basically a forgiveness of the lien because you’re ...

Many students appear to be completing assignments faster while learning less from them. This conclusion comes from one of the largest studies of how generative AI is changing student behavior and ...

Russia entered the war with vast stockpiles, manpower, and resources—but no military can ignore the numbers forever. This ...

Think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance. For any amount of dots, what is the greatest possible number of pairs that can be ...

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 ...

From Isaacson's biography, the impression I got was that Musk cares enormously about the products his companies are producing. He seems to be intimately involved in a lot of the design and ...

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 ...

This is an edition of the WSJ Technology newsletter, a weekly digest of tech columns, big stories and personal tech advice. If you’re not subscribed, sign up here. So long, #Tokenmaxxing. We hardly ...

Working memory is like a mental chalkboard we use to store temporary information while executing other tasks. Scientists worked with more than 200 elementary students to test their working memory, ...