A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach. 1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer ...

Latin squares are arrangements of symbols in a grid in which every symbol appears exactly once in each row and column. These ...

AI can rifle through enormous libraries of information to connect far-flung ideas—conceptual leaps remain a purely human skill. The planar unit distance problem, or Erdős problem 90, has intrigued ...

Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to ...

OpenAI’s latest research paper diagnoses exactly why ChatGPT and other large language models can make things up – known in the world of artificial intelligence as “hallucination”. It also reveals why ...

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now. Here’s a simple-sounding problem: Imagine a circular fence that encloses one ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...