Hallucinations of language models are not an engineering problem: they stem from mathematical limits proven since the 1930s.

One idle evening last October, Mehtaab Sawhney took up an old pastime. He began perusing the website erdosproblems.com, an updated record of the 1,179 conjectures left behind by the eccentric and ...

Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance ...

In October 2024, news broke that Facebook parent company Meta had cracked an "impossible" problem that had stymied mathematicians for a century. In this case, the solvers weren't human. An artificial ...

Abstract: The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems. This ...

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Consider someone who’s perfectly content with their office chair. It’s not ergonomic, it doesn’t have lumbar support, but it works. Then, during a meeting or a visit to a friend’s office, they sit in ...

Entrepreneurs who build successful businesses often possess a unique ability to see what others don't—the critical bottlenecks hiding in plain sight that create frustration, inefficiency, and lost ...

Word problems try and tell students a story about the math problem in front of them. They are a useful way to connect abstract numbers to concrete situations, so students can learn early on to apply ...

The Post Correspondence Problem (PCP) is an undecidable problem. It asks whether a set of domino-like pairs of strings can be arranged in a sequence so that the top and bottom strings match. There's ...