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 ...

Combinatorial optimisation for permutation problems addresses the challenge of arranging discrete elements in an order that minimises or maximises a given objective function. Such problems include the ...

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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 ...

What are the most pressing global crises in 2026? Each year, the International Rescue Committee’s (IRC) Emergency Watchlist identifies the countries at greatest risk of new or worsening humanitarian ...

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 ...

Microsoft’s MSFT-0.12%decrease; red down pointing triangle Copilot chatbot has become central to its artificial-intelligence strategy as the company’s close partnership with OpenAI diminishes. But the ...

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 ...

We look into the mental health crisis affecting American youth. By Sam Sifton I am the host of The Morning. The numbers are staggering. Nearly one in four 17-year-old boys in the United States has ...