For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the ...

On May 20, OpenAI said an internal reasoning model had produced a counterexample to Paul Erdős’s 1946 unit distance ...

OpenAI has revealed a breakthrough proof that overturns a nearly 80-year-old geometry conjecture posed by Paul Erdős.

Then it’s kind of a mystery to try to figure out why and how they’re related.” The Riemann hypothesis has proved to be a font ...

A ripple tells you something happened, but not exactly what. That is the core problem behind a hard class of equations that scientists use when they try to work backward from what they can measure to ...

We spend a lot of time thinking about the difficult people in our lives—the friend who can't take feedback, the partner who always has to be right, the coworker who turns everything into a fight. But ...

Abstract: Recently, transformers have garnered significant attention due to their exceptional capability to capture long-range dependencies in data. A critical factor contributing to their superior ...

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-0.63%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 ...

You probably don’t need more time. By Jancee Dunn When I look back on all the major decisions I’ve dithered over, I could scream. It took me a decade to commit to becoming a parent. I wavered for a ...