A harmonic increment provides a new way to improve smooth approximations of the minimum function. In a recent paper, ...

When identical charges repel each other but are confined to the surface of a sphere, they seek the arrangement with the lowest possible energy. The idea is simple, but the problem gets harder to solve ...

Since you last thought about math, the people who think about math every day have been freaking out. A month ago, when OpenAI announced that one of its powerful internal models had cracked a ...

OpenAI has posted hundreds of solutions and progress toward 372 major math problems in a release of 722 manuscripts on GitHub, the company announced. The breakthroughs from an unreleased ChatGPT ...

After a previous solution angered mathematicians, the company characterized the new release as being more responsive to concerns about A.I. disrupting research. By Kenneth Chang and Siobhan Roberts ...

The mathematics community is still in shock. On September 8, 2026, OpenAI announced that an artificial intelligence model may have solved one of the most significant problems in the field, the ...

OpenAI on Tuesday said its artificial intelligence technology has cracked one of the Millennium Problems –– seven famously difficult and unsolved questions in mathematics that have stumped even the ...

Projects translating research into public good — spanning fields from medicine and climate to civics and arts — win $4 million from new Harvard fund Curbing the spread of malaria, catching breast ...

“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...

A high-tech executive I coached, Anna*, was told she had a “blind spot” just a year into her role. Her CEO admired her decisiveness, respected her clarity, and valued her confidence. At the same time, ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

Scientists who employ various research methods in psychology and make breakthroughs that enhance our knowledge about psychology can have a significant impact on our lives. From influencing the ...