In the warp-drive literature, a shortage of imagination has never been the most recalcitrant hindrance. It has been one, savage demand: the demand of negative energy “exotic.” Recent theoretical ...

Human language may seem messy and inefficient compared to the ultra-compact strings of ones and zeros used by computers—but our brains actually prefer it that way. New research reveals that while ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the ...

By now, ChatGPT, Claude, and other large language models have accumulated so much human knowledge that they're far from simple answer-generators; they can also express abstract concepts, such as ...

A marriage of formal methods and LLMs seeks to harness the strengths of both.

The method has two main features: it evaluates how AI models reason through problems instead of just checking whether their final answers are correct, and it evaluates the quality of training data so ...

Frustrated by the AI industry’s claims of proving math results without offering transparency, a team of leading academics has ...

For many of us, mathematics was not a subject to love—it was a subject to pass so we could progress to the next academic stage. Through years of conversations with executives, educators, parents, and ...

BATON ROUGE, La. — About two dozen second graders sat on the carpet at the front of Jacquelyn Anthony’s classroom, reviewing how to make tens. “Two needs eight!” the students yelled out together. “Six ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

You’d be surprised how many young people can’t read this. One of its conclusions tells the sad tale. “Between 2020 and 2025, the number of students whose math skills fall below high school level has ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...