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

Microsoft Research announced on October 21, 2026 that Xinzhi Zhang, a senior researcher in its Machine Learning and Optimization group, and collaborator Zhao Song have proved the ...

For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to ...

Version 1.3, 2026-10-15. Text and data CC BY 4.0, code Apache-2.0. Related problem record: Justin Sun Prize JSP-000015, "Kakeya dimension conjecture (general dimension)" (MathDB #315983). The Justin ...

Brian Christian has spent 20 years thinking about how artificial intelligence will change our minds and our world. His 2020 book The Alignment Problem has been praised as one of the best on AI, and ...

Exam-style questions on algebraic fractions for Edexcel IAL Pure 3 (WMA13): algebraic fractions and improper fractions, with full worked solutions. This resource covers the whole of Chapter 1 ...

Read about how mathematicians are dealing with the AI takeover of their field in our feature here. But with the dust still far from settled, a different controversy is emerging: Did OpenAI even solve ...

NYU mathematics professor Tristan Buckmaster announced three proofs on Tuesday with a preliminary finding on one of the major unsolved problems in theoretical mathematics. The findings, made in ...

The company’s announcement is the most dramatic sign yet that artificial intelligence is fundamentally transforming the field of higher mathematics. By Cade Metz OpenAI said on Tuesday that its newest ...

Let’s start here: math’s most famous problem is no closer to being solved than it was a week ago. Neither humans nor artificial intelligence have made progress on the Riemann hypothesis. But AI did ...

Critics of artificial intelligence caution that, as a relatively new technology, its long-term effects on the human brain are still unknown. But a new study shows that AI could be dangerous even in ...

Using AI chatbots for even just 10 minutes may have a shockingly negative impact on people’s ability to think and problem-solve, according to a new study from researchers at Carnegie Mellon, MIT, ...