Abstract: In real life, there will be a lot of uncertainty problems, one of which is due to the vagueness of the concept of things, that is, it is difficult to determine whether an object conforms to ...

‘Artificial Intelligence’ became an everyday phrase in 2025, with generative AI tools spreading rapidly across offices, classrooms and consumer products. That pace of adoption has been matched by ...

Large reasoning models often show counterintuitive behavior, putting more computational effort into simple tasks than difficult ones while producing worse results overall. Researchers have established ...

The ball rolls across the floor because it was kicked, just as Earth orbits the sun because it is tugged by gravity. The connection between cause and effect is fundamental to how we understand the ...

Get your news from a source that’s not owned and controlled by oligarchs. Sign up for the free Mother Jones Daily. Last week, the New York Times reported a rare bright spot in public health: The ...

Diophantus, who likely inherited foundational ideas from Thymaridas of Paros, laid fundamental work for algebra by exploring solutions to linear equations that later influenced modern mathematics.

According to @o3_labs, O3 AI is introducing advanced artificial intelligence algorithms to accelerate computations and pattern recognition in number theory, enabling researchers to solve complex ...

Ananyo Bhattacharya is chief science writer at the London Institute for Mathematical Sciences and the author of The Man from the Future: The Visionary Ideas of John von Neumann. One of the biggest ...

Comparison of Gauss's and Legendre's formula in approximating the prime counting function along with results analysis. Unified constructive and non-constructive proofs of three number theory problems: ...

I have had a fascinating few months. “Abundance,” the book I wrote with Derek Thompson, is either going to save the Democratic Party or destroy it. You think I’m kidding. Here’s The Wall Street ...

This is the twenty-third in a series of annual workshops sponsored by the New York Number Theory Seminar at the CUNY Graduate Center on problems in combinatorial and additive number theory and related ...