Andrew Ludwig's January 20 Another Voice on polarized opinions relies on ideas from mathematical logic, but a few logical steps are mixed up.

Take the pressure off of problem solving with engaging thinking games that encourage students to work together to find solutions. Like many teachers, I used to think of problem-solving as something I ...

When I was in grad school at St. Bonaventure studying to become a school district leader, one of my professors told the class that math teachers make the best school administrators because of their ...

Bo Nix and the Broncos have won 11 in a row. Justin Edmonds / Getty Images DENVER — After yet another raucous party inside the Broncos locker room early Sunday evening had subsided, a bass-thumping ...

ABSTRACT: The simulation of the Heteroclinic Loop and Homoclinic Loop in a controlled Chen system is finished. The controlled Chen system is Z 2 symmetric, and the limit cycle loop or the attractor is ...

Hallucination is fundamental to how transformer-based language models work. In fact, it’s their greatest asset: this is the method by which language models find links between sometimes disparate ...

When engineers build AI language models like GPT-5 from training data, at least two major processing features emerge: memorization (reciting exact text they’ve seen before, like famous quotes or ...

Mathematical proof debunks the idea that the universe is a computer simulation by Patty Wellborn, University of British Columbia edited by Gaby Clark, reviewed by Robert Egan Editors' notes The GIST ...

ABSTRACT: This paper revisits the nature of school mathematics by examining its philosophical foundations and the implications of these views for contemporary pedagogy. The paper examines how ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...

Artificial intelligence is advancing across a wide range of fields, with one of the most important developments being its growing capacity for reasoning. This capability could help AI becomes a ...