A 150-year-old geometry rule has been overturned after mathematicians found two different torus surfaces with identical ...

Logic studies how arguments work, and how ideas can fit together. Decision theory studies how decisions should be made, especially under uncertainty. Game theory considers how we reason strategically, ...

Researchers at Stanford and Caltech have found some critical reasoning failures in advanced AI models. LLMs are great at recognizing patterns, but they have trouble with basic logic, social reasoning, ...

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 ...

You’ve locked in on your weight loss goals, consistently cut back on calories, and made time for daily workouts. Yet after initially losing a couple of pounds, you just can’t get that number on the ...

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 ...

Get set theory explained in a clear and complete way, covering everything you need to know from basic definitions to key operations and ideas. This video walks through sets, subsets, unions, ...

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

Teacher education often receives criticism for being too theoretical. Many students lack more training in how to teach in practice when they enter schools. They now receive this at the University of ...

The idea that we might be living inside a vast computer simulation, much like in The Matrix, has fascinated philosophers and scientists for years. But a new study from researchers at the University of ...