By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far ...

Mathematical logic and set theory provide the foundational language for modern mathematics, articulating precise notions of proof, computability and the hierarchy of infinities. Central themes include ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? Here’s what you’ll learn when you read this story: Because our eyes perceive color ...

David E. Dunning explores how mathematical notation is a social, world-building technology. It’s natural to think of math as being fundamentally abstract. Whether it’s invented or discovered, its ...

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, ...

In addition to ascertaining that the internal vitality of the mathematical sciences is excellent, as illustrated in Chapter 2, the current study found a striking expansion in the impact of the ...

Abstract: This article presents a geometric reachable-set-theory-based solution for spacecraft orbital rendezvous under constant-magnitude continuous thrust, addressing two problems: minimum-time ...

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 ...