Abstract: The paper is about formalization of Set Theory and Elementary Algebra theorems in mathematics and their proofs in a new programming language called LEAN 4 Theorem Prover. The paper describes ...

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 ...

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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, ...

Cool Math Games offers access to a wide range of free math challenges that help students sharpen their mathematical skills. These include free thinking, strategy, and logic games. Cool Math games are ...

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, ...

We publish deeply researched (and often vastly underread) academic papers about our collective omnipresent media bias. We publish deeply researched (and often vastly underread) academic papers about ...

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 ...

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 ...

Earlier this month, 36 sharp-witted high school students from around the globe stepped foot on the warm and breezy campus of Stanford University. Out of more than 4,000 students from more than 2,000 ...

Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets, ...