which is the most commonly studied form of set theory and the most well known set of axioms as well. From these nine axioms, one can derive all of mathematics. These provide the foundation of ...

For nearly a decade, Voevodsky has been advocating the virtues of computer proof assistants and developing univalent foundations in order ... into a form that computers can use to check proofs. So ...

Brain-imaging techniques have made it possible to explore the neural foundations of logical and mathematical cognition. These techniques are revealing more than simply where these high-order ...

How did these layers fit together, and did the order matter ... These results raise questions about the universality of mathematics and the form that math takes in other cultures.

In its most basic form, infinity is defined as a never ... that lie ahead may change the way we view the very foundations of mathematics. In conclusion, the new findings in the study of infinity ...

As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change. As a science of abstract objects, ...

the so-called "father of algebra," established the fundamentals for solving equations that we began to set the foundations for modern mathematics. In this excerpt from her new book "Vector ...