Constructive mathematics reconsiders traditional foundational approaches by emphasising explicit constructions and algorithmic content rather than relying solely on non-constructive existence proofs.

Most of us first hear about the irrational number π (pi)—rounded off as 3.14, with an infinite number of decimal digits—in school, where we learn about its use in the context of a circle. More ...

Researchers found mathematical structure that was thought not to exist. The best possible q-analogs of codes may be useful in more efficient data transmission. Researchers found mathematical structure ...

It's a truly remarkable fact that our deepest understanding of the material world is embodied in mathematics, often in concepts that were originated with some very different motivation. A good example ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

A newly-developed mathematical method can detect geometric structure in neural activity in the brain. The method is a first step toward developing a new mathematical toolkit to uncover the structure ...