Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

Our attempts to establish scientific proof can harden into dogma. The target of “statistical significance” leads some to massage data.

In 2019, mathematicians finally solved one of the hardest math problems—one that had stumped them for decades. It’s called a Diophantine Equation, and it’s sometimes known as the “summing ...

Numbers game: Is math the language of nature or just a human construct? Scientists still debate whether our mathematical models of the universe objectively exist ...

Axiom uses zero-knowledge proofs, a type of cryptographic proof that can prove the validity of a statement with only selectively revealing any information about the statement itself, and one of ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture ...

However, things get wonky when comparing these new infinities with a foundational concept of mathematics known as the Axiom of Choice, which says that you can make a new set of numbers by picking ...

For that reason, some experts specifically indicate when they use the axiom of choice in a proof—and there are mathematicians who have wanted to overhaul the subject without this axiom.

NEW ORLEANS — A high school math contest has turned into a history-making event thanks to a pair of young girls. These two teenage math stars have developed five new proofs of the Pythagorean ...

But a proof assistant also has drawbacks: It often complains that it does not understand the definitions, axioms or reasoning steps entered by the mathematician, and for this it has been called a ...

Axiom uses zero-knowledge proofs, a type of cryptographic proof that can prove the validity of a statement with only selectively revealing any information about the statement itself, and one of this ...