The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be ...

It might come as a surprise to some people that this prediction hasn’t already come to pass. Given that mathematics is a subject of logic and precision, it would seem to be perfect territory for a ...

Discrete mathematics gets easier when you know how to approach proofs. Direct reasoning, induction, and contradiction each have specific steps that can be learned and practiced. Pairing these methods ...

DeepMind’s AlphaProof system solved four out of six problems at the 2024 International Mathematical Olympiad, generating formally verified proofs through reinforcement learning trained on millions of ...

New computer tools have the potential to revolutionize the practice of mathematics by providing more-reliable proofs of mathematical results than have ever been possible in the history of humankind.

Mathematician Kevin Buzzard of Imperial College London is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem. Resolving the problem isn’t the point.

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...

MATH 79SI: “Proof Positive: Principles of Mathematics” is a new student-initiated class that introduces students to basic mathematical proof-writing techniques. The one-unit class is designed to serve ...