Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major ...

J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

https://doi.org/10.4169/amer.math.monthly.122.03.233 https://www.jstor.org/stable/10.4169/amer.math.monthly.122.03.233 The Monthly publishes articles, as well as ...

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 ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

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 ...

The same branch of mathematics that helped Einstein to formulate his theory of general relativity could now allow scientists to peer with unprecedented accuracy into impenetrable objects—such as the ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...