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 ...

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

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 ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

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 ...

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 ...

All equals are not created equal—mathematicians sometimes play fast and loose. In programming, equal signs mean different things, and variables have different types. Turning intuitive math expertise ...

When it comes to understanding the shape of bubble clusters, mathematicians have been playing catch-up to our physical intuitions for millennia. Soap bubble clusters in nature often seem to ...