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 ...

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs ...

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 ...

A simple question about a spinning needle has haunted mathematicians for more than a century. It led to the Kakeya conjecture ...

Professor of Mathematics Jeremy Kahn won the 2012 Clay Research Award — one of the most prestigious awards in mathematics — for his work on hyperbolic geometry. Kahn and his collaborator Vladimir ...

"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This ...

In their peer-reviewed work, Calcea Johnson and Ne'Kiya Jackson present five new ways of proving Pythagoras' Theorem via trigonometry. They also detail a new method for finding proofs that yield at ...

Students who make relevant arm movements while learning can improve their knowledge and retention of math, research has shown. Now researchers at Southern Methodist University, Dallas, and the ...

For over two millennia, mathematicians agreed on one thing: you can’t use trigonometry to prove Pythagoras’ Theorem—because ...