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 ...

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 ...

Math students may not blink at calculating probabilities, measuring the area beneath curves or evaluating matrices, yet they often find themselves at sea when first confronted with writing proofs. But ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

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 ...

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 ...

Kevin Buzzard's video lecture, "The Future of Mathematics?" begins with a story about both him and his romantic partner finding boxes from their youth. For Buzzard, the box was a prize for mathematics ...

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 ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I examine an insightful AI research study ...