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 ...

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 ...

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In the ...

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 ...

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 ...

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 ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...

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 ...

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 ...