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 ...

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist ...

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 ...

Paul Erdős, the famously eccentric, peripatetic and prolific 20th-century mathematician, was fond of the idea that God has a celestial volume containing the perfect proof of every mathematical theorem ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future. In May, a ...

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 ...

The International Mathematical Olympiad (IMO) is probably the most prestigious competition for preuniversity students. Every year students from around the world compete for its coveted bronze, silver ...