The next number has to be 32, right? The pattern is clear: To find the next number, double the current one. We have 1 × 2 = 2; 2 × 2 = 4; 4 × 2 = 8; 8 × 2 = 16. The next number should be 16 × 2 = 32.

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 ...

What if engineers could design a better jet with mathematical equations that drastically reduce the need for experimental testing? Or what if weather prediction models could predict details 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 ...

A mathematical problem more than 300 years old gets a formal proof with the help of computer formal verification. A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler ...

One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

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 ...