In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

Einstein's 1917 paper, "Cosmological Considerations in the General Theory of Relativity," applied general relativity to the universe as a whole, establishing a firmer basis for cosmology. To create a ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and a ...

Most famous equation: Einstein's E = mc2, which means energy is equal to mass times the speed of light squared. Known digits of pi: More than 105 trillion digits Digits of pi NASA uses for equations: ...