Liouville proved the following property of the divisors of the divisors of a number: 1) Start with a number (e.g. 10) 2) Write down its divisors (1,2,5,10) 3) Write down the number of divisors of each divisor (1,2,2,4) 4) (1+2+2+4)²=81=1³+2³+2³+4³

438,579,088 and 3,435 are the only 2 numbers with this property

Here's a challenge: can you find a prime of the form pᵖ+2 where p is prime, apart from 29?

This is how the penguin diagram name in quantum field theory was born: particle physicist John Ellis lost a bet playing darts at a bar and had to put the word penguin into his next paper.

This is the only known solution to n! = a!b! apart from the general pattern, (n!)! = n!(n! - 1)!

Plato, tutored by Theodorus, questioned why Theodorus stopped at √17. The reason is commonly believed to be that the √17 hypotenuse belongs to the last triangle that does not overlap the figure.

π to the power of π

Here's a 1,400 years old approximation to the sine function (0 ≤ x ≤ π) by Mahabhaskariya of Bhaskara I