Do You Know ?

that there are 6 unsolved mathematics problems whose solutions will earn you one million US dollars each?

that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?

that every natural number can be written as the sum of four squares?

that the largest known prime number is over 12 million digits long?

that the set of rational numbers is equal in size to the subset of integers; that is, they can be put in one-to-one correspondence?

that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.

that it is unknown whether π and e are algebraically independent?

that a nonconvex polygon with three convex vertices is called a pseudotriangle?

that it is possible for a three dimensional figure to have a finite volume but infinite surface area? An example of this is Gabriel's Horn.