a couple of math 'funs'

Fun #1: Back in the day I was a professional statistician. Every once in a while it became necessary for me to numerically (via computer) evaluate integrals. I picked up a book to help, Asymptotic Expansions of Integrals:

"The prerequisites for such a course are minimal. Indeed, we feel that any student having a good background in advanced calculus, differential equations, and complex variables can adquately handle the contents."

Some folks' concept of 'minimal' does not quite coincide with my own!

Fun #2: 16.

16 = 2^(2^2) = (2^2)^2,
with '^' representing exponentiation (e.g., 2^3 = 2*2*2 = 8; 3^2 = 3*3 = 9).
'2' is the ONLY integer satisfying this associative property of exponentiation!
[3^(3^3) does NOT equal (3^3)^3]

I've got a proof if anyone's interested.

Fun #2 was realized when host of "Opera and Broadway Open Mic Night" suggested 1607 was the year that opera was first performed.
1607 is a good year: 1607 is prime. 7 is prime. 16 satisfies the remarkable exponentiation identity stated above.
Number Theory really is fun!