This Geek Clock can only be read by rocket scientists

Well, time to turn in my geek card. I can't make heads or tails of this Geek Clock, which has a crazy equation for every hour of the day. Lucky for us (you're with me on this, right?), the product listing says each clock comes with a cheat sheet.
A Geek Clock can be yours for only $25. Bonus points if you decipher any of the glyphs above (working them out, I mean — obviously all the answers are right there).
UncommonGoods, via GeekSugar

-- from DVICE
Cheat Sheet (included with each clock):
1 - Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function. Its value is now known to be exactly 1.
2 - A joke in the math world: An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says, "You're all idiots," and pours two beers.
3 - A unicode character XML "numeric character reference."
4 - Modular arithmetic, also known as clock arithmetic, is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value. The modular multiplicative inverse of 2 (mod 7) is the integer /a/ such that 2*/a/ is congruent to 1 modulo 7.
5 - The Golden Mean...reworked a little.
6 - Three factorial (3*2*1=6)
7 - A repeating decimal that is proven to be exactly equal to 7 with Cauchy's Convergence Test.
8 - Graphical representation of binary code.
9 - An example of a base-4 number, which uses the digits 0, 1, 2 and 3 to represent any real number.
10 - A Binomial Coefficient, also known as the choose function. 5 choose 2 is equal to 5! divided by (2!*(5-2)!)
11 A hexadecimal, or base-16, number.
12 - a radical