1. It's impossible to comb all the hairs on a tennis ball in the same direction without creating a cowlick. [This is called the hairy ball theorem]. *- Notsoace*

2. There is an entire book explaining how 1+1=2 works and makes sense.*- MrPandaCzar*

3. The guy that proved the existence of irrational numbers was murdered for his finding.*- rngisforfailures*

4. There's exactly 10! seconds in 6 weeks.

n! (pronounced n factorial) means n*(n-1)*(n-2)*(n-3)*....*2*1. So 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800.*- Krissam*

5. The decimal fractions of seven are the same six recurring digits, in the same order, but starting from a different one each time.

1/7 = 0.142857142857...

2/7 = 0.285714285714...

3/7 = 0.428571428571...

4/7 = 0.571428571428...

5/7 = 0.714285714285...

6/7 = 0.857142857142...*- king_olaf_the_hairy*

6. The Fibonacci sequence is encoded in the number 1/89:

1/89 = 0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + 0.0000000034...*- Euerfeldi*

7.

x% of y = y% of x

y(x/100) = x(y/100)

yx/100 = xy/100

So, in order to calculate a percentage in your head it might be easier to turn it around.

Example

What is 2% of 50? It's the same thing as 50% of 2.*- Lindby*

8. The creators of Futurama actually had to create a new mathematical formula to solve the brain swapping issue they had. It's called The Futurama Theorem*- Randomdude2846*

9. If you put 23 people in a room, there's over 50% chance that at least two of them have the same birthday.*- usthcd*

10. The BanachTarski paradox: Given a solid ball, there exists a decomposition of the ball into a finite number of disjoint subsets, which can be put back together in a different way to yield two identical copies of the original ball.*-luckypech*

11. There are different kinds of infinity, and some are larger than others.*- mightbethrownaway*

12.

22/7 is closer to the actual value of pi than 3.14 is.*- JamesIgnatius27 *

13.

it relates some of the most important mathematical constants into one equation.

edit: Since there seems to be a lot of confusion or wonder as to why this is so neat, read the explanation of its mathematical beauty.*- OZONE_TempuS *

14. How big is the number of possible permutations when shuffling a 52 cards deck. Specifically the example to give us the faintest perception of how ridiculously big 52 Factorial is.

EDIT: u/LotharWilhelm reported that this video gives us a visualization of what Scott Czepiel wrote in the original link I gave. It starts at 14:00 though.

EDIT II: In this video posted by another redditor the guy uses a different example:

"If every star in our galaxy had a trillion planets, each with a trillion people and each of these people had a trillion pack of cards, and somehow they managed to shuffle all a thousand times at second, and they have been doing this since the Big Bang, they would only just now being starting to repeat shuffles."*- Munninnu*

15. Tetration is the iteration that follows exponentiation.

^{n} a = a^{aaa...} with an n number of a's.

Also, it is referred to as "a to the *superpower* of n"*- PlasmicDynamite*

with your friends!