It's been suggested a couple of times, so here goes, a new home for your favourite formula, lemma, theorem or statistician.

If you're really well behaved, I may even pose a "problem of the week".  But only if you have behave well.

A couple of my faves then:

Euler's identity

A mathematical classic.  But a genuine WTAF when you first learn it.  It's still hard to imagine how three numbers, one of which is imaginary, can cancel each other out so elegantly.  Arguably the photo doesn't do it justice.



There's loads of other crazy stuff with exponents and sequences.  And fourier shizzle.  But not for today, as you haven't been good enough.

Next up, Liouville's theorem:

Any bounded, entire (differentiable-everywhere) function must be constant.  (This refers to 'complex' numbers, i.e. C->C.)

i.e. there's nothing like a sin wave, which is bounded, differentiable everywhere, but not constant, if you treat it over the whole complex plane.  (The sin function goes a bit ape if you start doing it on imaginary numbers, so isn't bounded.)

That's another one that, to be, just defies expectation.

What else then?

Last for today, the Central Limit Theorem:

If you take _any_ probability distribution, and sample from it enough times, you end up with the normal distribution.  

Madness.

Anyway, hope you're having fun.  Do add your own faves, or ask questions, or tell me to get a life.