the riemann zeta function is universal, which means that somewhere in it (in the complex plane) it contains any other function*
*approximate arbitrary non-vanishing holomorphic functions arbitrarily well.
for funzies, you can use this to come up with a data compression* algorithm:
*compressed data will be larger than original
translational invariance --> conservation of linear momentum
rotational invariance --> conservation of angular momentum
time invariance --> conservation of energy
* physics is the same in all (non-accelerating) reference frames
* the speed of light is the same in all reference frames
einstein sat down and derived the rest of SR just from that
that means integrals over entire regions are related to just their values on a boundary
this is a simple version of Stoke's Theorem
Then later some dude (cohen) came along and proved its independent of the axioms of ZFC
Einstein later took a position at princeton just to work w godel. At godels citizenship hearing he tried to bring up that he found a logical inconsistency in the constitution. AE stopped him
Reasoning with set theory breaks your brain. Set theory: not even once
Fuck england, and fuck homophobia.
many have gone mad looking for it
these problems can be reformulated w/o complex numbers FWIW, but its often very ugly
mathematicians have now retreated to more abstract topics with no military applications (yet)
the axiom of choice: For any set X of nonempty sets, there exists a choice function f defined on X.
a number of theorems in mathematics and physics assume the Riemann hypothesis is true, as it SEEMS to be, and then you can prove some cool stuff assuming it is.
it is not possible in the real world bc the universe is discrete (c.f. QM)
hey, everyone's wrong sometimes.
float-precision errors anyone?
we only recently proved the higgs boson exists, and we had to built the most powerful particle accelerator ever to do that
maybe we'll figure it out someday