>>10957396It says that the p(x|y), probability for x being observed given y having been observed, is proportional to two things:
* x being observed generally
* the likelihood p(y|x) of your observation observation y in the first place having come from x
Wikipedia gives the following task in pic related, which is a good example (it also states the answer).
If you look at a system that is described by a joint distribution f(x,y) (where f(u, v)/f(a, b) say how much more often u,v is seen together than a, b), then you can normalize (with sum or integral) that f to 1, thus obtain a joint probability and in that case, Bayes rule is actually a provable theorem.
That is, if the the correlations can be statistically sampled before you start using the theorem (e.g. by doing statistically evaluating how often OP is fag, getting hard numbers), then Bayes theorem is, in fancy terms, a straight forward functional analysis result stemming from normalization (sum/integral) being linear.
Whether think Bayes rule about conditional probability is relevant to events without possible statistical data and where you have to pull priors out of your ass ("Will the Queen die next March?") is up to your interpretation of chance.
>>10957732sl(2,C), su(3)
>>10958159It will not happen overall, but you can do it if you're influential and opinionated.
>>10958197That's good willed, but it leaves out the detail that much of research mathematics is not based on axioms - it's dabbling around with should-be relations and the axiomatic is often done in the upcoming decade, where the strong theorems and low hanging famous fruits have already been plugged on relatively speaking informal grounds.
Moreover, logicians and type theorists tend to complain that university mathematics is often leaving out details, even for decades, and in their head do things like identifying x and {x} and isomorphisms like that. There's no limit to formality - until you're a computer.
