/sci/ - Science & Math

I recall a fair number of Australians managing nLab, so it's not completely out of the question that Australia upends ZFC and replaces it with some kind of categorical or type-theoretic foundation (we already know how to translate between the various formulations anyway, so the choice of which one to use is simply a matter of convention).

I've probably drunk too much of the computational trinitarianism kool-aid, but I can legitimately envision a near-future where mathematics and programming are completely integrated under the umbrella of formalism (if only on the "back-end"), and if the integrated system is type-safe, then it would alleviate a lot of security concerns.

>>8982331
>I thought mathematicians liked beauty and all that.
"Two unique divisors" is ugly though.
If you want to see a beautiful definition, try this:

>A prime number is a positive integer p such that for any factorization of p into a product of finitely many positive integers [math]p = \prod_{i=1}^k n_i[/math] there is an i such that [math]p = n_i[/math].

This covers the case p=1 naturally, because there is a factorization of p that doesn't contain p itself as one of the factors: namely, the empty product (k=0).

As a bonus this definition of primality generalizes to any other type of mathematical structure for which a product is meaningful (which is just about everything).

>Proofs:
[eqn]I:= [z\mapsto z]:Z\to Z[/eqn]
[eqn]B:=[x\mapsto y\mapsto z\mapsto x(y(z))]:(Y\to X)\to(Z\to Y)\to Z\to X[/eqn]
[eqn]C:=[x\mapsto y\mapsto z\mapsto x(z)(y)]:(Z\to Y\to X)\to Y\to Z\to X[/eqn]
[eqn]W:=[y\mapsto z\mapsto y(z)(z)]:(Z\to Z\to Y)\to Z\to Y[/eqn]
[eqn]K:=[z\mapsto y\mapsto z]:Z\to Y\to Z[/eqn]

Until the cat is observed in its final resting state, it exists in a superposition of both the up state and down states at the same time.
The relative probabilities govern the cat's "spin statistics", which manifests itself as uncertainty in the observation of its angular frequency.

We should define the kilogram in terms of the gravitational constant, just like we used the speed of light to define the metre.

>>8422980
>be statsfag
>publish model in econ and finance journals
>model assumes errors follow a normal distribution
>they actually use it, the absolute madmen
>financial crisis happening
>recession happening
>all those jobs lost
>all those taxpayer monies
>mfw