[foobar_]

No one uses mathematical notation for practical purposes. This is just like the medival music notation which is neither practical nor what modern composers use, which is more visual in nature. Infact modernism is a rejection of medievalism.

I think in the future programming will force all mathematicians to code or give out simulations. Most mathematical notation was intended to be throwaway by the original authors, thats why there are so many notations. Trying to find relevance in them is a pointless exercise. Much like 80x20, tabs vs spaces ... most of the original intent is lost and what survives is guff meant for ceremonious purposes.

[wheresmycraisin]

Programming != proofs, or in general communicating abstract mathematical ideas. Writing mathematics is nothing like writing software.

[yw3410]

I don't think this is true (or at least not true for all programs); there's a whole discipline of software which shows how close writing software is to formal logic/inductive proofs in Agda Coq, etc.

[foobar_]

What I am trying to convey is writing software is better than writing maths, just like medieval music notation vs modern notation. Programming is better than proving because most proofs are mere tautologies or artificial constraints. This is why theorem provers in code rely on term rewriting.

A triangle has a sum of 180 ? Well how about if you push the triangle inside out. In code you can easily run a more complex simulation which gives you all possible values of the sum ... which is why ascertaining useful facts like 180 ad-nausea is boring at best. In fact most mathematics if it can't be simulated can't exist.

[parralelex]

If you ever found yourself lost in Plato's cave, you'd be super confused as to what those black splotches on the cave wall are.