[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.

[wheresmycraisin]

Ok, then convince me. Write 'software' of, say, the proof of the the dominated convergence theorem or something else reasonably advanced and let's compare it to the proof in conventional math notation.

[foobar_]

I'm guessing there was a physical intuition behind the theorem, if you can simulate it you will probably do something better than the proof. Now it's your turn to tell me why 1 + 1 = 2.

[augustt]

Honestly what are you talking about. You can simulate for 100 years without finding a counterexample, but that doesn't make a proof. The whole point of math is to understand why things are true, not to just be satisfied that it seems true.

[foobar_]

The way I see it ... Most mathematicians nowadays use mathematica or matlab or even python, proving my point. The notation is medieval ... and probably the only reason it survives is because of form factors of paper.

> Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

I see simulating as a part of the experiment. If the proof is wrong it wouldn't last a seconds worth of simulation. I suppose a proof in essence is a pattern or an invariant of the system ... but most proofs have really no meat to them. The notation is merely intimidating like obfuscated code.

[jjgreen]

See Principia Mathematica, A. N. Whitehead and B. Russell, Proposition 110.643

[foobar_]

1 + 1 = 10

[gspr]

> Now it's your turn to tell me why 1 + 1 = 2.

By construction.

[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.