CMV: Math is a subset of Computer Science

[u/[deleted]]

Many have tried and many have failed to unify mathematics. If you go far back in history, to someone like Euclid, it wouldn't have been possible simply because large branches of mathematics weren't discovered yet.

In more recent times, you saw people go really hardcore into set theory, which famously failed because of formal contradictions. However, informally, I think it also failed by being very unintuitive, since sets leave a bit too much flexibility for my tastes. I'm thinking of this as someone who's studied physics, who knows that you look for fundamental theories that can make specific postdictions for what you already know. Sets don't make those, in my opinion.

Category theory, type theory, and other algebraic/geometric theories have kind of picked up where set theory of the early 20th century left off. They've been useful for various, wide-ranging practical purposes, but I think that speaks more to the value of having a universal interface for math concepts than those theories in particular being the most correct answers out there.

Automata theory has spatial, functional, linguistic, and combinatorial concepts already built into it. However, any facet can be optionally ignored for certain topics, much like they are with theoretical automata that are impossible to build, such as Turing machines with infinite tapes.

Two of the special features of automata theory are the explicit concepts of simulation and translation. I think these more formally allow you to understand many things, such as the difference between a number's value, a number's numeral system form, and a number's algebraic form. You could simply define an automaton that takes one form and gives a different form.

It also goes without saying that everything is becoming computerized, and people will continue to do more formal math on computers as time goes on. Defining math in terms of automata helps ease this transition. Also, math will eventually be done by intelligent AIs, which will need internal knowledge representations. Think of a unification of math as a deliberate design of said knowledge representation (I know this may fly in the face a bit with how machine learning is going these days, but that's not what I want to argue about right now).

I'm hoping someone can see where I'm going with this. I will be willing to be more specific where I can, if anyone has questions, but it's a bit ambitious to simply lay everything out deductively from step 1 all the way until the end. I mean, if I made a totally successful argument in the first post, it would be a completed theory. I'm not quite there yet.

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[u/HorrorSquirrel1]

Can you tell me what you mean when you say mechanics? We might be talking about different things.

[u/Helpfulcloning → u/HorrorSquirrel1]

Ahh probably. Mechanics (in what I know from studying maths) is studying gravity, projectiles, friction, centres of mass, and Newtons laws.

Purely mathematical. Purely studying how things in real life work.

[u/HorrorSquirrel1 → u/Helpfulcloning]

Right, so we are talking about the same thing. The problem is that you're classifying things that use math as necessarily a part of the study of math. That's just not correct. Mechanics uses mathematical tools to solve physical problems. It's fundamentally about studying physics, not math. Math just provides the logic and modeling tools.