Simply not true. Most mathematical statements, e.g. proofs of existence have no relation to a "program".
>math is geared and targeted for people who like doing symbolic logic by hand.
No, it is not. There is absolutely nothing interesting about symbol manipulation, it is always the least interesting part of a proof. It usually is the part the author handwaves away, while focusing on the actual interesting parts, the idea behind the proof and the possible intuitions for them. Textbook might include them, but as training and because you need to be more explicit when teaching.
Okay. What is a proof other than a step by step explanation for why something’s true? You’re getting caught up in “program” when it’s objectively the case that all math follows a series a steps. A lot of those steps are “handwavy” I’ll give you that. That’s not relevant to what I said though.
>there is nothing interesting about symbol manipulation
Cool. You missed my entire point again. Math education is geared towards a certain set of people who pick up on (and gain an interest in) the language of math. Only once you get to higher level math do you even start to get alternative visualizations etc (at which point you’ve weeded out a ton of people who would have benefited from e.g. visualizing numbers as groups of shapes). There are a million ways to teach math and we’re leaving a lot of people behind. That was my point
Cooking instructions are a series of steps as well. Would you also claim cooking, mathematics and programming really are all the same thing?
It seems to me that it is an important point though.
> Even a non-constructive proof of existence for x can be significant in a programmatic context
Which has no relation whatsover to proofs and programms being the same thing.
There is a reason Turing is considered one of the greatest minds to ever live. He didn’t just invent a concept. He invented a completely new branch of science. We would’ve gotten there eventually but his idea to solve the Entscheidungsproblem using his machine was such a step ahead of the times that we christened him the father of an entire science.
There is no doubt that Turing was bright, very bright indeed, but next you'll be claiming he cracked the Enigmna Code or something.
Much (most?) of math is quite different from it. Proving that there is a well ordering of the reals, and simultaneously proving that it is impossible to show you such an ordering: Very different from skills needed in programming.
This is actually a problem of interest to me, so I’ve definitely been exposed to it and the limits of modern computation. But I’m not speaking strictly about the modern day CPU.
The set of computable real numbers is countable and thus has measure zero. In other words, almost all real numbers are non-computable, and almost all has an exact definition.
So you can’t compute the real numbers unless you’re meaning something else by computing.
That doesn't make any sense. What do you mean by that?
> I agree it’s been more difficult learning math than programming for myself as well: but that’s because math is geared and targeted for people who like doing symbolic logic by hand.
Mathematics is not about symbolic logic. Mathematics is the study of idealized structures, their properties, and their relationships. Symbols are just a convenient shorthand. They are not the mathematics in and of themselves.
> The fact we don’t have a nice and intuitive way of writing math via a keyboard is proof that these two fields are not on the same page.
What does that have to do with anything? Although LaTeX and the like are pretty decent at it, there's a lot of things we can't do easily via a keyboard. Why is that a constraint on anything or relevant?
Not trying to be provocative, but I honestly have little idea what you're talking about.
I will agree it’s been more difficult learning math than programming for myself as well: but that’s because math is geared and targeted for people who like doing symbolic logic by hand. Math people think we’re a level below them (we are in some ways from a working perspective) so they tend to write off complaints like this as us just wanting to make math more like programming.
The fact we don’t have a nice and intuitive way of writing math via a keyboard is proof that these two fields, which should be tightly coupled, are not on the same page.