[srcreigh]

The core of math, as GP mentioned, is learning proofs.

I would go as far as to say that most high school “math” and “math” taught in many college courses is borderline irrelevant.

It’s like learning how to paint by memorizing names of colors. Learning to fix a car by reading parts list.

Painters can tell you about colors and mechanics parts but you don’t become like them by making those things your goal.

The only way to learn math is to learn proofs rigorously.

Calculus isn’t math, it’s just calculus. Algebra, linear algebra, they’re not math. Any “math” without rigorous definitions and theorems with proofs for each one isn’t math. (memorizing names of colors isn’t being a painter)

This book seems a good start. This is not advanced math. It’s an introduction to math- if you don’t know this you don’t know math. https://richardhammack.github.io/BookOfProof/Main.pdf#page=8

Stuff like what’s in this book is taught starting in week 1 for Waterloo computer science degree.

It’s life changing knowledge because you can use math to understand almost anything.

[anon291]

I think there's a problem in American english in particular. We call the subject 'math', but I think the british 'maths' is more appropriate. There's multiple different kinds of mathematics. Not just one. The American misnomer makes a lot of people falsely believe that grade-school/high-school math is the 'path' into higher math. It's not.

That's not to dismiss the importance of arithmetic (and this is what I believe we should call grade school math operations): everyone should know how to add, subtract, multiply, divide, etc. But the core of mathematics is logical thinking and reason, not numbers

[MichaelRo]

> The core of math, as GP mentioned, is learning proofs.

Well it may be the core but it's not the purpose. As an engineer and later quant I actually use math for practical purposes in everyday life. It wasn't like this in the beginning, I remember primary school was a torment of being fed math olympiad-style problems and hating it. Then somewhere in gymnasium I discovered electronics and everything changed. Math became not just useful but inevitable and from then on learning of math for my own purposes went hand in hand with practical applications in electronics, from simple equations to matrices to differential equations, numeric calculus etc.

Of course there's also always the "standard math" (for passing the SAT/baccalauréat) and entering the good schools, that's inevitable. One can say that "Learning Math Ahead of (the vast majority of) Others" is the way to get ahead :)

[Jensson]

> The core of math, as GP mentioned, is learning proofs.

That is the midpoint, the core goal of math is getting enough intuition that facts are obvious, the proofs are just a guide to get you there.

This means you shouldn't study proofs, you should study facts, the proofs are just an example of how to support that fact, you can prove things in many different ways and also many things can be constructed in many different ways and still have the same properties. All of that is much easier when you think in terms of facts instead of proofs.

If you struggle with proving something then you don't understand it. If you memorize a proof for it, then you still don't understand it. The right path to take is to build understanding and then the proofs comes on their on.

[srcreigh]

It’s a cliche mathematician debate. I don’t disagree. In any case, if you aren’t able to do proofs, you don’t do math.