Ask HN: I suck at math, where to start?

Sal Khan is a great teacher

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I am doing now a uni course (economy/informatics) and had to brush up on calculus and other math areas. Khan Academy helped me understand a lot of required concepts.

If you want to understand computational complexity theory, for instance, you need a different set of "fundamentals" than you do if you want to understand high-school physics. It'll be a different thing if you want to read econ papers, and a different thing if you want to study machine learning.

Within the intersection of all these fundamentals is probably basic arithmetic and algebra. Those tools are basic requirements for everything else. Beyond that, you need to define your goal before you decide what math to learn.

Same happened to me. I completed a BS in CS and learned just enough algebra, trig & calculus to pass the classes and then forgot almost everything. Many years after graduation, I came across an interesting post in comp.lang.java - somebody was asking how to create a java applet that could draw a 3D block arrow that could orient itself in any direction. I'm pretty sure somebody was asking for help with his homework, but I thought it was an interesting problem so I started looking at it and the first issue I ran into was drawing a line perpendicular to another. I vaguely remembered that there was a formula for computing the slope of a line perpendicular to another and when I looked it up - in context to a problem I was trying to solve - it just kind of "clicked" and I found it interesting. From there I fell down the rabbit hole of re-learning everything up to differential equations that I was supposed to be learning when I was an undergraduate.

First, pick a topic that you believe you can be fully engaged with. Here are some examples. But you can look at the threads of these from middle school through first year graduate school.

* Geometry (From Euclid to Topology to tensor analysis)

* Linear Algebra (From vectors to Convex Optimization)

* Calculus (Trig to PDEs')

* Algebra (From Groups to Number Theory)

Second, is do the work. With math is easy to trick yourself, in the moment, that you know the solution and understand the concept. But that mistake acrues, you get to a point where everything is opaque and there isn't a starting point without a hint. This feeling of self-assurance needs to be challenged. You need to do the work, rewrite the proofs, do the exercises completely, and explore the concept on your own a bit.

Why I bring this up, is because often I've thought that the innovators of mathematics probably benefited from this action: probably it is what enabled them to solve and derive problems we still today have difficulty resolving.

I bring this up to highlight a point about the philosophical underpinnings of mathematics--that as necessary as it is to understand the syntax and grammar of mathematics today, it is just as necessary to wrestle with the ideas in a form more palpable to your mind: language.

So what I'm saying, really, is that if you find yourself having difficulty with mathematics, as much as it is a matter of "doing the work" (solving the problem, crunching the number) as it is with any other skill, it is as equally important (and maybe even "more" helpful) to approach and take on the logical reasoning as a function of what you can put into words... At least, doing so, I think and hope it would help you render yourself more capable of tackling mathematics.

A good book to start you off in this way, is Bertrand Russel's Introduction to the Mathematical Philosophy. If you have to read it several times, it's been shown rewatching something as higher playerback speed is more effective than just reading it once, so don't be afraid to reread sections (or even in math) as many times as it takes for the knowledge to become explicit to you.

Oh and Khan Academy is a great resource.

Finally, if you have some money you can definitely find a math tutor--if you can find one who you can relate to / who speaks to you, it'll make a radical difference too.

Hope this helps!

Afterward: if you want a problem that'll stump any mathematician, take a look at the Collatz Conjecture: very simple, but understanding it might help you understand how to approach problems in mathematics (although this one has still yet to be proven, and as Paul Erdos said, mathematics is still not yet equiped to prove it, despite how simple it is).