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Comment by silentOpen | Hacker News Reader

I've found that mostly it's just that mathematics is usually taught extremely poorly. Mathematicians and mathematics educators typically gloss over definitions and use terrible notation. Further compounding the problem, the mechanical aspects of mathematical computation are rarely formally defined -- talking about elementary operators and objects of a mathematical subfield is rare.

I've recently discovered abstract algebra and I love it. We need to find and celebrate good explanations of mathematics both to do better work and to give future generations the mathematical education we didn't get.

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What do you love about abstract algebra?

I'm asking because I found myself deeply disappointed with it when I took it in school. It seemed to me just a haphazard collection of definitions and puzzles. Why, for example, does anyone care how many non-abelian groups of order 18 there are? I found myself unable to retain much of anything, due to the lack of any coherent explanation of "What is the point?"

In computers, by contrast, no one hides the point. Searching, sorting, bits and bytes, languages that make it easier to express things without making mistakes—there's no mystery about the purpose or importance of anything.

I wonder, if someone showed me what is attractive about abstract algebra, maybe I would find myself just as addicted to math as to programming.

I know nothing of abstract algebra. In fact I don't even know what it is :). I do however view mathematicians in the same way I see the programming languages crowd: they like to play with these ideas and extend them for their own sake. The solve these puzzles and show that this principle is true, or that group of formulae can be generalized like so. It's up to the rest of us to notice when a particular problem fits some solution they have provided. Another part of this is: math is like alpha, and computer programming is blub, at least according to the math guys.

I love that it provides a systematic way of thinking about structures and proving properties of said structures that I am working with in code. It's amazingly powerful to say "type t defines a monoid with operation k: t -> t and identity Nil" because it comes with a whole slew of properties and theorems. It meshes very well with strongly typed functional languages that support algebraic data types (e.g. Haskell and OCaml).

I don't much care for theoretical abstract algebra (e.g. non-abelian groups of order 18) and I am by no means a master (or even an amateur!) but I find abstract algebra's concepts useful and I hope to learn more!

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