Math, Programming, and Language Learning

An anonymous reader writes: There's often debate amongst modern programmers about how much math a professional developer should know, and to what extent programming is math. Learning to program is often viewed as being on a spectrum between learning math and learning spoken/written languages. But in a new article, Jeremy Kun argues that the spectrum should be formulated another way: Human language -> Mathematics -> Programming. "Having studied all three subjects, I'd argue that mathematics falls between language and programming on the hierarchy of rigor. ... [T]he hierarchy of abstraction is the exact reverse, with programming being the most concrete and language being the most abstract. Perhaps this is why people consider mathematics a bridge between human language and programming. Because it allows you to express more formal ideas in a more concrete language, without making you worry about such specific hardware details like whether your integers are capped at 32 bits or 64. Indeed, if you think that the core of programming is expressing abstract ideas in a concrete language, then this makes a lot of sense. This is precisely why learning mathematics is 'better' at helping you learn the kind of abstract thinking you want for programming than language. Because mathematics is closer to programming on the hierarchy. It helps even more that mathematics and programming readily share topics."

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[GiganticLyingMouth]

I think part of the problem is that "programming" is itself so diverse. If you were to be a graphics programmer, you would certainly need your linear algebra, geometry, etc. If you worked with scientific computing, you'd need even more math (e.g. differential equations, statistics, etc). If you worked as a DSP programmer, you'd need to know calculus (and then some). In contrast, web development doesn't really require any of these. However, they all involve "programming", and the people writing the software can all be called "programmers", even if one's writing a website (no math) and another is doing a fluid dynamics simulation (lots of math).