Mathematics and programming

Jeff Atwood disputes the theory that competent programmers should be mathematically inclined.  His conclusion may or may not be correct – I don’t have any evidence one way or the other.  His reasoning, however, is wrong.

Jeff observes that “the vast bulk of code that I've seen consists mostly of the ‘balancing your checkbook’ sort of math, nothing remotely like what you'd find in the average college calculus textbook, even,” and gives the example i = j++ / (x + v) -- “not,” he rightly observes, “exactly the stuff mathletes are made of.”

Right, and nothing to do with being mathematically inclined either.  Jeff seems to be one of those people who believes that what mathematicians do is sit around doing ever harder calculations.  The sort of people who can only imagine Andrew Wiles proved Fermat’s Last Theorem by a fiendishly complicated process of long division.

In reality, the bulk of mathematical effort goes not into performing calculations, but into hypothesising and proving general truths.  Let’s take a quick run down of the kind of skills mathematicians really use in doing this:

• Identifying useful abstractions – separating out the salient points of a problem.
• Formulating a path from A to B – building a high-level plan of attack for a problem or proof.
• Turning that plan of attack into a series of precise and rigorous steps, expressed using an abstract and formal notation.
• Bundling up appropriate partial results into handy lemmas – another example of identifying useful abstractions.
• Thinking about special cases that might invalidate the assumptions of the proof or require special handling.

The core skills of mathematics sound awfully like the core skills of programming.  It is only “very hard … to draw a direct line from ‘good at math’ to ‘good at programming’” if you confuse mathematics with “mathletics.”