Think in Math, Write in Code

I do that. Then people hate me because all my variable names are single letters...

At least, for functions use self-documenting names instead of "f", "g", as in math.

I like that Python is quite close to my raw thoughts for simple problems. So writing an algorithm in Python almost feels like writing pseudocode. Heck, these days given an option between writing pseudocode and writing Python code, I choose Python for simple problems.

Is there a similar programming language that makes mathematicians feel at home? Something that makes them feel that they would rather write their implementation in that language itself instead of writing it with math notation on paper first?

I think that the total programming man hours spent on writing pure math computation would be dwarfed by the much larger number (I think) spent on doing menial computation: fetching data, transforming it and sending it forward/rendering some output. I suppose this article is targeted at that privileged former group.

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications.

Sure, mathematical thinking can be useful, but it's only one type of logical thinking among many types which can be applied to programming.

I've been programming so much for so long now that before I even start writing code my mind launches into an esoteric process of reasoning that I'm not confident would be considered "thinking in math" since I'm not formally skilled in mathematics. It's all just flashes of algorithms, data structures, potential modifications, moving pieces, how they all affect each other and what happens to the entire entangled web when you alter something. Fortunately, my colleagues are often pleased and sometimes even impressed with my code, and yet I'm not so sure I would consider my process "thinking in math."

So, this isn't necessarily a direct refutation to the article. In fact, maybe what I'm talking about is the same thing as what this article is talking about. But, anyway, my point is that I feel that there's more ways to think about problems and solutions than pushing the agenda of applying formal mathematics.

As an aside, I noticed this part of the article:

"Notice that steps 1 and 2 are the ones that take most of our time, ability, and effort. At the same time, these steps don’t lend themselves to programming languages. That doesn’t stop programmers from attempting to solve them in their editor"

Is this really a common thing? How can you try to implement something without first having had thought of the solution?

I think single letter variable names are fine within the scope of a single function. Especially if I'm doing something with a lot of math, like a lighting calculation, the computations are often more readable with short variable names. I'll also usually give a detailed description of what the variable is in comments for clarity.