by godelski | 2026-01-21 04:52:43+00:00
> I think that is a developer's superpower.

I do too, but only because we can do both.

I think comparing math education to programming education is quite apt here. After all, programming is math[0]. Both are extremely abstract subjects that require high amounts of precision. In fact, that's why we use those languages![1]

One of the absolute most difficult parts of math is that you don't have feedback. Proving you did things correctly is not automated. You can't run it and have an independent (not you) mechanism tell you that the output is what you expect it to be. This leads to lots of frustration as you sit there thinking very hard about what you've done wrong. It is frustrating because you're often blind to the mistakes as that's why you've made them in the first place! But the upside is that you quickly become attentive to details and learn those pitfalls very well. This also means you can abstract very well (the entire point of math) as you learn to abuse things on purpose. The struggle is real, but the struggle is important to the learning process. You learn very little if there's no struggle. Your mind is made to remember things that are hard better than things that are easy.

In programming we typically have the opposite problem. You get instant feedback. This makes iteration and solving your specific problem much faster. You can experiment and learn faster as you poke and prod seeing how the output changes. BUT there is a strong tendency to leverage this too much and use it to outsource your thinking and analysis. Iterating your way to success rather than struggling and analyzing. This doesn't result in as strong of neural pathways, so you don't remember as well and you don't generalize as well. Having taught programming I can tell you that countless students graduate from university[2] thinking that because the output of their program is correct that this means that their program is correct. This is a massive failure in logic. Much easier to see in math that just because 3+3=6 and 5+1=6 doesn't mean that the process is equivalent[3]. The correctness of the program is the correctness of the process, not the correctness of the output.

While that's the typical outcome of learning programming, it isn't a necessary outcome and there's nothing stopping anyone from also using the same approach we use in math. Math is only that way because we're forced to[4]! Both have their strengths and weaknesses, but neither is strictly better. The strictly better learning path is the combination and that is the superpower we have. It's just easy to abdicate this power and only do the easy thing.

[0] We can really say this from Church-Turing but if you really have concerns with this statement you'll need to read more up on the theory of computer science and I suggest starting with lambda calculus.

[1] https://www.cs.utexas.edu/~EWD/transcriptions/EWD06xx/EWD667...

[2] and even graduate degrees. You'll also see this idea prolific on HN and I'm sure someone will respond to this comment countering the point

[3] You can abstract this, I'm not going to do some long calculation here but I'm sure most people have done a long calculation where they got the right answer but the process was wrong and they had a professor still mark them wrong (and correctly so).

[4] If you're going to lean on me I'll concede