This has a practical consequence that we'd primarily benefit from extracting the tooling and results of mathematicians, not as much the mindset. We don't need to know how to prove the binomial theorem to make it super useful to us
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Similarly, the vast majority of programming knowledge has no relevance to doing proofs. Some aspects, like proof assistants, do, and many mathematicians can deeply benefit from learning to program, but it makes a lot more sense to think of them as disjoint fields.
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In particular, I want to reject the common idea I see in programmers that programming is logic and abstraction, which are math. Logic and abstraction appear universally in all human knowledge. Math doesn't have a monopoly on that.
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Replying to @hillelogram
What differentiates between mathematicians and programmers?
Mathematics is the language to quantify our observations and to understand the working of nature. The core of programming is logic which is mathematics.
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Now one thing I gotta be REALLY explicit about: "programmers aren't mathematicians" is not a problem with programming. I believe it's *good* that we (the general programmer) are not mathematicians. The mathematician profession is very good at doing proofs & not much else
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And I also worry that people who *want* to say that we're mathematicians have a rosy-eyed view of what it means to be a mathematician. To my understanding, "math envy" is prevalent in many intellectual professions and causes far more harm to them than good
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(And, to reiterate again, I'm a strong advocate for using more math in programming and work hard to make that a reality. Which is why I was so riled by the "snide erasure" quote. It makes it sound like I'm mocking something I very deeply care about)
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APPENDIX: Why am I comfortable saying "programmers aren't mathematicians" but "software engineers are engineers"? It's about the same "overlap in the principles and body of knowledge" in the professions, though engineering is more complicated.
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Replying to @candeira @hillelogram and @GabriellaG439
I also find ironic that you would take exception to "programmers are mathematicians" when you wrote "programmers are engineers" without flinching.
Either both or none, amirite?
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That's because "engineering" is an umbrella of disciplines that share principles, not a single body of knowledge. The same thought experiment that argues programming is dissimilar to math also shows SE is dissimilar to mech eng... but also that ME is dissimilar to elec eng
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But the practice of SE is surprisingly similar to the practice of ME and EE, at least according to crossovers I interviewed, and all three are closer to each other than any are to professional mathematics. That changes the scope of what they can learn from each other
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"What we can learn from each other" motivates a *lot* of my questions about "is X similar to Y", because ultimately I love interdisciplinary knowledge transmission and I ask these things in service of it. Similarity shapes the conversation around said transmission
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Replying to
This is pretty important. Investigating how programming and mathematics are currently practiced *is* interesting and important, but I do think we need to be very careful not to clarify when this is not intended as a normative assessment of what they *should* be.
I still think mathematics and programming still have a great deal to learn from each other as fields! And I think it's absolutely ok to be envious of the useful stuff each of us have developed, and seek ways to integrate those, while avoiding taking on the less helpful trappings.
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