Comment by CogitoCogito
4 years ago
> Being good at math requires being able to solve problems whose solutions often do not have any practical uses or whose practical uses may not be clear to you. This is very different from how software problems should be approached.
I don't really agree. Being good at mathematical research requires recognizing the "core organization structure of a system" and solving the "core problem at hand". I'd argue that it's essentially the same in programming (and business) as well. The main difference is that a mathematical researcher is able to ignore non-pertinent information, while in practice those issues (usually) need to be dealt with.
That said I wouldn't say that PhDs (math or otherwise) make great developers. Their skill in development is a result of experience in developing software within the software industry and not something they gain simply due to "being intelligent" or by working on their on on their POC research implementations. But I'd point out that it's basically the same for professional software developers as well.
However, there are probably infinite organization structures describing a complex system and there isn't any ontological reality to Occam's razor. Programming is really much about deciding where and at what level to allocate partial structure, which again informs the broader picture of the core organization – and some of this may be even intuitive.
Are we actually in disagreement? I could just as well describe math as "deciding where and at what level to allocate partial structure..." in the same way. Mathematical researchers also build intuition over time allowing them to see certain big picture ideas more easily.
If I really take a step back and re-think this whole thread, I'd say the main different between mathematical researchers and programmers is just incentives. Funding and output are just fundamentally measured differently and the work is done very differently with respect to cooperation with others.
Still I'd say that the thing holding back mathematicians from being good developers is simply that research mathematics does not provide development experience.