> The fact that so many software developers "don't like math" is ironic, because they're perfectly happy to manipulate symbols such as "x", "file", or "user_id" that stand in for other things every day. The entirety of mathematical knowledge is very much like a gigantic computer language (a formal system) in which every object is and must be precisely defined in terms of other objects, using and reusing symbols like "x", "y", "+", etc. that stand in for other things.
I don’t find it ironic, because I wouldn’t expect engineers to make good mathematicians implicitly (nor vice versa). There is some similarity between math and programming, but there is also a collossal amount of dissimilarity that makes them different things entirely.
For example, notation and terminology in mathematics is not actually rigorous. It’s highly context dependent and frequently overloaded (take the definition of “normal”, the notation of a vector versus a closure, or the notation of a sequence versus a collection of sets). As another example, consider that beyond the first few courses of undergraduate math you’re wading into a sea of abstraction which you can only reason about. There is no compiler flag to ensure your proof is correct in the general case, and you don’t have good, automatic feedback on whether or not the math works. In this sense, the entirety of mathematical knowledge is actually very much not like a formal computer language.
Beyond that, the ceiling of complexity for theoretical computer science or applied mathematics is far higher than programming. It’s not so much motivation (though that can be an issue too), it’s that learning the mathematics for certain things simply takes a vast amount of time. Meanwhile a professional programmer has to become good at things that mathematicians and scientists don’t have to care about, like version control or the idiosyncrasies of a specific language.
They're really orthogonal disciplines, for much the same reason that engineering isn't like computer science. There is a world of difference between proving the computational complexity of an algorithm and implementing an algorithm matching that complexity in the real world.
> Meanwhile a professional programmer has to become good at things that mathematicians and scientists don’t have to care about, like version control or the idiosyncrasies of a specific language.
Really depends on what kind of mathematician or scientist you are to be honest though. How good is someone's data analysis of an experiment if they can't reproduce it? Or if they've got 6 different versions of an application with 100k lines of code in a single file, each labelled "code_working(1).f90", "code_not_working.f90", etc... These are real problems with what people actually do in science; software development skills are poor and people do things badly.
There're organisations like Software Carpentry globally and the Software Sustainability Institute in the UK which exist to try and promote some thought about developing software as researchers, and making the software sustainable in the long term rather than letting it die every time a PhD student leaves.
That's essentially my point. Programming and mathematics are so different from each other that, without special effort, a professional in one domain shouldn't be expected to be meaningfully better than average in the other.
This applies in both directions most mathematicians and scientists have such poor version control and development hygiene because mathematics doesn't imbue them with any special insight about how to be an engineer.
That said, the math we're talking about (that is, the math necessary for understanding, say, the sequence of transformations that make up a convnet) lies far below the ceiling of complexity you mention.
I'm not sure symbol reuse and overloading are as much of an issue. I've run into people who are quite proficient with Perl and routinely use complicated regular expressions who say they didn't like math growing up.
I don’t find it ironic, because I wouldn’t expect engineers to make good mathematicians implicitly (nor vice versa). There is some similarity between math and programming, but there is also a collossal amount of dissimilarity that makes them different things entirely.
For example, notation and terminology in mathematics is not actually rigorous. It’s highly context dependent and frequently overloaded (take the definition of “normal”, the notation of a vector versus a closure, or the notation of a sequence versus a collection of sets). As another example, consider that beyond the first few courses of undergraduate math you’re wading into a sea of abstraction which you can only reason about. There is no compiler flag to ensure your proof is correct in the general case, and you don’t have good, automatic feedback on whether or not the math works. In this sense, the entirety of mathematical knowledge is actually very much not like a formal computer language.
Beyond that, the ceiling of complexity for theoretical computer science or applied mathematics is far higher than programming. It’s not so much motivation (though that can be an issue too), it’s that learning the mathematics for certain things simply takes a vast amount of time. Meanwhile a professional programmer has to become good at things that mathematicians and scientists don’t have to care about, like version control or the idiosyncrasies of a specific language.
They're really orthogonal disciplines, for much the same reason that engineering isn't like computer science. There is a world of difference between proving the computational complexity of an algorithm and implementing an algorithm matching that complexity in the real world.