"I find it no surprise that the larger companies have made foundational maths, such as category theory and abstract algebra, the underlying abstraction for their general frameworks."
I would like to learn more; do you have a specific example?
Having worked with real "engineer" engineers, I've found that they have, and value, a considerable amount of mathematical education, but that education is all in continuous mathematics; abstract algebra and formal logic have about the same amount of respect as basket weaving. Unfortunately, continuous math isn't particularly useful for software.
As an electrical engineer who briefly flirted with computer engineering, I had 4 semesters of continuous math and 1 semester of discrete math[1]. I also had classes like linear systems and electromagnetics where I had to actually use continuous math heavily.
While I do not think continuous math is particularly useful for general software development, I think it is very valuable for specific problem domains. I have found my Calculus/DiffEq foundation to be very valuable for my work with radar signal processing and NLP code, more so in the former because it was basically translating electrical engineering algorithms, formulas, and concepts into C. It is also important for any type of development that makes heavy use of geometry.
As a side note, I saw some of the bias you describe out of the more "pure" EEs I worked with when I first started. There was a strong bias against software engineers, particularly those who went the CS route, because they didn't understand the math and physics behind the hardware. Admittedly, some were clueless and probably should not have been writing software for multi-million dollar hardware[2]. Most were competent, though, and able to pick up the basics they needed to know when tutored for a bit.
[1] Which was actually titled "Discrete Mathematics", and was just covered basic set theory, combinatorics, and linear algebra.
[2] Like the one who added a reset routine that blindly opened power contacts on the UUT without verifying that the power supplies were off first. Fortunately, that was caught before they actually opened with hundreds of amps going through the bus.
As you say, continuous math (to my mind, calculus, diffeq, and linear algebra; anything involving reals) is necessary for some problem domains. But accounting is necessary for some problem domains as well. And molecular biology.[1]
But if I get worked up into a good froth, I can make a case that software development is applied formal logic or applied abstract algebra (or both). I don't believe you can do professional software development (in Weinberg's sense) without some serious discrete math, in the same way you can't do signal processing without calculus.
[1] If you've got something that mixes the three, let me know. It's probably something I should stay away from.
I must admit to ignorance of Weinberg's books and other writings. My interest is piqued now, though.
That said, based on your second statement nearly all scientific and engineering programming would not qualify as "professional software development". The code I worked on had little to no discrete math or formal logic in it. There was not an integer to be found save loop counters and array indices Do you not consider an (electrical engineer | mechanical engineer | physicist | molecular biologist) who can code and spends the vast majority of their time writing production code like this a professional software developer?
Two good examples from the Scala community would be Algebird[1] from Twitter which uses Monoids as a main abstraction and Spire[2], which might be the best numerical library out there and heavily rooted in Abstract Algebra.
I considered editing my other comment but decided instead to break it out.
There are a couple of complexities that your comment illustrates well:
First, continuous math _is_ available and immediately applicable today. The problem is that we often reason in and program to the implementation, not the abstraction - a subtle difference, but an important one. Not only that, but by reasoning in a flawed representation, we often miss important derivations that result in dramatic simplifications and reductions in the problem domain. I would also argue that we already do use continuous math regularly - for example, linear algebra, combinatorics, and set theor: most of us only know them as arrays, random, and SQL.
Secondly, not enough effort is made in formal education for applying 'pure' math to computer science. Some branches, such as linear algebra, have obvious implementations and analogies already available but others are quite a bit less clear - I fault this more on curriculum silos than an engineer's innate abilities. It's a learned skill that just isn't often taught.
I would like to learn more; do you have a specific example?
Having worked with real "engineer" engineers, I've found that they have, and value, a considerable amount of mathematical education, but that education is all in continuous mathematics; abstract algebra and formal logic have about the same amount of respect as basket weaving. Unfortunately, continuous math isn't particularly useful for software.