For example, I have to read data from one source, and write it to another. I can have a single app provide api for both the writing source and the reading source, or I can have two separate apps and two separate apis. But I can't get away from the problem of reading and writing. That's irreduceable. If I have separate apps for the two apis, I have a configuration management issue. If I have a monolithic app that does both, I have a coupling issue.
Imagining that Bleeding Edge Technology of the Month will make this go away is wishful thinking. But facing the truth is awful, so we choose the wishful thinking.
If you compare software engineering to another field like aerospace or structural engineering it's laughable how little rigour and formality takes place in most software. It's shocking how much disdain programmers show for mathematics which gives us the tools to prove that our applications are correct.
I personally think these things are great but too expensive. My customers care about solving their problems not perfection. There's a balance to be struck and I'm not excusing bad software, but if the customer isn't willing to pay for better and is happy with the current quality, there is little incentive to put in this extra effort (and therefore cost) when the resources could instead be put to work on providing value in ways the customer does care about.
I guess after you exceed the customers quality requirements/expectations, there are diminishing returns.
I'd love to produce perfect software, but nobody will pay me to do it.
I didn't say you had to do all of this yourself. I don't believe every programmer has to have a degree in mathematics. Where I take issue is with the refusal to take advantage of the hard work of others. There exist languages, tools and libraries which have a strong mathematical basis that are ignored in favour of the latest fad. Places like stackoverflow are full to the brim with people asking for help solving problems that they wouldn't have to deal with if they'd chosen better tools.
I do, however, think there's a "which kneecap" problem to rigor as well. Rigor isn't free - it comes with costs, in learning curve, in the quality of developer required, etc.
I've been bouncing back and forth between not-rigorous Ruby, kinda-rigorous Go, and pseudo-rigorous Java. I don't think rigor is a killer solution, nor do I think it's a gruesome waste of time. But I find the really ugly problems to be at the requirements and architecture level, not the code level. Not surprising, considering coding isn't my primary work.