If given a good spec, a clearly written formula, I don't think it's too unreasonable to expect a seasoned programmer to implement it despite not understanding the science that prompted the math. Maybe I'm wrong for some kinds of exotic math, but I've certainly implemented a few mathematical formulas that looked like Greek to me, at least when I started.

Moreover what I propose is that every researcher have a programmer available to consult with, who would perhaps write small amounts of code (perhaps make sure the code builds before it's published?) I don't suggest that researchers not write code, I think they should write code. But I think an expert in writing code should be available to help keep the standard of code high.

In my view, it would help a lot to provide scientists with resources for learning how to write quality software. Most of us don't even know how to write a specification, except by writing the code, and don't have an idea of what we want until we see something begin to work. Today, a lot of the math we use is written directly in code.

This stuff evolves over multiple iterations. Many of my programs never run more than once. Testing them requires being connected to the equipment if any kind of closed-loop control is involved.

I work in an R&D setting in industry. If something I make threatens to become a product, the thing I hand over to the software team is a proof of concept, that could include a hardware design and working code.

I've had these same ideas when working on physics-related code. They should have a few actual software experts around to consult and / or do the development.