I definitely see the parallel, but I'm not actually sure this is true.
A lot of the deep functional stuff I'm learning right now are more about finding connections and shortcuts between things that we used think were different.
For me, comparing functional programming to older languages is more like comparing "tally marks" or "roman numerals " to a modern "place value system".
Now back to the physics analogy. The gap between quantum physics and chemistry is both a theoretical and computation limit.
There are also seen to be very distinct layers where the lower level don't seem to correlate with higher levels.
But I can also see this might apply to the Curry-Howard correspondence.
Hmmm. I have to think about it more...
In your example, the two things are separated by at a minimum one layer of emergence: your example is more like saying biology is just chemistry. In maths and programming, they are both at the same level, no emergence.
I also haven’t found what you say to be true at all— As I’ve been learning more maths and more programming, and learning more about the link between the two, I have found that the ability to see problems from more than one angle has had a dramatic impact on how clearly I think and how efficiently I solve problems. Not useless whatsoever.
But that's quite different from your other claim. Maths and programming are not at the same level. When one writes a "hello world" program, math does not figure into the final text of the code at all. Similarly, when one writes code to implement a system interacting with multiple dependencies, one is not doing mathematics, except in the trivial sense of your original comment. That is to say, at such a remote distance that it's meaningless to describe the activity as a mathematical one.
