Programming language research has also shown that there are many mathematical structures, e.g. in lambda calculus, category theory, graph theory etc. that map directly to useful computational structures. These tend to be more rigorously defined and more generic than the programming equivalents, which are often limited, ad-hoc, special case instantiations of more general structures.
This argues for the opposite of your claim: if you want to reason about programming, you are seriously limiting yourself and your ability to reason about programming by ignoring the mathematical models that underlie the code you're working with.
This is exactly what happens when one tries to create an iO obfuscator mentioned in the article by using FHE encryption.
No way one can do that unless they understand how deeply information and data, computation and math are intervened together.
Touching the LISP is enlightening experience that allows to find all those missing links between aforementioned disciplines. Especially by creating a simple LISP machine in your language of choice. You will touch the holy grail of computation and the world will never be the same again.
Like most insights it's very hard to stop seeing the connection, but that's not usually a bad thing.
Now, you can come up with some metrics to mathematically analyze certain aspects of the user interaction. I don't think that's what garganzol was talking about, though.
And we have done that! Fitts’ law [1] gives us a very good way of quantifying certain aspects of user interface design. I can’t tell you how many UIs I’ve used (lost count) that have ignored this very basic principle and as a result they’re extremely frustrating to use.
In any case, it may not be what garganzol was talking about, but it did resemble a comment I’ve seen made many times. In the vast majority of cases I’ve seen, people who claim that math is inapplicable to some problem are completely unaware of a rich and storied field of mathematics dedicated to that topic.