I really encourage you to read that wiki page.
| The quantum theory of the Lamb shift, as conceived by Bethe and established by Schwinger, is a purely mathematical theory and the only direct contribution of experiment was to show the existence of a measurable effect. The agreement with calculation is better than one part in a thousand."
I think you're missing a lot of context in that physics was highly non-mathematical in the past. Physicists called Einstein a mathematician. It isn't too hard to see when he asserted that his theories were correct and didn't need experimental confirmation. | Hamming argues that Albert Einstein's pioneering work on special relativity was largely "scholastic" in its approach. He knew from the outset what the theory should look like (although he only knew this because of the Michelson–Morley experiment), and explored candidate theories with mathematical tools, not actual experiments. Hamming alleges that Einstein was so confident that his relativity theories were correct that the outcomes of observations designed to test them did not much interest him. If the observations were inconsistent with his theories, it would be the observations that were at fault.
Hell, go read Ian Hacking, any metaphysics, or ask ChatGPT. They will confirm what I'm saying. Even some of this is discussed in An Opinionated History of Mathematics[0], though much more focused on math. I'm more mentioning it because it is good and helps provide some of that historical context.It is kinda crazy that a thing we created, without the specific intent of modeling the world, ended up being so great at modeling the world. That's the unreasonable effectiveness.
In fairness, to change my opinion, you would need to show me some chain of reasoning or a conversation Wigner is clearly responding to that involves religion. Because this is what I see, but around math not being physics, and is what drives my interpretation.
[0] https://intellectualmathematics.com/opinionated-history-of-m...