It is an entire collection of such stubborn patterns that would be the counterpart of a theory in mathematical logic, on the condition that these patterns sufficiently hang together in one way or another. — Tarskian
I can't take this too seriously. Have you studied much fundamental physics? Especially with quantum field theory and particle physics, the tendency has been just to apply the mathematical patterns and marvel how they force nature onto these stubborn outcomes.
The maths is "unreasonably effective". Somehow or other, nature keeps jamming itself into the arrangements described by permutation symmetries and matrix mechanics. You might need the Higgs field to force the SU(2) electroweak sector to crack diagonally into SU(2)xU(1), but because something had to do the job physically, the Higgs could be the fictional beast with its own SU(2) structure that could "eat" three of the electroweak's degrees of freedom, so allowing the U(1) photon to burst free.
It is a crazy tale of science being forced into a wild speculation. And yet tellingly – as this was the mindset that particle physics had learnt to adopt from painful experience – three groups came up with the same solution all at the same time, making the distribution of the Nobel prize uncomfortably contentious.
So there we have physics reaching the point where the maths constructs the patterns, and if the patterns are possible, nature must wriggle about until it has discovered a strange machinery to achieve the goal of fitting the forms preordained.
The Big Bang could have been halted at many points in its hot unfolding. But with every phase change, it kept on track to become as mathematically self-simplified as possible.
Inflation seems needed to have prevented an immediate gravitational collapse. The Higgs transition looks to have then stabilised the vacuum when inflation broke and dumped its energy into a lot of reheated particles. Even then particle physics was doomed as all the matter was going to be consumed by all the antimatter eventually. But another completely different kind of mechanism – the strong force with its SU(3) confinement – came into play, wrapping up quarks into proton balls and so allow a new game based on electron~proton electrodynamics to take over from matter~antimatter annihilation.
In just the first few minutes of the Big Bang, the physics had tumbled down a hierarchy of algebraic geometry – permutation symmetries – to become stable enough to now last "forever". It was composed of particles with no further possibility to decay, in a vacuum properly secured.
I would agree that the fact that this worked – believing that nature must find its way into mathematical-strength patterns – has itself become rather an issue for the practice of physics. Now we are flooded by every kind of maths-first theorising like string theory and a hundred more. A lot of speculative crap has followed as I don't think the way that the maths and physics have connected in symmetry terms is a trick that is properly understood.
This is why I mention topological order as the actual root that connects. And here physics has its own kind of lead in its condensed matter models and such-like. These are now becoming quite influential on mathematics. Ricci curvature and other thermodynamical flow models have proven some pretty big results.
And isn't that the healthy outcome? Some kind of mutual connection between maths and physics as cultures of inquiry? No need to make it a contest between logical rigour vs experimental validity. We have to come at nature from both these directions to grasp its truth.