The universe is mathematical and somewhat precise
Whenever anyone asserts that the universe is in some sense mathematical (especially if they are regurgitating or supporting Tegmark's extreme view) I am reminded of what one of the founders of QED said of his own theory, which is touted not only as the foundations upon which modern particle physics and the standard model is built but as the most accurate theory ever devised:
"I must say that I am very dissatisfied with the situation [in quantum electrodynamics], because this so-called "good theory" does involve neglecting infinities which appear in its equations, neglecting them in an aribtrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small- not neglecting it just because it is infinitely great and you do not want it!"
We formulate physical laws in mathematical language. We postulate that such laws exist or that principles such as least action exist. In fact, much of modern physics is formulated on the principle of least action which was originally based on the idea that physical laws should reflect the nature of the perfection of the God who created them and the universe (Maupertuis' put forth the idea, but it was Euler who first set what became the action principle into rigorous mathematical form). Much of the time it works, or at least when it fails we are able to say why quite clearly (e.g., because most differential equations don't have analytical solutions and nonlinearities are difficult to work with even when the number of equations governing the system dynamics is small).
But currently our best theory of the fundamental constituents of all reality yields are powerful predictive tool in which things we call "particles" that make up everything are really just linguistic devices used as organizing principles that we then have to correct in the manner that so bothered Dirac (quoted above) :
"it is illegitimate to say that the world is made of molecules, atoms, electrons or quarks. Rather, a description based on such theoretical concepts may, in a particular context, be useful or even the best possible one. Matter, as described by the first principles of quantum theory, resembles matter in the Aristotelian sense: It is not a substance, but the capacity to form patterns"
p. 92 of
H. Primas (2017).
Knowledge and Time. Springer.
I am not, in other words, entirely convinved that we have sufficient evidence to assert that our successes in the natural sciences (and our perceived successes too) combined with a rather dismal failure in biology and other sciences with respect to a formal mathematical framework constitute actual realization of the structures of reality more than they do our ability to render much of the physical realm sensible through such formalisms.
