An earlier version of this was posted as a comment to a Quanta article.
What is mathematicism? It is the inordinate belief that the human derived logical system based on counting we call mathematics, somehow and in some way, actually underlies and determines the nature of physical reality. In fact though, more often than not, mathematics obscures and obfuscates rather than explicates the nature of physical reality but mathematicism is blind to this fact.
Mathematics is not science. It is a useful and essential modeling tool of science, but it is only a tool. Used badly, math can take erroneous assumptions about physical reality and conceal the underlying errors by making the model based on them mimic reality in its outputs. The historical example of this is Ptolemaic cosmology which completely misrepresented physical reality but nonetheless made useful predictions for a millennium.
Modern physics, on the cosmological and quantum scales, is the contemporary equivalent, presenting as it does, models that do not in fact resemble physical reality in their particulars. These models, nonetheless, make accurate predictions of observed phenomenon. For mathematicists this is enough, but science requires more. Science seeks to understand the physical processes that math beclouds with its formalisms.
Like Ptolemaic cosmology, modern cosmology and quantum physics present a picture of physical reality that does not make sense in terms of physics. We must believe in quarks, singularities, dark matter, dark energy and more. There is no empirical evidence for any of these things and yet they are prominent, even defining features of the models. These models are the inelegant progeny of mathematicism; complex, elaborate and fanciful, they bear scant resemblance to observed reality.
Quantum physics is incoherent about the nature of physical reality; there are at least five current interpretations of the model that seek to explain its physical meaning. Four of those are physically absurd. The fifth, deBroglie-Bohm, holds out the promise of making physical sense but is disfavored apparently for the sin of being plausible.
Modern cosmology on the other hand is comprehensible (sort of) but absurd. The vast cosmos we observe, of unknown and most likely unknowable extent, is presented as a single, gigantic, inflating, four dimensional gas bag. This current state is supposedly the consequence of an inexplicable initial condition in which the ‘universe’ may or may not have been infinitely small or infinitely large or maybe something else. It depends on who you ask.
Science is now controlled by mathematicists. Researchers are sent to look for empirical confirmation of predictions made by models of mathematical convenience and should the results disagree with the model it is reality that is declared at fault. So we have dark matter to compensate for the faulty rotation curves predicted by mathematicists who can’t, to this day, seem to grasp that galaxies have a different physical structure than the solar system and therefore it is unwise not to mention incorrect to model them using the Keplerian method designed to take advantage of the solar system’s specific structure.
Mathematicism has made a mess of modern science. One can only hope it will not take another millennium for empiricism to reassert itself as the proper basis of all science.