My thesis is that mathematics is a branch of physics, and not, as is commonly presented, the other way round.

To elucidate, I believe the symbolic operations of mathematics (at the ordinary level encountered at school) are entirely determined or selected to model everyday observations about the world. We have a symbolic construct that "1+1=2" because we live in a universe and at scale where this is a good model of how physical objects behave when you aggregate them. If we lived at a quantum mechanical scale, we would have a different concept saying "1+1=something complicated depending on phase etc". I believe our mathematical concepts are entirely the products of our brains and computers, which are physical things, and thus our more basic mathematical concepts are technical devices to abstract (capture in reduced detail) the world. They are imperfect and evolving approximations. As for advanced mathematics I see it as primarily an idle pursuit, which may yield some useful abstraction devices.

The antithesis of my belief is the idea that mathematics is somehow pre-existing, transcendental, bound by its own rules, or more "pure" or superior to physics. I most strongly reject the idea that, because mathematics has a certain formal order, the physical universe "has to" be mathematical, that physics is somehow "bound" by mathematics, and so on. I think this is a backwards and conceited perception of the reality that the universe works a certain way, and we construct the symbolic system of mathematics to model that. I don't know why the universe runs by the rules it does, and I think this question is not answerable using available information, except weakly by an anthropic argument (if the universe were much less ordered we probably would not have evolved). The universe might, in fact, be ordered because God is running it as a simulation in his* computer - but we don't know that. What I reject is the belief that the universe is ordered because we can construct in our heads a few simple and ordered symbolic constructs.

My knowledge of the history of philosophy is poor, and so I don't know which other people have previously expressed this view. I see it as a very hard form of empiricism, of the same mould as the semi-philosophy that grew out of quantum mechanics in the early 20th century. I see it as absolutely antithetical to Platonism (as a natural philosophy), and probably antithetical to the rationalism of Descartes, etc, which also seems to me to over-emphasise cognitive constructs over the world, but I may be misunderstanding rationalism. I would like to note in passing that I find the prevailing belief (that mathematics is autonomous and abstract as opposed to a practical tool) very damaging to education. I hold it responsible for the great number of otherwise clever people who "can't get into maths". They can't because they have it presented to them as something conceited, elitist, and non-pratical.

(*) God is here imagined as male because of the highly geekish pursuit ascribed to him.