The question is not whether we "impose" mathematical concepts onto the physical Universe with our minds. That happens from time to time when people try to force a concept to fit a particular situation where it does not fit. Fortunately, peer review protects against this.
So, the question is whether mathematical concepts are solely imaginary (with no more power than Harry Potter's wand); or whether they are true independently of the human mind, with a propensity to interact with the physical Universe. Successes of modern science indicate the latter.
If mathematical concepts were solely imaginary, then they would be the product of random processes in our contingent brains, with no purpose but amusement, and no more relevance to reality than Harry Potter's wand. If just imaginary and random, it would be difficult to "impose" them on the physical Universe in a coherent way.
Are you saying here that the function of our brains are random? If so how do we manage to get anything done? How would we manage to hold and apply, sufficiently long enough, those mathematical concepts you so love?
If we, as you say, with this random brain of ours, couldn't "impose them on the physical universe in a coherent way" how does this brain of ours impose, with its 'randomness', on these so called incontingent, objective mathematical concepts that you claim are 'out there' as oppose to being 'in here'? These concepts have to be held and understood by our brains internally even if they are objective and 'out there'. You claim about the feebleness of our brains to 'impose' applies to all things which are 'out there', which would mean that the scope to understand these mathematic concepts would be out of our reach.
Your implication of imaginary is all wrong these concepts are developed from observations
etc. not from someone just sitting at a desk and making them up like a story or tale. And that is my point that the concepts that have been developed have come from what has been observed of our physical world. How else would we know that they are correct and represent the reality we see?
Numbers, squares of numbers, square roots, right angles, triangles, second derivatives etc are not visible in the natural world. For thousands of years, maths developed these concepts, aware of their usefulness for man-made things, but unaware of a relevance to the physical Universe.
However, in about AD 1590, Galileo dropped some stones frim the Tower of Pisa, and from then until AD 1905, he, Newton, Maxwell etc made objective measurement, followed by mathematical equations the critical factor in science - i.e. the certainty of science depended upon the certainity of its mathimatical concepts. How could that be if maths was just an imaginary product imposed by contingent brain?
To be coherent, science needs its maths to be as objective (independent of human mind) as the objectivity of its physical elements (e.g. moons around Saturn).
However, from AD 1905, the sequence of physics was turned on its head. Instead of experiment followed by maths, the more fruitful sequence became abstract maths followed by empirical experiment. Mathematical reasoning enabled forecasts of previously unsuspected phenomena to an extraordinary extent. I gave four examples in my previous post. I can give more examples if you wish.
One could "impose" equations upon a few things which are already known (if you can get around modern peer review and incoherence), but impossible to make your maths forecast new phenomena such as black holes, gravitational waves, Higgs field etc of modern physics unless the mathematical concepts are as objective as the phenomena they forecast.
So, if we accept the reality of the forecasts of modern physics, then we are forced to accept the reality of the abstract concepts used to make the forecasts. In modern physics, the Universe is contingent upon the maths.
God bless
As for forecasting that is just a function of the scope and range of the maths at hand etc. seeking out all the potentialities of the tools at our finger tips. This is an interlinked universe, it is not surprising that something found and developed in one aspect of it is found to relate to some other part of it.
I feel this isn't a thorough response to your post but I'm a little busy at the moment to delve fully into its nuances.