It seems the majority of scientists hold for a the hyper-effectiveness of mathematics in natural sciences as a sign that nature is deeply mathematical. Although I believe that some mathematisism is necessary to tackle the description of the world, I can't find the intuition behind the mathematical intelligibility of the univers to be grounded outside of a belief and the modern success of the "hard sciences", nothing really goes to prove that mathematics are embedded in Nature.
The opposite point of view, that which aligns with a selective-effectiveness of mathematics, is more reasonable as a stance. Mathematics is only efficient in that it chooses its field of effectiveness, it focus on structure, extracts it and deals with it. Here, one can go as far as imagining that Mathematics is a branch of psychology: we "conceive" Mathematics as we further harmonize our mental behavior and the world's (matter's ?) behavior. One can imagine that a real structure in the Univers is no truer than the effect of such an harmonization, it is only because we can picture the behavior of the world by way of the behavior of our mind (and vice-versa) that we project structure in the world.
My goal in the post is three fold: 1) to see if some scientistics have constructed a smiliar reasonning and how it influenced their work, 2) find out about philosophers who have persued with some depth the perspective of Mathematics as a branch of psychology, 3) get your take on it.
Thanks for your time.
P.S: I have not read the book with the title, just went for the expression as it seems to cristallize the stance very well.