Mathematics is completely distinct from physics; it just happens that if you use mathematical ideas to model physical reality then the predictions are startlingly accurate.<p>It is entirely reasonable for mathematics to have no basis in physical reality. Mathematics is all about relations between things (if this has that property; it follows that...) and this has implications far beyond physics (eg, statistics and probability have implications for physics, but applications almost literally everywhere - these ideas are bigger than physics). This essay is relevant to teaching mathematics to people who are more comfortable with physical examples than with abstract logic. Fair enough, realise that this is calling for 'mathematics for physicists' rather than a better way of understanding maths.<p>Making the connection that all the mathematics we do is done in the context of reality doesn't make mathematics a subset of physics any more than history is a subset of physics. If every theory we have about the universe was proven wrong tomorrow then physics people would need to get very busy indeed - but mathematicians wouldn't even notice.
In the Gleick's book about complex system the author proposes a theory of why Bourbaki (the collective behind the plague called «mathématiques fondamentales») was structured: it is mainly a question of ego.<p>Poincaré was said to not acknowleged the «french school of mathematics» as the origin of his discoveries. And the institution especially the elite called «ENS» (forming the best teacher for university) is said to have been quite disliking his attitude.<p>Since Poincaré was heavily relying on geometry, it is said that since they found it unacademic they decided to change the content of math learning to avoid new «casses burnes» mathematicians.<p>It is very funny at this title to look at the discrepancy between the story of Mandelbrot experience whether it is written in french or english.<p>French biography states mandelbrot LOVED polytechnic school (another super ivy league) and english said the opposite stating that mandelbrot reproved the lack of use of geometry.<p>To be honest, I don't know if this is true.
While not coming from a "mathematics is physics" angle, this bit from "Concrete Mathematics" by Graham et. al. also warns against too much abstraction:<p><i>Abstract Mathematics is a wonderful subject, and there's nothing wrong with it: it's beautiful, general and useful. But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance.</i>