TL;DR
This paper critiques extreme mathematical realism in physics, advocating for a moderate view that considers mathematics as partly human-constructed, and explores its philosophical and practical implications.
Contribution
It introduces a moderate stance on mathematical realism in physics, contrasting with extreme views, and discusses its philosophical and scientific consequences.
Findings
Arguments for a human-centric view of mathematics
Implications for the philosophy of physics
Potential impact on theoretical physics research
Abstract
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this--at first sight purely philosophical--difference in point of view.
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