Why Mathematical Chemistry Cannot Copy Mathematical Physics and How to Avoid the Imminent Epistemological Pitfalls

This paper argues that mathematical chemistry (MC) cannot just imitate mathematical physics (MP) but needs to develop its own interdisciplinary approach to avoid predictable obstacles. Although Kant's dictum that chemistry does not lend itself to mathematical treatment was already refuted during his own lifetime, any useful combination of mathematics and chemistry essentially differs from MP. While the latter has a longstanding disciplinary tradition of its own, MC requires true interdisciplinary work and needs to bridge two fundamentally different methodological traditions. I suggest that MC follows methodological pluralism and develops new mathematical theories of chemistry that avoid telling causal stories. However, this makes MC susceptible to various epistemological pitfalls to be explained with examples from the earlier history of mathematical chemistry. I argue that all these pitfalls can be avoided through the collaboration with experimental chemists and finally point to geometrical symmetry theory as a model of a non-causal mathematical approach in science that emerged out of interdisciplinary efforts in 19th-century mineralogy.