The role of pure mathematics in resolving complex biological problems: Applications to F1-ATPase, achievements, and future directions

Abstract

Mathematics should be a core component of biological research, not merely an auxiliary tool, to address intricate problems. Integration of pure mathematics into biological research offers a powerful avenue to address complex molecular-level problems whose complete elucidation has proven resistant to traditional experimental, theoretical, and computational approaches alone. This paper explores the application of mathematics in Nath's work on F₁-ATPase, such as combinatorics, number theory, graph theory, and highlights its ability to elucidate molecular mechanisms, model biological systems, predict complex behaviors, validate models, and provide definitive conclusions. We quantify the economic toll of flawed research, and propose a mathematical framework to advance biological discovery, positioning mathematics as a transformative force to solve biological problems.