09-01-2026, 10:22 PM
Mathematical Biology is Good for Mathematics
Author: Michael C. Reed
Publication:Notices of the American Mathematical Society, Vol. 62, No. 10, November 2015
DOI: 10.1090/noti1288
Michael C. Reed argues that the rapid rise of mathematical biology benefits not only applied mathematicians but mathematics as a whole. Biology has become one of the dominant areas of modern science, driven by new measurement technologies, major government and biotechnology funding, and widespread interest in medicine, human physiology, genetics, and ecology. Mathematics has responded accordingly: the proportion of mathematics PhDs specializing in mathematical biology was already growing strongly by the early 2010s. Reed emphasizes that the relationship is not one-directional—mathematics provides tools for biology, but biological questions also generate genuinely new mathematical problems.
A central theme is that biology may play for twenty-first-century mathematics a role comparable to the one physics played historically. Problems from mechanics led to dynamical systems, heat and wave phenomena stimulated partial differential equations, and quantum mechanics influenced functional analysis. Similarly, contemporary biology draws on and develops graph theory, topology, geometry, combinatorics, probability, stochastic processes, dynamical systems, harmonic analysis, and algebraic statistics. Examples include graph models of epidemics and gene networks, topology in neuroscience and cardiac fibrillation, geometry in protein folding, combinatorics in RNA structures, reaction–diffusion equations arising from morphogenesis, and mathematical methods for comparing evolutionary trees. Reed therefore predicts that biological questions will increasingly produce new concepts and theorems in core mathematics rather than merely serving as applications of existing techniques.
Reed also sees mathematical biology as strategically important for mathematics education and the public image of the subject. Biological and medical problems can attract students who would otherwise avoid mathematics because they immediately see how calculus, differential equations, probability, or graph theory relate to cancer, epidemics, neuroscience, genetics, and environmental questions. Undergraduate students can even participate in meaningful projects because many biological systems remain poorly understood. At the same time, biological applications make mathematics easier to communicate to the general public: people may not understand advanced mathematics itself, but they readily appreciate its contribution to disease research, medicine, ecology, and human health. Mathematical biology can therefore help attract new mathematics majors, create employment opportunities, and demonstrate the relevance of mathematics to society.
Key takeaways
ARTICLE [PDF]
Author: Michael C. Reed
Publication:Notices of the American Mathematical Society, Vol. 62, No. 10, November 2015
DOI: 10.1090/noti1288
Michael C. Reed argues that the rapid rise of mathematical biology benefits not only applied mathematicians but mathematics as a whole. Biology has become one of the dominant areas of modern science, driven by new measurement technologies, major government and biotechnology funding, and widespread interest in medicine, human physiology, genetics, and ecology. Mathematics has responded accordingly: the proportion of mathematics PhDs specializing in mathematical biology was already growing strongly by the early 2010s. Reed emphasizes that the relationship is not one-directional—mathematics provides tools for biology, but biological questions also generate genuinely new mathematical problems.
A central theme is that biology may play for twenty-first-century mathematics a role comparable to the one physics played historically. Problems from mechanics led to dynamical systems, heat and wave phenomena stimulated partial differential equations, and quantum mechanics influenced functional analysis. Similarly, contemporary biology draws on and develops graph theory, topology, geometry, combinatorics, probability, stochastic processes, dynamical systems, harmonic analysis, and algebraic statistics. Examples include graph models of epidemics and gene networks, topology in neuroscience and cardiac fibrillation, geometry in protein folding, combinatorics in RNA structures, reaction–diffusion equations arising from morphogenesis, and mathematical methods for comparing evolutionary trees. Reed therefore predicts that biological questions will increasingly produce new concepts and theorems in core mathematics rather than merely serving as applications of existing techniques.
Reed also sees mathematical biology as strategically important for mathematics education and the public image of the subject. Biological and medical problems can attract students who would otherwise avoid mathematics because they immediately see how calculus, differential equations, probability, or graph theory relate to cancer, epidemics, neuroscience, genetics, and environmental questions. Undergraduate students can even participate in meaningful projects because many biological systems remain poorly understood. At the same time, biological applications make mathematics easier to communicate to the general public: people may not understand advanced mathematics itself, but they readily appreciate its contribution to disease research, medicine, ecology, and human health. Mathematical biology can therefore help attract new mathematics majors, create employment opportunities, and demonstrate the relevance of mathematics to society.
Key takeaways
- Biology is becoming a major source of new mathematical questions, not merely a field where existing mathematics is applied.
- Mathematics used in biology spans an unusually broad range of areas, from PDEs and dynamical systems to topology, combinatorics, probability, geometry, and algebra.
- Reed suggests that biology could influence twenty-first-century mathematics as profoundly as physics influenced mathematics in earlier centuries.
- Mathematical biology can help attract students and improve the public perception of mathematics by connecting abstract ideas with medicine, health, genetics, and ecology.
ARTICLE [PDF]
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