Mathematical biology's biggest hits! =============================================== (Major advances in biology that relied on math) This is a biased list of examples I've found where mathematics has been used to help researchers make important contributions to biology. I'm always looking for more things to add to the list, and biology is such a broad field, I doubt I'll ever finish. If you see something is missing or have suggestions for other improvements, please let me know. - - - - - 1638 - Galileo on the allometric scaling of bone sizes 1760 - Daniel Bernoulli showed smallpox inoculation would prolong life expectancy. This was before doctors realized that cowpox infections were also protective. 1798 - Thomas Robert Malthus on the growth of populations and its consequences. While the manuscript does not explicitly use algebra or other mathematical devices, Malthus graduated from Cambridge with honors in math, and the essay is, at heart, math. 1866 - Mendel uses conditional probability arguments to infer particulate "Mendelian" inheritance. 1866 - William Farr predicts to time-course of Cattle plague using auto-correlated differences. 1867 - Jenkin's attack on evolution via blending-inheritance reveals a large gap in Darwin's theory. 1876 - Jorgen Gram publishes his first paper on forest management 1889 - Galton's "Natural Inheritance" popularizes his observation of "regression towards mediocrity" - first use of statistical arguments to understand patterns of heredity for continuously varying traits. 1900 - Mendel's laws rediscovered by Correns and others (but see Mendel!!!!) 1907 - Boveri and Wien show that chromosomes have individual identities using Montecarlo simulation 1911 - Ross's epidemic model showing threshold-behavior in malaria transmission 1913 - Sturtevant maps genes to linear chromosomes based on linkage 1917 - D'Arcy Thompson publishes "On Growth and Form" connecting life and geometry 1918 - Fisher introduces ANOVA to understand reconcile Mendel and Galton Subsequent work by Haldane, Wright, Dobzhansky, and others. 1925 - Fisher's ultimate refinement of Analysis of Variance, based on plant data 1925 - Lotka publishes "Elements of Physical Biology" connecting chemistry to population dynamics 1926 - Volterra's explanation of fisheries oscillations, independent of Lotka 1927 - Kermack and McKendrick's theory of disease 1937 - Fisher and Kolmogorov on invasion waves Subsequent extension and applications, including Kot on dispersal kernels, and Turrelli and Barton on Wolbachia 1937 - Torsten Teorell publishes the first modern pharmacokinetics theories 1952 - Hodgkin and Huxley action potentials in squid axon 1952 - Alan Turing, morphogenesis via reaction--diffusion 1954 - Schaefer and Gordon, maximum sustainable yield of fish. 1964 - Kimura published his monograph "Diffusion Models in Population Genetics", the origin of modern stochastic treatments of population genetics 1964 - Edwards and Cavalli-Sforza, first evolution-based algorithmic phylogeny (likelihood + parsimony) 1964 - Zuckerkandl and Pauling 1964, Molecular clocks by Poisson model (achieved fame with the genomics revolution in the 2000's) 1966 - Von Neumann universal constructor cellular automata 1970 - Conway's game of life 1971 - Knudson analyzes retinoblastoma data and develops multi-hit carcinogenesis theory, leading to the discovery of the first tumor suppressor genes. 1973 - John Maynard Smith's extension of game theory with ESS's 1975 - Arthur Winfree on the stability of biological clocks 1975 - John Kingman introduces the coalescent as a way to understand samples of (neutral) genes (1982's paper culminated?) 1976 - May and Oster paper on chaos in ecology models Subsequent experimental demonstration by Cushing et al in Tribolium along with McCauley, Nelson, et al in Daphnia 1975 - Arthur Winfree and Cardiac arrhythmia 1988 - Murray on animal coat patterning (building on Turing, 1952) 1993 - Kepler-Perelson theory of affinity maturation in immunology 1996 - Perelson and Nowak theory of HIV viral dynamics 1997 - Stephen Hubbell's unified Neutral biodiversity theory 2000 - Elowitz and Leibler on the repressilator and synthetic biology