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.
		Interestingly, Benjamin Franklin published an
		essay in 1755 that partially inspired Malthus.

1819 - Smallpox outbreak in Norwich, England, because the
       first modernly-documented epidemic suitable
       for epidemic modelling, thanks to
       the work of physician John Cross.

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