A History of the Mathematics of Populations

Course details

From £67.00

Sat 22 Jun 2019

A History of the Mathematics of Populations



The day will look at how mathematics was developed for dealing with populations of various types over the past 700 years.

The history of mathematical models of populations is often traced back to Fibonacci’s rabbit problem, published in 1202 as a textbook exercise.  The seventeenth centuries saw increasing interest in annuities, prompting John Graunt and Edmund Halley to develop ways of computing the price of life annuities; their work was built on as the life insurance industry grew rapidly in the eighteenth century. In 1760 Daniel Bernoulli tried to calculate the increase in life expectancy if smallpox, then endemic, could be eliminated. His conclusions were challenged by d’Alembert on moral grounds appealing to the question of the rights of the individual versus those of the state.

In the late nineteenth the rediscovery of Mendel’s laws of inheritance was soon followed by the realisation that informative mathematical models of the properties of genetic variation within populations could be constructed and analysed. This early work resolved a major difficulty faced by Darwin in relation to his theory of evolution by natural selection, by showing that the mechanism of inheritance preserves rather than destroys variation. Further theoretical developments, especially those contributed by R.A. Fisher, J.B.S. Haldane and S. Wright, led to a far deeper understanding of the mechanisms of evolution than was possible in the absence of knowledge of the nature of inheritance. The drive to reduce disease continued through the twentieth century, with models such as age-period-cohort being developed to compare two or more groups. For example, comparing mortality rates between men and women, or between geographic regions, may reveal health inequalities. The rising power of computer modelling has allowed increasingly complex models and the coming of age of the study of chaos and its role in population dynamics.

Programme details

Please note that the date of this course was originally published as 15th June 2019 but is now Saturday 22nd June 2019 and the description of the course has been amended.

9.30am            Registration


10.00am          Introduction and welcome

10.05am          On Fibonacci and mathematical conceptual streams in context around the 12th to 14th centuries in Italy

                        Raffaele Pisano (University of Lille)

10.55am           Counting people before 1800

                         Chris Lewin (Actuary)

11.45am           Coffee/tea

12.10am           Early probabilistic models: the Bernoulli-d’Alembert disputes on smallpox inoculation

                         Camilla Colombo (University of Milan)

1.00pm            Lunch

2.10pm            Mathematics and the genetics of populations from 1900-1930

                       Brian Charlesworth (University of Edinburgh)

3.00pm           Age-period-cohort models and their history

                        Theresa Smith (University of Bath)

3.50pm            Tea/coffee

4.10pm            A chaotic end to the day – Mitchell Feigenbaum, Robert May, and the nonlinear modelling of populations

                       Mark McCartney (University of Ulster)

5.00pm           Course disperses



Tuition (includes tea/coffee): £67.00
Baguette lunch: £4.90
Full lunch: £14.00


Brian Charlesworth


Brian Charlesworth is Senior Honorary Professorial Fellow at the Institute of Evolutionary Biology, University of Edinburgh. His research has centred around theoretical and experimental population genetics, molecular and genome evolution, and life-history evolution. He received the Darwin Medal of the Royal Society in 2000, and the Darwin-Wallace Medal of the Linnean Society in 2010.

Camilla Colombo


Camilla Colombo is a Post-doctoral Fellow at the University of Milan, Italy, with a PhD from the London School of Economics. Her work brings together decision theory, applied ethics, and the philosophy of biology. She has published on Daniel Bernoulli, d’Alembert, and the smallpox debate.

Chris Lewin


Chris Lewin is a retired actuary who researches the history of actuarial science, pensions and insurance. He is the author of Pensions and Insurance before 1800 – a Social History, and is currently researching the statistics used by John Graunt in his 1662 book Natural and Political Observations.

Dr Mark McCartney


Mark McCartney is a Senior Lecturer in Mathematics at Ulster University. His recent research is in chaotic dynamics and mathematical ecology, but he has also published widely in mathematics education and the history of science. He is current President of the British Society for the History of Mathematics.

Raffaele Pisano


Raffaele Pisano is a Professor at Lille University, France, and President of the Inter-Divisional Teaching Commission of the International Union for the History and Philosophy of Science and Technology. He researches the interactions between mathematics, science, and society in medieval and Renaissance Europe.

Theresa R Smith


Theresa Smith is a Lecturer in Statistics at Bath University. She has a BA in History and a BSc in Statistics. She researches statistical methods for data with spatial or spatiotemporal dependence and their applications in public health and the social sciences.

Dr Cezar Ionescu

Director of Studies

Dr Cezar Ionescu is Associate Professor of Data Science with the  Oxford University Department for Continuing Education.  His main interests include functional programming, correctness of scientific computing and machine learning algorithms,  and the role of computing science in education.

Isobel Falconer

Director of Studies

Isobel Falconer is a Reader in the history of mathematics at St Andrews University. She researches the interface between mathematics and physics in the nineteenth century. She also taught for the Open University, and was once curator of the museum at the Cavendish Laboratory in Cambridge.


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