**Pierre Verhulst** was a Belgian statistician who worked on population growth.

- Verhulst excelled in science but had other talents too, twice winning a Latin poetry prize.
- Two pupils in the same class as Verhulst were Joseph Plateau and Guillaume-Adolphe Nerenburger (1804-1869) and these three shared the top prize in mathematics in August 1822, the year they graduated from the Athenaeum.
- Verhulst and Plateau spent many hours in deep scientific discussions, while both were strongly encouraged by Quetelet who became their friend and advisor.
- When Verhulst graduated from the Athenaeum in 1822 he had not completed the full course of study there but he was keen to progress quickly with his university studies.
- Mathematics courses were being introduced at the museum and Verhulst was responsible for setting up the teaching of an analysis course.
- At this time Verhulst worked on the theory of numbers, and, influenced by Quetelet, he became interested in the calculus of probability and social statistics.
- In 1829 Verhulst published a translation of John Herschel's Theory of light.
- The Roman hierarchy did not take kindly with being told how to run their affairs by a Belgium (or probably by anyone, for that matter) so the police were summoned and Verhulst was ordered to leave Rome.
- While Verhulst had been in Rome there had been a rebellion in Belgium with much fighting between revolutionaries and Dutch troops.
- Verhulst was keen to get involved and, despite his illness and against the advice of his friends, in the middle of 1831 he enlisted in the army set up to oppose the Dutch forces.
- In 1832 Quetelet was assigned the task of drawing up mortality tables for the new Belgium State and he asked Verhulst to assist him in this.
- On Quetelet's recommendation, in 1834 Verhulst was appointed as a Répétiteur at the Academy to teach calculus.
- On 28 September 1835 Verhulst was appointed professor of mathematics at the Université Libre of Brussels.
- Verhulst had to resign from his position at the Université Libre of Brussels since it had been decreed that those teaching at the Military Academy could not teach in any other educational establishments.
- However, one project by Verhulst which Quetelet praised highly was his work on elliptic functions.
- This came about since Verhulst bought an edition of the complete works of Legendre in a public sale.
- Verhulst then wrote Traité élémentaire des fonctions elliptiques Ⓣ(Elementary treatise on elliptic functions) (1841) which was a critical résumé of these important contributions to the theory of elliptic functions.
- Quetelet praised the work highly and it must have been a contributory factor in Verhulst's election to the Belgium Academy of Science later in 1841.
- Quetelet does not seem to have appreciated Verhulst's most important contribution, however, namely his work on the logistic equation and logistic function.
- The assumed belief before Quetelet and Verhulst worked on population growth was that an increasing population followed a geometric progression.
- In the paper Verhulst argued against the model for population growth that Quetelet had proposed and instead proposed a model with a differential equation now known as the logistic equation.
- Another possible root of the term logistic could have been the French word "logis" (place to live) which was of course related to the limited resources for subsistence of a population, Verhulst was dealing with in his model.
- Based on his theory Verhulst predicted the upper limit of the Belgium population would be 9,400,000.
- Verhulst was elected president of the Belgium Academy of Science in 1848.

Born 28 October 1804, Brussels, French Empire (now Belgium). Died 15 February 1849, Brussels, Belgium.

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Astronomy, Origin Belgium

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive