Leonhard Euler
Pierre François Verhulst
Eda Paksoy
Pierre François Verhulst (born on 28th of October 1804 in Brussels) was a Belgian (then French Empire) mathematician primarily known for his work on logistic curve and population growth. He died on the 15th of February 1849 due to health problems that he was plagued with all his life. Even though there aren’t enough records about his illness, it appears that the most likely cause was tuberculosis. Pierre Verhulst was born into a wealthy family who made sure their son had a top quality education. His secondary education was at the Athenaeum of
Brussels that was known for giving a much broader education than other schools at that time, particularly in science. When Verhulst became ill, he decided to travel to Italy in hope that his health would improve. Due to his opinions on politics, he was asked to leave Rome, so he returned to Belgium. He worked in colleges as a professor and became the president of Belgium Academy, but his health declined over the last years of his life.
Verhulst's first important contribution was Remarks on the law that the population follows in its growth (1838). Earlier, the assumed belief was that an increasing population followed a geometric progression. However, his mentor and mathematician Adolphe Quetelet published a paper suggesting that populations could not grow geometrically. Quetelet believed that some forces tend to prevent this population growth and that they increase with the square of the rate at which the population grows. Verhulst disagreed with Quetelet’s model and instead proposed his own.
In 1838, Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population. He used data from several countries, in particular Belgium, to estimate the unknown parameters. He published a further paper on population growth in 1844 entitled Mathematical research on the law of growth of the population. He showed that forces which tend to prevent a population growth grow in proportion to the ratio of the excess population to the total population. Based on his theory Verhulst predicted the upper limit of the Belgium population would be 9,400,000. In fact the population in 1994 was 10,118,000, but that number includes the effect of immigration, so his prediction looks pretty close. To update these figures, the 2013 population estimate is 10,951,266 (with 90% being Belgian) and the projections for 2020 and 2030 are 11,662,00 and 12,278,000 respectively.
He produced a third important paper on this topic in 1847, namely Second memoir on the law of growth of the population. In this last paper, Verhulst put forward some criticisms of his own model of population growth, and this led to Verhulst's logistic equation being ignored for many years until it was rediscovered with the work of Raymond Pearl and Lowell Reed in 1920.
References
Hakobyan, Hrachya, and Yeva Tigranyan. “Figure 2.3: Pierre- François Verhulst Pierre-François Verhulst Was Born...” ResearchGate, 1 Aug. 2018, www.researchgate.net/figure/Pierre-Francois-Verhulst-Pierre-Francois-Verhulst-was-born-in-1804-in-Brussel-He-get_fig2_292314245.
“Pierre Verhulst - Biography.” Maths History, mathshistory.st-andrews.ac.uk/Biographies/Verhulst/.