I always knew that math had come a long way in the last 200 years, but I never thought that natural history would ever come into it. Until I went to Kevin Lambert’s talk this afternoon on Thomas Robert Malthus’ population principle.
Lambert, of Cal State Fullerton, discussed Malthus’ 1798 essay which argued that populations would always grow faster than their food supply. His argument was based on a comparison between growth rates: the food supply would increase arithmetically, while populations grow geometrically.
This was based on little evidence, and dismissed outright by some. Malthus provided questionable support for the idea that populations would always grow geometrically, and no support at all for his claim that the food supply would grow arithmetically.
In preparing a second edition of his book, Malthus joined two colleagues on an expedition to Norway, Sweden and Russia. There, he collected historical and environmental data–recording notes on the cultures he saw and scientific data like temperatures. He investigated the way the natural environment informed populations and incorporated his observations and reasoning into his arguments.
Lambert argued that this method was typical for researchers of the era. Cambridge mathematician George Peacock also used historical research to formulate his principle of the permanence of equivalent forms. This led to a so-called analytical revolution at Cambridge, establishing the study of algebra and creating space for ideas like imaginary and negative numbers.
Malthus’ work may have helped pave the way for someone like Peacock. It’s stories like these that remind us how far math has come in just a short time. Perhaps in 200 years, mathematicians will be similarly baffled by 21st century research techniques.