In 1798, Mathus published a book, called An Essay on the Principle of Population. In it, he describes the Malthusian growth model. He wrote that the growth of the population is exponential. The growth of the food supply however is only arithmetical. This means if there are no limits to the growth of the population, that it will not be possible to produce food for all of them. This is known as Malthusian catastrophe. Malthus wrote during the time of the Manchester School of thought.
The Tory party had paternalistic ideas such as charity for the poor. Malthus said this would not work, and it would only lead to increased numbers of the poor. The theory was developed into Whig economic ideas such as The Poor Law Amendment Act of 1834. Its opponents described the act as "a Malthusian bill designed to force the poor to emigrate, to work for lower wages, to live on a coarser sort of food". The act brought the construction of workhouses despite riots and arson.
By that time the ideas were widespread in progressive social circles. One supporter was the novelist Harriet Martineau whose circle of acquaintances included Charles Darwin. The ideas of Malthus were a significant influence on the inception of Darwin's theory.
According to Dr. Dan Ritschel of the Center for History Education at the University of Maryland,
The great Malthusian dread was that "indiscriminate charity" would lead to exponential growth in the population in poverty, increased charges to the public purse to support this growing army of the dependent, and, eventually, the catastrophe of national bankruptcy. Though Malthusianism has since come to be identified with the issue of general over-population, the original Malthusian concern was more specifically with the fear of over-population by the dependent poor!
One of the earliest critics of Malthusian theory was Karl Marx who referred (in "Capital", see Marx's footnote on Malthus from Capital - a reference below) to it as "nothing more than a schoolboyish, superficial plagiary of De Foe, Sir James Steuart, Townsend, Franklin, Wallace" and others, postulating that progress in science and technology would allow for indefinite exponential population growth.
Many people today still believe that Mathus was right about human population growth getting out of hand.
- Adrian Desmond and James Moore, Darwin (London: Michael Joseph, the Penguin Group, 1991). ISBN 0-7181-3430-3
- Marx's footnote on Malthus from Capital 
- Adrian J. Desmond,  (1989): 126.