Final answer:
Thomas Malthus posited that population grows geometrically, while food supply increases arithmetically, leading to a potential crisis where population outstrips food production, known as the Malthusian catastrophe.
Step-by-step explanation:
In 1798, Thomas Malthus published An Essay on the Principle of Population, arguing that the population increased at a geometric rate, while the means of substinence, primarily food, grew at an arithmetic rate. This fundamental difference in growth rates meant that population growth could potentially outrun food production.
According to Malthus, populations double geometrically (1, 2, 4, 8...), whereas food production increases arithmetically (1, 2, 3, 4...), eventually leading to a situation where the population exceeds the production of food, resulting in a Malthusian catastrophe, characterized by famine, disease, and war as populations fight over dwindling resources.