Malthus made this mistake. He thought that food supply could only increase arithmetically, whereas population must increase geometrically. He thought the result would always be more people than could be fed, with mass starvation and misery resulting. He was wrong about both the food supply and the population, as are present-day alarmists who speak of the future world "drowning in people" and call for urgent steps to limit population.
Humankind's ability to produce food has increased beyond anything Malthus could have envisaged. Improvements in agriculture, in developing higher yield grains and in better animal husbandry have all enabled more food to be produced per acre. The Green Revolution saw new crop strains combined with better agricultural management produce a huge increase in yields. Genetically modified crops now offer the prospect of crops bred to be drought tolerant, salt-water tolerant, pest resistant and self-fertilizing, and offer a second Green Revolution with not only higher yields per acre, but crops that can prosper on previously infertile land.
Far from increasing out of control, population growth is levelling off. As countries become richer, families do not need as many children to augment the family budget through their work. As people are able to fund social services, they no longer need children to support them when they grow old. The emancipation and education of women has played a significant role in this change. Population growth in rich countries levels off. In most European countries it is now negative, offset in some like the UK only by immigration.
The world's future population, predicted by some to reach 50 billion within a century, now is on course to level off at about 10 billion, and then to decline. The combination of more abundant food and a significant reduction in population growth suggests that the latter-day Malthusians and doomsayers are wrong. Population seems to be levelling off within a limit that modern day technology can provide adequate food for.