Is Malthus correct?

I ponder long and hard on how sustainable is the global food supply model and I was fascinated to read the article in Scientific American. The article states that 210 years ago (1798) Thomas Robert Malthus predicted that "short-term gains in living standards would inevitably be undermined as human population growth outstripped food production, and thereby drive living standards back toward subsistence. We were, he argued, condemned by the tendency of population to grow geometrically while food production would increase only arithmetically".

Jeffrey D. Sachs who wrote this article really struck a cord with me. He suggests that we have been able to address this problem historically with varied health and technological advances and resource availability.

I would argue that moving from horse power (literally) to diesel engine is a geometric advance; moving from non-irrigated to irrigated agriculture is also a geometric advance, but as the advances become arithmetic as we move forward and resources decline per capita can we make another geometric advance in the future? Some say that genetically modified food, high rise food factories and more intensive agriculture will give that geometric advance, but what if they are wrong? What if technology cannot keep pace?  Should we be looking at an alternative model that drives a reduction in demand so that we live within our means?