Mathus. "An Essay on the Principle of Population", 1798. The rate of population grows exponentially, while natural resources do not. He wasn't totally right, but his general argument has merit. And what he wrote is nothing new. it goes back at least 2000 years.
In reality, barring a cosmic event, "Life finds a way".
When we outgrow Earth, we will find cheap way to send our trash into space. When we run out of food, we will develop new methods to production. Almost anything can be synthesized. And if it can't, well then society will find a way to stay in balance. People won't spend resources to keep people alive and equilibrium will return. Whether that's medical, or a rampant disease, or monetary, or "you can pay half the poor to kill the other half". In some way, equilibrium will return when this is a major problem in say 100 years.
That being said, the biggest problem isn't the rate of birth. It's how long people live. Far less people die from disease, malnutrition, war, etc than ever. Resources (basically money to feed, cloth, and medicate) to keep people living from age 65-100 when they don't contribute to society are staggering. No, don't run off and kill all the old people. But it's a fact. Our society no longer looks as death in passive terms, so we do everything we can to keep people alive, and in the long run that may lead to some not so ideal ways to keep everything in equilibrium.