The "Singularity" is the idea that once we have built an artificial intelligence that is as good at programming (and thinking and invention in general) as a human, then it will be able to invent a still more powerful machine by itself, which will lead to an explosion in AI capability. (For instance, Deep Thought in the Hitchhiker's Guide series.)
Anyway, today I came across this quote which seems to be the earliest expression of the idea anyone has found yet: The Primitive Expounder in 1847. The author has his tongue-in-cheek, but he is also probably one of the first to worry about allowing calculators in the public schools:
"A Thinking Machine! Yes, we can now have our thinking done for us by machinery! The Editor of the Common School Advocate says—" On our way to Cincinnati, a few days since, we stopped over night where a gentleman from the city was introducing a machine which he said was designed to supercede the necessity and labor of thinking. It was highly and respectably recommended, by men too in high places, and is designed for a calculator, to save the trouble of all mathematical labor. By turning the machinery it produces correct results in addition, substraction, multiplication, and division, and the operator assured us that it was equally useful in fractions and the higher mathematics." The Editor thinks that such machines, by which the scholar may, by turning a crank, grind out the solution of a problem without the fatigue of mental application, would by its introduction into schools, do incalculable injury, But who knows that such machines when brought to greater perfection, may not think of a plan to remedy all their own defects and then grind out ideas beyond the ken of mortal mind!"