What is infinity? In life and mathematics alike, it is an abstract concept referring to something that is endless and limitless. Philosophers and mathematicians of yore, from ancient Greeks like Plato and Aristotle to Renaissance thinkers such as Isaac Newton and Galileo, had tackled this subject, only to be baffled by its seemingly unresolvable contradictions and paradoxes.
It wasn’t until the latter part of the 19th century that the idea of infinity was defined. In 1874, German mathematician Georg Cantor (1845–1918), the inventor of set theory, not only published the first proof of the existence and nature of infinity, but he also showed that multiple infinities—some larger than others—existed.
As March 3 marked the 175th anniversary of Cantor’s birth, it is a good time to note that the very notion of infinity is an enduring enigma. The concept of endless continuity—not just in the mathematical sense, but in the philosophical as well—is still puzzling. Is it, as Aristotle believed, potential rather than real? And is it possible for us to believe in infinity without actually being able to measure it?
We often say that there is an infinite supply of something. This could refer to intelligence and human ingenuity, for instance, or natural resources like solar power, wind, and energy, in general. Which of them are truly boundless and which are finite? Even the great Albert Einstein has pondered this question, famously quipping, “Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.”
We don’t know whether Cantor has ever offered an opinion on this subject beyond a mathematical one, but one thing is sure: when it comes to questions about infinity, there is no end in sight!