Where the infinity symbol came from

Wallis was writing a treatise on conic sections and found himself in a situation familiar to anyone who has to repeat the same long phrase over and over: he constantly needed to say "an arbitrarily large number." He introduced the symbol ∞ and explained exactly one thing - that it denotes infinity. The text says nothing about where the squiggle itself came from.

Guesses came later. The most common one is that it was adapted from the Roman notation for 1,000, CIƆ, which old texts sometimes used to mean "very many" rather than an exact number. Another version is the Greek omega, the last letter of the alphabet, with nothing beyond it. Both are plausible, both impossible to prove: Wallis left no explanation, and all we have are reconstructions by later historians of mathematics.

The figure-eight curve got the name "lemniscate" from Jakob Bernoulli in 1694, and that name is not about eternity either: lemniscus is Latin for a ribbon, the hanging ends of a wreath. The mathematician simply described the shape: a loop like a bow.

The ouroboros, a snake biting its own tail, really is thousands of years older and does indeed mean a cycle. But there is no direct line from it to the ∞ symbol: Wallis never mentions it, and the resemblance between a ring and a figure eight was noticed after the fact. A mystical reading was added in the 19th-20th centuries: a similar figure eight appears in occult books from the mid-19th century, then spread widely with a 1909 Tarot deck, where it hangs above the Magician's head. From there, it made its way onto rings, pendants, and tattoos as a "symbol of eternal love."

Curiously, in mathematics ∞ never became a number. It is still shorthand: a way to write that a quantity grows without limit, not the name of something that exists. And at the end of the 19th century, it turned out that infinities can have different sizes - there are fewer whole numbers than points on a line segment - and separate symbols were needed for those sizes. One figure eight does not cover the whole group.