Nobody knows why John Wallis picked a sideways eight to mean infinity
In 1655 the English mathematician John Wallis put a looping figure into print as the sign for infinity and never said why. Ranchers call the same shape a lazy eight, Vikings carved it on combs, and camera lenses use it to mark focus set at the far horizon.
Wallis introduced the symbol in De sectionibus conicis, his work on conic sections. Guesses about its origin abound. It might be a variant Roman numeral, perhaps the sign for 100 million, which looked like the same loop inside a rectangular frame, or the old CIↃ notation for 1,000. Or it might descend from a lower-case omega, the final letter of the Greek alphabet. The shape is also called a lemniscate, after figure-eight curves studied in algebraic geometry, and it was a decorative motif long before Wallis. Printers did not always have it: one Leonhard Euler paper used something like a sideways, mirrored S, and O–O has served as a stand-in.
In mathematics the sign usually signals a process that keeps going, a variable growing without bound in a sum or a limit, rather than a finished infinite quantity. It can also denote an actual infinite object, such as the extra point that closes up a projective line or compactifies a space, or an infinite measure. Other infinities get their own notation: aleph-null for the size of the natural numbers, and omega for the smallest infinite ordering.
Outside mathematics its meanings multiply. Bookbinders use it to flag acid-free paper that will last, and it is probably among the oldest markings on cameras. Modern mystics merge it with the ouroboros, the snake swallowing its tail, sometimes drawn as a figure eight. Vladimir Nabokov scattered figure eights through The Gift and Pale Fire, whose title poem praises the miracle of the lemniscate, and James Joyce and David Foster Wallace used the shape too.
Designers love it. The Métis flag, flown by Canada's Métis people since the early 19th century, centres on it, with readings ranging from an unending future for a culture blending European and First Nations roots to echoes of dances and Celtic knots. A rainbow version stands for the autism rights movement, and Bakelite, Fujitsu, Cell Press and the 2022 FIFA World Cup have all worked it into logos.
Source: Infinity symbol
