The infinity symbol, a beautiful concept captured in the simple elegance of an endless double loop, seems the perfect encapsulation of the concept it represents. So, where does it come from?
The infinity symbol is often also called a lemniscate, a word also used in mathematics to describe any figure 8 shaped curve found in algebraic geometry. The word lemniscate was coined by Jacob Bernoulli 1693 in his study of the shape, and he derived it from the Latin Lemniscus, which means a ribbon. That means the infinity symbol can be seen as an endless band of ribbon which perfectly represents the endless reach of infinity, and also is the shape of a lemniscate. The two have become interchangeable, so it seems an ideally reasonably explanation for its use, except…
The man credited with introducing the infinity symbol was John Wallis, a 17th century mathematician who had used it in his De Sectionibus Conicis in 1655, nearly 40 years before the word lemniscate was being used. John Wallis never gave the reason behind his choice of the symbol, but there are several theories:
The first is that some cultures would use a large number to substitute for infinity. The Chinese used 10,000, while the Romans often used 1,000 as a substitute. The Roman numeral for 1,000 can be written as either CƆ or CIƆ, so one theory is that the infinity symbol is just a stylized extension of this roman numeral.
The second is that Wallis derived it from the Greek letter Omega (Ω). Omega is the last letter of the Greek alphabet and the symbolism as applied to the infinity symbol has Biblical roots. In the Book of Revelation God says: “I am the Alpha and the Omega, the Beginning and the End, the First and the Last” (Revelation 22:13) meaning that Omega is the endpoint of everything. So, Omega is the ultimate end of everything, making a symbolic representation of the span of infinity.
The third reason is entirely pragmatic. When De Sectionibus Conicis was published, all typesetting had to be done by hand; creating a new symbol for a published text was not an easy matter. The infinity symbol however circumvented the problem by being a figure 8 laid on its side, thus allowing it to be printed without creating a whole new physical typesetting block.
We will never know why John Wallis chose the symbol he did. It could be one of a combination of the three theories described above, or maybe something completely different. Personally, I like that these three theories situate the infinity symbol in historical, spiritual and practical vantage points, a nod to its eternal nature.