Infinity symbols


John Wallis



Roman Numerals

Of Cones

The modern version of the symbol, looking very much a like a figure eight that has lain down on its side, was first recorded in print in 1655. In De sectionibus conicis (On Conic Sections), John Wallis described cross-sections of a cone using Descarte’s new coordinate geometry. Possibly the second-most important mathematician of his day, after Newton, Wallis had achieved prominence at an early age, appointed a professor geometry at Oxford in 1649 as a reward for his role in deciphering coded Royalist messages during the Civil War (1642-1648). In effect, he was a relative newcomer to the field when De sectionibus conicis was published. But the question remains to this day–did he just make it up?

Of Romans

Although Wallis may have scribed it in a new way, the notion of infinity did not originate with Wallis. In fact, vying for the earliest mention of the word, we find not only the Greeks, circa 400 BC, but also Indian mathematical texts from roughly the same time period. But, as in so many things western, especially western writing, we must turn to the Romans as a potential source for the modern glyph.

The Roman numeral system, still taught in classrooms throughout the world, begins with I for the number one, II for two, and so on. Today, we use M to stand for the number one thousand, but M wasn’t the only way to create that number. Earlier, one thousand was represent by an X in a circle. As it morphed over time, however, it came to resemble something closer to a C followed by a vertical line followed by a backwards C. In addition, as the form morphed, so did the meaning. Formerly a way to write one thousand, the symbol also started to stand in for the notion of ‘a really big number’.

According to many mathematical and historical thinkers, it was this version of one thousand, in terms of meaning and form, that inspired Wallis.

Of Beauty

No matter the inspiration, however, Wallis came up with a winning design. Although the latin word for this shape, lemniscate (ribbon), suggests something of its shape, it isn’t strictly a ribbon (or a mobius strip). Although it twists in the middle, the modern symbol for infinity is also not a knot. Some tattoo designs that incorporate the infinity shape combine it with the ouroborous (the cyclic snake that eats its own tail), twisting the snake circle once in the middle. Still others make a passing reference to it where it is included in classic tarot imagery (see a user contributed example here). One of the best aspects of the symbol, however, especially in terms of tattoos, is its ability to stand alone and stand for so much.

De sectionibus conicis, 1655.
First use of infinity symbol circled in red.