When we encounter the symbol ∞ on a piece of jewelry, a tattoo, or an equation, we are dealing with a sign whose shape has a precise material history. The English mathematician John Wallis first introduced it in his work De sectionibus conicis, published in 1655. This gesture was not trivial: it allowed infinity to be given an operational status, usable in calculations, distinct from the theological and philosophical debates that had surrounded the notion since antiquity.
The word lemniscate comes from a ribbon, not a formula
We often refer to the “lemniscate” to denote the figure-eight curve that represents infinity. The reflex would be to seek the origin in pure mathematics. In reality, the term comes from the Latin lemniscatus, “ornamented with ribbons”, itself derived from the Greek lemniskos, which referred to the decorative ribbons tied to the crowns of victors in ancient Rome.
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This lineage changes the perspective. Before being a geometric abstraction, the figure-eight was a concrete object: a ribbon that crosses itself. When tracing the meaning and origin of the infinity symbol, this visual and artisanal dimension of the knotted ribbon sheds light often absent from usual presentations.
The transition from the physical ribbon to the mathematical curve occurred gradually. Jakob Bernoulli formalized the lemniscate as an algebraic curve at the end of the 17th century, but the shape already existed in the collective imagination long before it was given an equation.
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Bernoulli’s lemniscate and other figure-eight curves: distinct tracings
A common trap is to believe that “lemniscate” refers to a single curve. In practice, several figure-eight curves bear this name, each defined by different geometric properties and equations. Bernoulli’s lemniscate is the best known, but it is not the only one.
This detail has a concrete consequence when using the symbol ∞ in a technical context. The curve drawn freehand on a board or engraved on a pendant does not necessarily correspond to Bernoulli’s polar equation. We are dealing with a family of shapes, not a unique tracing.
Why the distinction matters
For a jewelry designer or a tattoo artist, the symmetry of the tracing varies depending on the chosen reference curve. Bernoulli’s lemniscate has central symmetry and two axes, resulting in a regular appearance. Other variants produce uneven loops, sometimes sought after for their organic character.
Feedback varies on this point: some artisans favor strict geometry, while others prefer a freer tracing that strays from mathematical rigor.
Infinity symbol in mathematics: separating calculation from metaphysics
Before Wallis, discussing infinity fell under philosophy or theology. In Aristotle’s view, one distinguished between “potential” infinity (an endless process) and “actual” infinity (a completed totality, deemed impossible). For medieval Christian thinkers, only God could be truly infinite.
The introduction of the sign ∞ brought about a practical rupture. By assigning a symbol to infinity, Wallis made it manipulable in series and limits. One could write that a quantity “tends towards ∞” without having to settle the debate on the actual existence of infinity.
A tool, not a philosophical answer
This separation remains relevant today. In mathematical analysis, ∞ is not a number: it is a notation that indicates behavior. When we write a limit, we describe a trend, not a value reached. The symbol ∞ describes a movement, not a destination.
This particular status explains why mathematical infinity and symbolic infinity (that of jewelry, tattoos, popular culture) do not quite refer to the same thing, even if they share the same tracing.
Infinity symbol in everyday life: tattoo, jewelry, logo
The meaning of the infinity symbol far exceeds the realm of mathematics. In everyday life, it is found in three main areas:
- Tattoos, where it often represents a permanent emotional bond (love, friendship, memory of a loved one). The simple tracing makes it an adaptable motif for the wrist, neck, or ankle.
- Jewelry (bracelets, pendants, rings), where it conveys an idea of unity and balance between two people or two forces. The sign lends itself to compositions with names or stones.
- Logos and visual identities, where the figure-eight shape suggests perpetual motion, continuous transformation, or connection between two worlds.
In each case, the strength of the symbol lies in its graphic simplicity. A single continuous line, with no beginning or end, legible at all scales. This economy of means explains its longevity and ability to transcend cultures.
Symbolic meaning according to context
The meaning attributed to ∞ changes depending on who wears it and why. In a spiritual context, it is associated with balance between opposites (masculine/feminine, matter/spirit). In a romantic context, it evokes duration and fidelity. In a creative context, it signals limitless exploration.
None of these interpretations is “the right one.” The symbol functions as a receptacle: each bearer projects their own meaning onto it.
Why the symbol ∞ retains its visual power
The infinity symbol combines two rare properties. On one side, a verifiable technical origin (Wallis, 1655, then Bernoulli for the curve). On the other, a universal symbolic charge that does not depend on any language or religion.
This dual nature allows it to circulate in both a mathematics textbook and on a bracelet given as a birthday gift. The ancient ribbon, the algebraic curve, and the tattoo motif share the same shape, but each tells a different story. The tracing remains identical; what changes is the perspective we have on it.