# Infinity symbol
The infinity symbol (∞) is a mathematical sign shaped like a horizontal figure eight, introduced by the English mathematician John Wallis in 1655 to signify an infinite number and now one of the most widely recognized symbols in mathematics.[1](https://mathshistory.st-andrews.ac.uk//HistTopics/Infinity/) In algebraic geometry the same shape is called a [lemniscate](https://www.edgepedia.org/lemniscate), though the symbol and the mathematical curve it resembles have separate histories.[2](https://www.divinityatlas.com/articles/infinity-symbol-the-lemniscate-and-a-mathematicians-mark)
| Key fact | Detail |
|---|---|
| First printed use | John Wallis used ∞ in *De sectionibus conicis* (1655) and again in *Arithmetica infinitorum* (1656)[1](https://mathshistory.st-andrews.ac.uk//HistTopics/Infinity/) |
| Wallis's wording | Cajori records the Latin phrase *Esto enim ∞ nota numeri infiniti*, "let ∞ be the sign of the infinite number"[3](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf) |
| Adoption | The symbol came into use in the calculus at the beginning of the eighteenth century[3](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf) |
| Lemniscate curve | Described mathematically by Jacob Bernoulli in a 1694 paper in *Acta Eruditorum*, where he named it *lemniscus*, Latin for a hanging ribbon[2](https://www.divinityatlas.com/articles/infinity-symbol-the-lemniscate-and-a-mathematicians-mark) |
| Unicode encoding | U+221E INFINITY, present in the standard since Unicode 1.1[4](https://www.unicode.org/versions/Unicode1.1.0/appI.pdf) • [5](https://www.unicode.org/charts/PDF/U2200.pdf) |
| Emoji form | ♾️ approved in Unicode 4.1 (2005) as "Permanent Paper Sign" and given emoji presentation in Emoji 11.0 (2018)[6](https://emojipedia.org/infinity) |
## Origin with John Wallis
John Wallis (1616–1703), born in Ashford, England, was a mathematician and clergyman who contributed to infinitesimal calculus, number theory, and cryptography.[7](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html) He introduced the sign ∞ to signify infinite number in *De sectionibus conicis* in 1655, and used it again in *Arithmetica infinitorum* of 1656.[1](https://mathshistory.st-andrews.ac.uk//HistTopics/Infinity/) • [3](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf) The same sources credit Wallis, in 1657, with also introducing fractional power notation.[8](https://www.nku.edu/~longa/classes/mat305/resources/www.math.tamu.edu/~dallen/masters/infinity/infinity.pdf)
**Adoption was gradual.** Although Wallis introduced the symbol in the seventeenth century, its use spread over the following centuries; Cajori's *A History of Mathematical Notations* records that the symbol entered the calculus at the beginning of the eighteenth century, and today it is integral to mathematical notation across science and engineering.[3](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf) • [7](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html)
**Possible precursors.** The German mathematics teacher Karl Menninger (1898–1963) reported in *Number Words and Number Symbols* that at one time 100,000 was the "last" number known to the Romans, and that it was denoted by ∞ enclosed under a ∩, a usage attested on a tablet from the archaeological record.[9](https://www.artofmathematics.org/sites/default/files/books/theinfinite_0.pdf) Whether this older mark influenced Wallis is not settled by the sources; what is documented is Wallis's own introduction of the sign for infinite number in 1655.[3](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf)
## The lemniscate curve
The symbol is often conflated with the lemniscate curve, but the two have separate histories. The curve was described mathematically by [Jacob Bernoulli](https://www.edgepedia.org/jacob-bernoulli) in a 1694 paper in *Acta Eruditorum*, some forty years after Wallis had put a similar-looking mark to an unrelated use. Bernoulli named it *lemniscus*, Latin for a hanging ribbon, for its resemblance to a looped ribbon lying on its side.[2](https://www.divinityatlas.com/articles/infinity-symbol-the-lemniscate-and-a-mathematicians-mark) In geometry, a lemniscate is a unicursal plane curve defined from two given points, the foci, separated by a distance of 2d; the name derives from the Latin *lemniscatus*, "decorated with ribbons".[7](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html)
The curve matters in mathematics beyond its shape: the lemniscate belongs to the family of curves that helped give rise to the study of elliptic functions, profoundly important mathematical objects.[9](https://www.artofmathematics.org/sites/default/files/books/theinfinite_0.pdf) A related figure-eight shape appears in nature and observation: the analemma, the curve traced by the sun's position in the sky when observed from a fixed point at the same time each day over a year, resembles a figure eight.[7](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html)
## Infinity in mathematical notation
The symbol ∞ is not the only notation mathematics uses for infinity, and modern usage distinguishes several concepts the single sign can stand for. In set theory, [Georg Cantor](https://www.edgepedia.org/georg-cantor)'s cardinal numbers measure the sizes of infinite sets: the smallest infinite cardinal is \( \aleph_0 \) (aleph-null, written with the first letter of the [Hebrew alphabet](https://www.edgepedia.org/hebrew-alphabet)), the natural numbers are the finite ordinals, and \( \omega \) denotes the order type of their standard ordering.[10](https://plato.stanford.edu/entries/set-theory/basic-set-theory.html) • [11](https://maths.anu.edu.au/files/introduction_contemporary_mathematics.pdf) The cardinality of the real numbers is uncountable and greater than \( \aleph_0 \), though which cardinal it is remains unresolved.[10](https://plato.stanford.edu/entries/set-theory/basic-set-theory.html) Cantor also recognized, in the unreachability of the totality of all ordinals or cardinals, a notion of "absolute infinity" beyond any single symbol's grasp.[12](https://plato.stanford.edu/entries/infinity/?trk=article-ssr-frontend-pulse_little-text-block)
In everyday mathematical writing, ∞ typically appears in limits and extended number lines, for example as an endpoint of the real line or as a bound in an integral, representing unbounded growth rather than a number that can be operated on like finite values.[7](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html)
## Encoding and popular use
The symbol has long been part of character standards: U+221E INFINITY appears in the Unicode 1.1 character list and in the current Unicode charts.[4](https://www.unicode.org/versions/Unicode1.1.0/appI.pdf) • [5](https://www.unicode.org/charts/PDF/U2200.pdf) A separate character, ♾️, was approved as part of Unicode 4.1 in 2005 under the name "Permanent Paper Sign", originally a symbol for acid-free paper, and was later given emoji presentation as the infinity emoji in Emoji 11.0 in 2018.[6](https://emojipedia.org/infinity)
Beyond mathematics, the symbol's simple design and associations with endlessness have made it a popular emblem in fashion and accessory design, most commonly in jewelry and tattoos.[13](https://www.dictionary.com/culture/pop-culture/infinity-symbol) One account of its cultural trajectory describes its path from an unexplained piece of notation to an emblem of eternity and devotion, and to what it calls the most-worn mathematical symbol in the world.[14](https://symbolic.institute/atlas/infinity/)
## References
1. [Infinity, MacTutor History of Mathematics](https://mathshistory.st-andrews.ac.uk//HistTopics/Infinity/)
2. [The Lemniscate, and a Mathematician's Mark, Divinity Atlas](https://www.divinityatlas.com/articles/infinity-symbol-the-lemniscate-and-a-mathematicians-mark)
3. [A History of Mathematical Notations, Florian Cajori](https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf)
4. [The Unicode Standard, Version 1.1, Appendix I: Character List](https://www.unicode.org/versions/Unicode1.1.0/appI.pdf)
5. [The Unicode Standard, Version 17.0, U+2200 chart](https://www.unicode.org/charts/PDF/U2200.pdf)
6. [♾️ Infinity Emoji, Emojipedia](https://emojipedia.org/infinity)
7. [Este es el origen del símbolo del infinito, HuffPost](https://www.huffingtonpost.es/sociedad/este-origenmbolo-infinito-asi-nombre-alternativo-desconocido-hpe1.html)
8. [The History of Infinity, Texas A&M lecture notes](https://www.nku.edu/~longa/classes/mat305/resources/www.math.tamu.edu/~dallen/masters/infinity/infinity.pdf)
9. [Discovering the Art of the Infinite, Art of Mathematics](https://www.artofmathematics.org/sites/default/files/books/theinfinite_0.pdf)
10. [Set Theory: Basic Set Theory, Stanford Encyclopedia of Philosophy](https://plato.stanford.edu/entries/set-theory/basic-set-theory.html)
11. [Infinity, Australian National University lecture notes](https://maths.anu.edu.au/files/introduction_contemporary_mathematics.pdf)
12. [Infinity, Stanford Encyclopedia of Philosophy](https://plato.stanford.edu/entries/infinity/?trk=article-ssr-frontend-pulse_little-text-block)
13. [Infinity symbol, Dictionary.com](https://www.dictionary.com/culture/pop-culture/infinity-symbol)
14. [Infinity, Symbolic Institute](https://symbolic.institute/atlas/infinity/)
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*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Numbers and algebra › Arithmetic and number systems › Number systems › Ordinal and cardinal numbers › Cardinal numbers › Aleph and beth numbers and cardinal notation*
*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*
*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*
License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license