The Origin and Significance of the Infinity Symbol

An illustration of the infinity symbol

Hooked on Infinity: A Glimpse into the Concept

The infinity symbol, “∞”, is easily recognized even by those with limited mathematical knowledge. While it has been used to represent the concept of infinity since the 17th century, its historical roots stretch much further back. In this article, we’ll uncover the fascinating origins of the mathematical symbol for infinity and its connection to various fields.

Defining Infinity: A Limitless Concept

In mathematics, infinity refers to something without an end or limit. For instance, numbers are considered infinite because the sequence continues indefinitely. Represented by the symbol “∞”, infinity is immeasurable and not a real number. Although primarily an idea without an end, it can occasionally be utilized as a number, as in the operation ∞ + 1 = ∞.

Tracing the Roots of the Infinity Symbol

The infinity symbol, or lemniscate (derived from Latin “lēmniscātus” and Greek “λημνίσκος”), is connected to not only mathematics, but also astronomy, spirituality, and philosophy. Its origins are uncertain and often linked to religion and alchemy. Many believe it originated from a lemniscate curve resembling a closed loop, symbolizing a bond between the divine and human realms.

John Wallis: Introducing Infinity to Mathematics

English philologist and mathematician John Wallis wrote “De Sectionibus Conicus” in 1655, where he distilled the concept of infinity into the symbol “∞”. This marked the beginning of the infinity symbol’s use in mathematics from the 17th century onwards. Wallis employed the symbol to denote a quantity that is infinitely large or boundless. The symbol is derived from the Latin word “infinitas”, meaning “limitless” or “unlimited”.

Decoding Wallis’s Choice: Hypotheses on the Infinity Symbol

John Wallis never explained his choice of symbol for infinity, leaving room for conjecture. Two primary hypotheses have gained prominence:

  1. Roman Numeral Thousand: Some believe Wallis’s choice was based on the Roman numeral for one thousand, “CIƆ”, as it represented a large number.
  2. The Greek Ouroboros Snake: Hailing from Greek and Egyptian cultures, the Ouroboros Snake depicts a serpent biting its tail, forming a never-ending circle similar to the modern infinity symbol.

Bernoulli’s Lemniscate and the Infinity Symbol

Bernoulli’s Lemniscate is a curve that, when graphed, produces an image resembling the infinity symbol. Despite its association with the symbol, John Wallis is credited with introducing the infinity symbol in mathematics. Historically, the “∞” symbol was linked to alchemy and religion but was not applied to mathematics until the 17th century.

The Lasting Legacy of Infinity

John Wallis’s introduction of the infinity symbol in the 17th century solidified its place as a fundamental notation in mathematics. Representing a never-ending quantity, the symbol has become an essential part of mathematical language. Though Wallis never documented the reason for his choice of symbol, the fascinating conjectures surrounding its origins only add to the intrigue of this enigmatic mathematical concept.

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