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Numerology (known before the 20th century as arithmancy) is the belief in an occult, divine or mysticism relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in words and names. When numerology is applied to a person's name, it is a form of onomancy. It is often associated with astrology and other divination arts.
Number symbolism is an ancient and pervasive aspect of human thought, deeply intertwined with religion, philosophy, mysticism, and mathematics. Different cultures and traditions have assigned specific meanings to numbers, often linking them to divine principles, cosmic forces, or natural patterns.
The term numerologist can be used for those who place faith in numerical patterns and draw inferences from them, even if those people do not practice traditional numerology. For example, in his 1997 book Numerology: Or What Pythagoras Wrought (), mathematician Underwood Dudley uses the term to discuss practitioners of the Elliott wave principle of stock market analysis.
The practice of using alphabetic letters to represent numbers developed in the Greek city of Miletus, and is thus known as the Milesian system. Early examples include vase graffiti dating to the 6th century BCE. Aristotle wrote that the Pythagoreanism, founded in the 6th century by Pythagoras of Samos, practiced isopsephy, the Greek predecessor of Hebrew gematria. Pythagoras was a contemporary of the philosophers Anaximander, Anaximenes, and the historian Hecataeus, all of whom lived in Miletus, across the sea from Samos. The Milesian system was in common use by the reign of Alexander the Great (336–323 BCE) and was adopted by other cultures during the subsequent Hellenistic period. It was officially adopted in Egypt during the reign of Ptolemy II Philadelphus (284–246 BCE).
By the late 4th century AD, following the Edict of Thessalonica in 380 AD and the subsequent enforcement of Nicene Christianity under Theodosius I, departures from the beliefs of the state church were classified as civil violations within the Roman Empire. Numerology, referred to as isopsephy, remained in use in conservative Greek Orthodox circles, particularly in mystical and theological contexts.
Some alchemical theories were closely related to numerology. For example, Arab alchemist Jabir ibn Hayyan (died c. 806−816) framed his experiments in an elaborate numerology based on the names of substances in the Arabic language.
Numerology is prominent in Sir Thomas Browne's 1658 literary discourse The Garden of Cyrus. Throughout its pages, the author attempts to demonstrate that the number five and the related quincunx pattern can be found throughout the arts, in design, and in nature particularly botany.
Some approaches to understanding the meanings of the Qur'an (the book of Muslims) include the understanding of numerical meanings, numerical symbols and their combination with purely textual approaches.
The Mandaeism number alphasyllabary is also used for numerology (Mandaic language: gmaṭ aria). The Book of the Zodiac is an important Mandaean text on numerology.
| A | B | C | D | E | F | G | H | I |
| K | L | M | N | O | P | Q | R | S |
| T | V | X | Y | Z | I | V | HI | HV |
Note that the letters U, J, and W were not commonly considered part of the Latin alphabet at the time.
The first system of English gematria was used by the poet John Skelton in 1523 in his poem "The Garland of Laurel". The next reference to an English gematria found in the literature was made by Willis F. Whitehead in 1899 in his book, The Mystic Thesaurus, in which he describes a system he called "English Cabala".
In 1952, John P. L. Hughes published The Hidden Numerical Significance of the English Language, or, Suggestive Gematria, based on his lecture delivered at Holden Research Circle on July 4, 1952. A system related to the Spiritualist Agasha Temple of Wisdom was described by William Eisen in his two volume The English Cabalah (1980–82).
William G. Gray proposes another system in his 1984 book, Concepts of Qabalah, more recently republished as Qabalistic Concepts. This system includes correspondence attributions of the English letters to the positions on the Tree of Life. Michael Bertiaux described a system called Angelic Gematria in his The Voudon Gnostic Workbook (1989).. Republished as . David Rankine described a system of English gematria using which he calls Prime Qabalah in his book Becoming Magick (2004).
The best known example of "numerology" in science involves the coincidental resemblance of certain large numbers that intrigued mathematical physicist Paul Dirac, mathematician Hermann Weyl and astronomer Arthur Stanley Eddington. These numerical coincidences refer to such quantities as the ratio of the age of the universe to the atomic unit of time, the number of electrons in the universe, and the difference in strengths between gravity and the electric force for the electron and proton. (See also Fine-tuned universe).
Wolfgang Pauli was also fascinated by the appearance of certain numbers, including 137 (a prime number), in physics.
British mathematician I. J. Good wrote:
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