Divinity Atlas

Sacred Correspondences
Numbers

57

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Origin 1908 to 1965

Fifty-seven is 3 x 19, not prime, though it is guessed prime often enough to have acquired a nickname: the Grothendieck prime, from the story that Alexander Grothendieck offered it when pressed for a concrete example. It has no traditional symbolic use of substance, and the meanings assigned to it in modern systems come from adding its digits rather than from anything in the record. In digit-reduction numerology it reduces to 3.

Facts
Origins
Origin Period
1908 to 1965 1
Origin Period
500 BCE to 300 CE 2
Origin Period
The arithmological reading of the first numbers, one as source, two as division, four as justice, seven as virgin, ten as completion, reaches us through Platonic and Neopythagorean writers of the centuries after Plato. Burkert's finding is that it cannot be traced to Pythagoras himself, whose activity was religious rather than mathematical: the doctrines were credited backwards to him. 2Tradition: Pythagorean and Neopythagorean number lore
Origin Period
The system that gives a number a personality, and a person a number, was assembled in the United States in the first half of the twentieth century out of New Thought material. Balliett's The Philosophy of Numbers appeared in 1908; the chart positions, pinnacles and cycles were added by her successors over the next fifty years. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Place of Origin
The Greek world, and above all the Greek cities of southern Italy where the Pythagorean societies were established; the arithmological literature itself is later and largely eastern Mediterranean. 2Tradition: Pythagorean and Neopythagorean number lore
Place of Origin
The United States, and specifically the New Thought circuit of the north-eastern seaboard; Balliett worked from Atlantic City. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Attributed Author / Compiler
Attributed by the tradition to Pythagoras. Burkert's study is the standard demonstration that the number-doctrines carrying his name are the work of later hands, and that almost nothing in them can be shown to go back to the sixth century BCE. The attribution is recorded because it is what the tradition says, not because it holds. 2Tradition: Pythagorean and Neopythagorean number lore
Attributed Author / Compiler
Mrs. L. Dow Balliett, who published the first version of the modern system in 1908 and to whom Dudley devotes a chapter. What later authors added, the pinnacles, the challenges, the cycles, the personal year, is theirs, and this atlas's own numerology-position entries cite four different authors between 1908 and 1965 for what is presented as one system. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Origin of the Name
Pythagorean numerology is a twentieth-century label. The system it names has no demonstrable descent from Pythagoras, from the Pythagorean societies, or from the ancient arithmological literature; the letter-value chart it rests on was drawn up in the United States after 1900. The name borrows a pedigree, the oldest move in the subject. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Status
Standing as a Comparative Category
Largely abandoned as a comparative category 1
Open Questions
Origin of the Name
Fifty-seven is known in mathematical folklore as the Grothendieck prime, after a story in which Alexander Grothendieck, asked for a prime number to work with, offered fifty-seven. It is not prime; it is three times nineteen. 3Tradition: Mathematical folklore
The nickname is real and in current use among mathematicians. Whether the exchange behind it took place is not established. The tellings disagree about the setting and about the wording, no first-hand account from anyone present has been published, and no contemporary written record of it has been produced.
Modern Numerology
Reduction in the Modern System
The modern system reduces every number above nine by adding its digits: 5 + 7 = 12, then 1 + 2 = 3. Whatever the system says of 57 it therefore says of 3, because it holds no separate doctrine for the higher numbers. The stated exceptions are 11, 22 and 33, which it leaves unreduced and calls master numbers. 1Tradition: Modern name numerology (Mrs. L. Dow Balliett and her successors)
Contested Use
Contested or Appropriated Modern Use
Numerology has been sold since Balliett as a basis for decisions: which name to take, which date to marry on, which house number to buy. Dudley's survey of what numerologists sell is the standard critical account and its finding is blunt, numbers have power over minds, not over events. These entries record what the tradition says, not advice. 1
Learn More
A Composite Without Lore

Fifty-seven is three times nineteen and reduces to twelve and then three. It has no traditional religious symbolism, and the honest treatment is to say so plainly. Its one widely recognised use is commercial: the Heinz slogan of fifty-seven varieties, adopted in 1896, was chosen by Henry Heinz as a memorable figure rather than an accurate count, and it lodged the number in popular culture without giving it any deeper meaning.

Fifty-seven falls outside Cheiro's original 1926 compound-number scheme, which runs only from ten to fifty-two, so this atlas gives it no reading attributed to his book; Balliett's 1908 chart reduces it instead to three, self-expression and sociability in the standard modern keyword list, a reading that predates Henry Heinz's 1896 slogan by more than a decade and has no connection to it, the marketing coinage and the American numerology chart having been devised independently for entirely different purposes. In chemistry, fifty-seven is the atomic number of lanthanum, the element that gives its name to the whole lanthanide series of the periodic table, elements fifty-seven through seventy-one, popularly if imprecisely known as the rare earths. Lanthanum itself was first isolated in 1839 by the Swedish chemist Carl Gustaf Mosander, who named it from the Greek lanthanein, to lie hidden, since it had escaped detection within a supposedly pure sample of another rare-earth compound.

What the Systems Assign

Modern numerology reduces fifty-seven to three and reads it, like all numbers resolving to three, as a figure of expression, creativity and sociability, the three approached through a five of change and a seven of enquiry. This reductive reading is the only symbolic account the number attracts, and it applies a standard set of digit-meanings rather than anything specific to fifty-seven. The candid description is a number famous for a marketing slogan and otherwise without lore.

The digit seven within fifty-seven carries a genuinely mixed reputation in Chinese tradition: it is sometimes read as auspicious, its sound associated with togetherness, but the seventh lunar month is also Ghost Month, Gui Yue, when the gates of the underworld are traditionally held to open, a folk-religious association that makes seven, unlike the consistently favoured six, eight and nine, a digit Chinese numerology treats with genuine ambivalence rather than settled preference. Fifty-seven has a small place in mathematical folklore as the Grothendieck prime: an anecdote holds that the eminent mathematician Alexander Grothendieck, asked to name a specific prime, offered fifty-seven, which is not in fact prime, being three times nineteen, a story mathematicians still tell as an example of how abstract genius and concrete arithmetic do not always keep company.

Cross-Tradition Connections

Disciplines That Use This

The modern numerological system assigns this number a meaning, which is why the atlas records it as a subject in its own right, though this does not endorse what the discipline says about it. This link shows only that the discipline works with this particular number; the readings of the number itself belong to whichever tradition holds them.

Source Numerology: Or, What Pythagoras WroughtUnderwood Dudley
Sources
1. Numerology: Or, What Pythagoras Wrought
Underwood Dudley, Mathematical Association of America (Spectrum series), 1997View the Source
2. Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaos und Platon (Lore and Science in Ancient Pythagoreanism)
Walter Burkert, Harvard University Press, 1962View the Source
3. Comme Appele du Neant, As If Summoned from the Void: The Life of Alexandre Grothendieck
Allyn Jackson, Notices of the American Mathematical Society, volume 51, number 10, 2004View the Source
Numerology: The Romance in Your Name
Juno Jordan, DeVorss, 1965on the reduction of numbers to a root digitView the Source
Open Questions (1 open question)
Did Alexander Grothendieck really offer 57 as an example of a prime number?

The anecdote is very widely told and 57 is called the Grothendieck prime because of it. Its literal veracity is disputed within mathematical folklore, and the tellings do not agree on the setting or the wording.

What would resolve this A first-hand account from someone present, or a contemporary written record of the exchange.
History of mathematics, and oral history of the Grothendieck circle.Allyn Jackson, Comme Appele du Neant, As If Summoned from the Void: The Life of Alexandre Grothendieck
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