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45

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Origin 1908 to 1965

Forty-five is triangular, the sum of 1 through 9, and equals 3 x 3 x 5. It is also the total of all nine cells of the three-by-three magic square, whose rows each sum to 15. That square is the Lo Shu of Chinese tradition, associated with a legend of markings on the shell of a turtle emerging from the river Luo, and it is the oldest magic square known. Forty-five's own symbolic use is slight; its real interest is as the sum of the first nine digits, which is why every multiple of nine has a digit sum that reduces to nine. In digit-reduction numerology it reduces to 9.

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
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
Modern Numerology
Reduction in the Modern System
The modern system reduces every number above nine by adding its digits: 4 + 5 = 9. Whatever the system says of 45 it therefore says of 9, 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)
Attestation
Meaning in the Attesting SourceSourced to the subject's own account
Agrippa gives Saturn the smallest of the planetary squares, three by three, holding the numbers one to nine. Each row, column and diagonal adds to fifteen and the whole square to forty-five, which is also the sum of the first nine numbers. 3Tradition: Renaissance planetary magic (Agrippa, Three Books of Occult Philosophy)
Learn More
The Number of Adam

Forty-five is nine times five, a triangular number equal to the sum of one through nine, and reduces to nine. In Jewish gematria it is the number of Adam, whose name, aleph, dalet, mem, totals one, four and forty, making forty-five, so the number stands for humankind. Lurianic Kabbalah gives it a further and central role: of the ways the Tetragrammaton can be spelled out letter by letter, the expansion whose total is forty-five is called Mah, and it is associated with Adam and with the work of cosmic repair, tikkun, the rebuilding of the shattered vessels of creation. Forty-five thus carries the weight of the human being as the agent of restoration in the Kabbalistic scheme.

Cheiro's 1926 Book of Numbers assigns forty-five the reading already given to twenty-seven, the Sceptre, authority, power and command earned through the productive intellect; the two numbers share a digital root of nine, forty-five by four plus five and twenty-seven as three cubed, so the compound number carrying the gematria of Adam and the Lurianic Name in Jewish mysticism also carries, in the wholly separate American tradition, the same authoritative reading already given above to twenty-seven. In chemistry, unconnected to gematria or Kabbalah, forty-five is the atomic number of rhodium, one of the rarest and most valuable of the precious metals, named for the Greek rhodon, rose, after the rose-coloured salts its compounds form in solution.

Forty-Five in the Bargaining of Abraham

The number appears in one of the most striking passages of Genesis, where Abraham bargains with God over the fate of Sodom, asking whether the city will be spared for fifty righteous men and then, step by step, lowering the number, forty-five, forty, thirty, twenty, ten, in a dialogue on the arithmetic of mercy. Forty-five is the second figure in that descent, the fifty less five. As a triangular number, the sum of the first nine integers, forty-five also has the tidy structure that number-mystics prize, and its reduction to nine ties it to completion. Its firmest traditional content, though, is the gematria of Adam and the Lurianic Name of forty-five.

Florence Campbell's 1931 Your Days Are Numbered and Juno Jordan's 1965 systematisation both preserved Cheiro's Sceptre reading for forty-five without alteration, one of several cases in this family of articles where a number's deep Kabbalistic weight, the gematria of Adam, the Lurianic expansion of the Name, and its comparatively thin twentieth-century American reading, borrowed wholesale from a lower number, sit side by side with no awareness of one another in either source. Forty-five is also a Kaprekar number: squared, it gives two thousand and twenty-five, which splits into twenty and twenty-five, and the two parts sum back to forty-five itself, a self-referential property shared by only a handful of numbers.

Cross-Tradition Connections

Disciplines That Use This

Numerology, Disciplines

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. Three Books of Occult Philosophy
Heinrich Cornelius Agrippa, Llewellyn, 1533View the Source
Encyclopaedia Judaica, 2nd edition
Michael Berenbaum and Fred Skolnik (eds.), Macmillan Reference USA, 2007s.v. Gematria (Adam = 45); the Name MahView the Source
The Hebrew Bible (Tanakh)
Anonymous (multiple authors)Genesis 18:24-28View the Source
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