75

Seventy-five is three times twenty-five and reduces to twelve and then three. Its scriptural anchor is the age of Abraham when he left Haran at God's call to go to the land he would be shown, stated in Genesis as seventy-five years, so the number marks the beginning of the patriarchal journey and the covenant. Seventy-five appears again in the New Testament, where Stephen's speech in Acts numbers Jacob's household that went down to Egypt at seventy-five souls, following the larger count of the Greek Septuagint against the seventy of the Hebrew text, a discrepancy that has occupied commentators.

In chemistry, seventy-five is the atomic number of rhenium, named after the Rhine, Latin Rhenus, and one of the last naturally occurring stable elements to be identified, in 1925.

Seventy-five factors as 3 x 5^2 and carries 6 divisors in all. Summing its proper divisors gives only 49, short of the number itself, which places it among the deficient numbers in the same classical scheme.

The whole apparatus of digit-reduction numerology is a twentieth-century invention rather than an inheritance from antiquity. Mrs. L. Dow Balliett published the first systematic version, The Philosophy of Numbers, in 1908, fixing the letter-to-number chart still used today and ruling that eleven and twenty-two must stand as master numbers rather than reduce further; her colleague, the physician Julia Seton, is credited with coining the word numerology itself around 1912.

Beyond the age of Abraham's call and the Septuagint count of Jacob's household, seventy-five carries no developed symbolism. Modern numerology reduces it to three and reads it through that root as a number of expression and growth. The number's honest content is the two scriptural figures, one fixing the start of the Abrahamic covenant and one preserving a textual difference between the Hebrew and the Greek Bible.

Florence Campbell, a student of Balliett's, restated and extended the chart in Your Days Are Numbered in 1931, and Juno Jordan, founder of the California Institute of Numerical Research, standardised the modern four-part chart of life path, expression, soul urge and personality numbers in 1965; both writers worked from name and birth date rather than from any older number philosophy.

The genuine Pythagorean number philosophy that this modern chart borrows its name from left no writings of its own: Pythagoras and his early followers taught only by mouth, and what survives of their number theory comes instead through Nicomachus of Gerasa, whose Introduction to Arithmetic of the first century CE became the standard authority for a thousand years, and through Iamblichus, who drew on Nicomachus two centuries later; neither wrote anything resembling a name-and-birthdate numerology.