Beyond the gematria of chaim, sixty-eight carries no traditional symbolism; it is a composite number the older systems did not develop. Modern numerology reduces it to five and reads it through that root as a number of change and freedom. Its honest core is the value of the plural life in Hebrew, a genuine but minor thread beside the far better-known chai of eighteen.
A separate and older-claimed system, generally called Chaldean numerology, assigns letters to digits irregularly rather than in Balliett's repeating one-to-nine sequence, and deliberately omits nine from the chart as too sacred to attach to an ordinary letter; its popular billing as a genuinely ancient Babylonian system rests on assertion rather than on any textual evidence that has been traced back that far.
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.