A line of poetry
The classic statement of the Roman preference for odd numbers is a half-line in Virgil’s Eclogues: numero deus impare gaudet, usually translated “the god delights in an odd number”. It comes from the Eighth Eclogue, in a song sung by a speaker who is performing a love charm. In the passage the charm is built from threes: threads of three colours, repeated three times, knots tied in sequence. The line serves as a short justification for this pattern.
Two points about the verse are worth stating plainly. First, it is a line of poetry in a ritual scene, not a Roman law or a formal doctrine. It shows that the idea was familiar enough for a poet to use as a proverb, but it does not tell us how many Romans acted on it or how strictly. Second, the context is magic rather than state religion, and that matters, because the surviving evidence for Roman religion and for Roman magic does not always point the same way.
The Pythagorean background
The idea that odd numbers are special has a Greek philosophical background. Aristotle reports that the Pythagoreans drew up a list of ten pairs of opposites, in which odd stands with limit, one, right, male and light, and even stands with the unlimited, plurality, left and female. How much of this goes back to Pythagoras himself is uncertain, since the reports come from later writers, but the table of opposites is the best-known form of the idea.
A Pythagorean argument for the oddness of limit comes from the way numbers were pictured as arrangements of dots. Adding odd numbers in sequence to a single dot makes a square: 1 plus 3 is 4, plus 5 is 9, plus 7 is 16. Each result is a square, an orderly and complete shape. Adding even numbers in sequence, 2 plus 4 plus 6 and so on, gives oblong shapes, such as 2 times 3 or 3 times 4, which were counted as less regular. This visual picture helps explain why odd numbers could be linked with order and limit. The broader outlook belongs to what is often called Pythagorean number philosophy, and the best-known emblem of that school is the Pythagorean tetractys, a triangle of ten points.
None of this shows that odd numbers are lucky. It shows that some Greek thinkers assigned odd numbers a favoured place in a system of opposites, and that such a system could later be absorbed by writers working in Latin.
Roman practice: what is documented
Later Roman writers did describe odd numbers as having a special status, though they are not always consistent. A frequently cited example is the Roman calendar. Before the reform of Julius Caesar, the year had 355 days, and its months were of 29 or 31 days, both odd, except for February with 28. Adding up four months of 31, seven months of 29 and February’s 28 gives 124 plus 203 plus 28, which is 355. Some later authors say that this arrangement reflected a belief that odd numbers were fortunate and that the even-numbered February was the unlucky month, associated with rites of purification and the dead. These accounts were written long after the calendar was set up, so they are better read as Roman explanations than as proof of the original reason. Practical astronomical reasons for the lengths of months are also possible.
Odd numbers also appear in ritual repetition. Spells, prayers and ceremonies in the ancient world often involve threefold repetition, as in Virgil’s passage, and thrice-repeated actions are a common feature of Greek and Latin literature. Three is both odd and a number with its own long history in folk narrative, so it is hard to separate a preference for odd numbers from a preference for three.
Several claims found in modern popular writing go beyond what the sources support. One is that Romans avoided even numbers in all gifts, banquets or offerings. Another is that there was a rule for sacrifices based on parity. Some ancient authors do connect odd numbers with heavenly gods and even numbers with gods of the underworld, but this is stated by particular writers, and it should be called a tradition recorded by them rather than a universal Roman practice.
Later echoes
The belief did not end with antiquity. A well-known later echo is the saying that things come in threes, treated in its own article on the rule of three. Another is the custom, reported in Russia and some neighbouring countries, of giving flowers in odd numbers to the living and even numbers at funerals. Such customs are interesting as survivals, but it is hard to say whether they descend from ancient practice or arose independently.
The English phrase “lucky seven” has a different pedigree. Seven in antiquity had its own religious weight, based on planets and days, and that does not need Roman ideas about odd numbers to explain it. Odd numbers are not unlucky everywhere either: Chinese tradition often favours even numbers for celebrations, which shows how local this kind of rule is.
What to take from it
The odd-number belief is a good example of how a philosophical classification can turn into a proverb. A Greek system of opposites, a Latin poet’s phrase and a few later explanations of the calendar combine into the compact idea that the god is pleased by odd numbers. The line is real and well attested. The wider claim that Romans lived by a rule of odd-number luck is much less certain, and the careful statement is that some Romans, in some contexts, held the idea, and that they could cite a respected poet and an older philosophical tradition when they did.