Madam, - As Christmas approaches, it is salutary to reflect that we do not know the exact year or day of Christ's birth.
The two Nativity accounts in the Gospels - Matthew 2:1-2 and Luke 2:1-20 - contradict each other. Matthew presents the familiar story of Herod, who died in 4 BC. If this story is true, then Christ was born in 4 BC or earlier. But Matthew's account of Christ is suspiciously like Lord Raglan's myth pattern of the Hero, and must be regarded as a pious fiction.
Luke is much more promising. He says that Christ was born when Publius Sulpicius Quirinius - who is an otherwise attested Roman politician - was Roman governor of Syria in 6 AD. The census Luke mentions cannot be a general census of the Roman Empire, but the historian Josephus states that Quirinius conducted a census of Judea in 6 AD. Accordingly, a birth date for Christ in 6 AD is very probable.
The date of December 25th is heavily over-determined; it is close to the winter solstice; it is close to the Roman festival of Saturnalia; it is the birthday of the sun god. As so often, Christian feasts are superimposed on existing pagan ones. - Yours, etc,