Augustus
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I don't know whether Paganism had any influence on Christmas, but I've always wondered whether Judaism may have had some influence on the choice of the 25th day of December.
Because the first day (not first evening) of Chanukah falls on the 25th of the Hebrew month of Kislev.
Christmas Eve and the first evening (eve') of Chanukah each fall on the 24th day of their respective months.
Coincidence? Or deliberate?
It is connected to Judaism, but the Christmas date is via Easter and thus Passover.
25 Dec is 9 months after the Annunciation which was early Christians viewed as happening on 25 March for theological reasons.
Thanks to the paschal table of Hippolytus, we can be sure that 25 March played an important role in Christian chronology as the date of the crucifixion since at least the early third century, thus laying the ground for an influential calendrical tradition in the Western church.
Since it was established early on that Jesus died on 25 March, and since it was also assumed, based on Luke’s annunciation narrative, that he was born in winter, early Christians would have been tempted to re-interpret 25 March as the day of conception, whereby they could then arrive at 25 December as the date of the nativity. The attractiveness of 25 March and 25 December – the vernal equinox and the winter solstice – as cardinal points in the life of the Savior was naturally further underscored by a widespread solar symbolism, which viewed Christ as the “sun of righteousness” and is clearly present in chronological texts such as De pascha computus and the aforementioned On the solstices. CP Nothaft - Early Christian Chronology and the Origins of the Christmas