Evidence of a feast
The earliest literary evidence we have of a date for a celebration of the Nativity of Christ is in the Roman Chronograph of Furius Dionysius Philocalus - sometimes called the Philocalian Calendar - written between 336 and 354 AD. Philocalus was a Christian interested in chronological information.

This document consists of two chronological lists. The first is a list of the consuls of Rome thus indicating a year; the second, entitled Depositio Martyrum, indicates death dates (and so memorial dates) of the more famous Christian martyrs and saints. Among those listed are: Saints Peter and Paul (29th June), St Sylvester (31st December) and African martyrs Saints Perpetua and Felicity (7th March) as well as St Cyprian (16th September). But also included is the Chair of Peter (22nd February). And at the head of this list is an entry: VIII Kal. Ian. Natus Christus in Bethleem Iudeae (“on the eighth day before the Kalends of January {= 25th December} Christ born in Bethlehem of Judea”).

This suggests that a Christmas feast was first celebrated among Christians at Rome between 336 and 354.

True birth date unknown
Although there is evidence during the late second century AD of disputes about different dates of the birth of Jesus – 6th or 10th January, 19th or 20th April, 20th May and 18th November – there is no reliable evidence of an actual birth date.

Writing in his Chronographiai before 221, Sextus Julius Africanus places both the dates of the annunciation and of the passion of Christ on 25th March. This would point to 25th December as a birth date.

The Alexandrian Christian theologian Origen (185-232) stated that “only sinners” celebrate the birthdays of their kings, such as Herod and Pharoah, and that Christians celebrated the death dates of their martyrs as their dies natalis (“birthday into heaven”).

Why 25th December? Two theories
Two sets of hypotheses or theories have been offered to explain why 25th December was chosen as the feast of the Nativity. The first is based on the idea of Sextus Julius Africanus that the date of the conception of Jesus coincided with the date of his death - on 25th March. Add nine months for Mary's pregnancy and you get 25th December. This is called the calculation hypothesis or computationist theory. The other hypothesis is based on the link between the feast of Christmas and the celebration of a pagan feast of the winter solstice of  in honour of the sun god. This is called the history of religions theory.

Computationist theory
Proponents of the computationist theory are: L. Duchesne (1889), H. Engberding (1949) and Thomas Talley (1991). It stems from a tradition about the Hebrew patriarchs, who were supposed to have lived a full number of years, since the perfection of God could not have tolerated the imperfection of fractions! In this belief the patriarchs were said to have died on their birthday!

So in the case of Jesus, if the date of his death was 25th March and the Annunciation also is marked on 25th March, a full nine months would give a birth date of 25th December (or 6th January in the East where the Annunciation is celebrated on 6th April).

An added argument for this theory is the belief that the creation of the world coincided with the spring equinox and so Jesus, the true sun, was generated at the same time.

A weakness of this theory is that there is no clear reason why the conception date of Jesus should be substituted for the birth date in the case of the patriarchs.

The history of religions theory
Advocates of the history of religions theory are: H. Usener (1889), H. Lietzmann, F.J. Dolger (1925) and Bernard Botte (1932). This theory starts from the fact that 25th December was the date of the winter solstice on the Julian calendar.

Add to this five other facts that we know:

• The pagan devotees of the Iranian (Persian) mystery god Mithra introduced his cult into Rome in the third century and celebrated 25th December in his honour as the DIES NATALIS SOLIS INVICTI, “the birth day of the unconquered sun”.
• The popularity of this cult led the emperor Aurelian to proclaim the Sun-God as principal patron of the Roman Empire on 25th December 274 and dedicate a temple to him in the Campus Martius.
• The emperor Constantine was converted to Christianity as a result of his seeing the sign of the cross of Christ in the sky at the Battle of the Milvian Bridge (312).
• At the Council of Nicea (325) major theological disputes with the Arian heresy that had undermined the divinity of Jesus were settled by the Council Fathers declaring that Jesus was of the same substance (Greek homoousios, Latin consubstantialis) with God the Father. This could have been the catalyst that saw the celebration of the divinity and humanity of Jesus in a nativity feast.
• From the early part of the 3rd century AD many Christian writers had been applying the text of the prophet Malachi 3:20 “the sun of justice will rise with healing in its wings” to Jesus and from this time onwards we find the fathers of the church using the winter solstice as an image of the birth of Christ.

These facts certainly set a context in the early years of the 4th century where the emergence of a feast of the birth of Jesus as the real “Unconquerable Sun” does not seem culturally controversial.

An argument in favour of this hypothesis is that “baptising” or appropriating a pagan or civil feast would wean people away from the Roman and Mithraic religions, from the excesses of the pagan Roman Saturnalia (a time of  lighting of candles, exchange of gifts, merrymaking and even licence) which preceded it (17th-19th December) or the civil New Year which followed it (1st January).

An argument against it, however, is that the early Christians consistently defined their identity in opposition to their cultural environment and especially in relation to other religions. However, that argument might have lost some of its validity with the conversion of Constantine, which occurred just before this time.

Syncretistic tendencies may also have played a part. Even in the middle of the fifth century Pope St Leo I (d. 461) was scolding Christians who turned to greet/bow to the rising sun before entering the basilica of St Peter on Christmas Day (PL 54:218). Certainly the comparison between Jesus and the sun expressed in the fathers of he church owed much to the cultural climate and state ideology of late imperial Rome.

Another argument against this position is that Constantine died in 337 at his eastern capital Constantinople, which did not celebrate Christmas until the 380s, and so we should not overrate his influence on the inception of the feast.

Spirituality
Whatever about its origin, certainly the central theme of the Nativity celebration in Rome is the universal saving grace of a share in the divine life of God that is available to all humanity through the incarnation/birth of Jesus. This is clear from the beautiful opening prayer of the Christmas Night Mass as it was celebrated in the Roman Liturgy of the fifth century: This ancient prayer is still the Opening Prayer of the Mass of Christmas Day in the Roman Missal.

O God,
who both wonderfully created the dignity of our human nature
and still more wonderfully restored it,
grant us, we beseech you,
that we may come to share in the divinity of Jesus Christ, your Son,
who humbled himself to share in our humanity.

The prayer celebrates the sacramentality of Jesus’ incarnation: in the baby born at Bethlehem, God shares our human condition so that we can share his divine nature. Some of the fathers of the church saw the mystery of the incarnation as a sacred wedding banquet, a sacrum commercium, uniting divinity irrevocably with humanity.

Pope St Leo I stressed this theme of the "sacred interchange" in his Christmas homilies:

Without detriment, therefore, to the properties of either substance which then came together in one person, majesty took on humility, strength weakness, eternity mortality: and for the paying off of the debt, belonging to our condition, inviolable nature was united with passible nature, and true God and true man were combined to form one Lord, so that, as suited the needs of our case, one and the same mediator between God and men, the man Christ Jesus, could both die with the one and rise again with the other....  Christian, acknowledge your dignity, and becoming a partner in the divine nature, refuse to return to the old baseness by degenerate conduct (Sermo 21).

Perhaps Harry Belafonte put this more simply when he sang:

And man will live for evermore
because of Christmas Day.

Development of the feast in North Africa and the West
A sermon of Optatus of Mileve in Numidia, North Africa (present-day Algeria) gives evidence of an actual Nativity celebration there in the 360s. Optatus uses the gospel text of Herod’s massacre of the innocents to encourage the people to resist the persecution of the emperor Julian the Apostate.

The feast was known in Milan in the time of St Ambrose (d. 397) who wrote several hymns with Nativity themes. The letter of Pope St Siricius (384-399) to Himerius, bishop of Tarragona, Spain (PL 13:1134) shows that Christmas was celebrated in Spain by 384. Earliest accounts of the feast in Gaul are in the calendar of St Perpetuus, bishop of Tours (d. 491) (PL 71:566).

A feast in the East celebrating a divine manifestation
A Christmas feast on 25th December did not develop in the East until the late 4th century. The earliest evidence is from a Sermon of St Basil (329-379) (PG 31:1457-76). In 379 or 380 Gregory of Nazianzus preached a Christmas sermon in Constantinople (PG 36:311-334); he also referred to himself as the originator (or possibly celebrant) of the feast (PG 36:349).

Already in the East there had been a feast of the divine manifestation (epiphania or theophania) of Christ on 6th January, celebrating the baptism of Jesus in the Jordan. This seems to have originated in Egypt and is mentioned by Clement of Alexandria (Stromata 1:21; PG 8:887).

That date may also have been the christianising of a pagan feast, since in the Egyptian calendar the winter solstice and a feast of the sun-god were observed that date. On the night before, pagans of Alexandria commemorated the birth of their god Aeon, supposedly born of a virgin.They also believed that on this night the waters of rivers, especially the Nile, acquired miraculous powers and even turned into wine. Such beliefs could have prompted the addition of the themes of the miracle of Cana, the multiplication of the loaves and the birth of Jesus.

In Syria the feast celebrated the birth, the baptism and the Magi. The Apostolic Constitutions (8.33.8; Funk, DidConst 1:541) forbade work on 6th January because of the manifestation of the divinity of Christ at his baptism.

The existence of this Epiphany/Baptism feast in the East may have been the reason why St. John Chrysostom, preaching in Antioch in 386, had difficulty in persuading his congregation to accept the Nativity feast on 25th December.  It probably seemed to them an imported and alien feast. John resorts to unconvincing spurious arguments: that everyone had always known that the authentic birth date of Jesus was 25th December - affirmed in the census records from the time of Caesar Augustus. Obviously not true!  But he adds an argument from the calculations of the respective birth dates (at the winter and summer solstices) and conception dates (at the spring and autumn equinoxes) of Jesus and John the Baptist (PG 49:351).

We know that a nativity celebration took place in Alexandria on 25th December 432 since on that day we are told that Paul of Emesa gave a Nativity sermon in the presence of St Cyril (PG 77:1433-44).

In Jerusalem, however, the birth of Jesus was celebrated on 6th January (Egeria, Itinerarium 25) until the middle of the 7th century, when 25th December was accepted.

The Armenians alone, even to this day, never accepted 25th December.

After Christmas on 25th December was established in the remainder of the East, the baptism of Jesus was celebrated on Epiphany, 6th January, there. In the West, however, Epiphany was the day on which the visit of the Magi to the infant Jesus was celebrated.

Russia, Serbia, Greece and Mount Athos
Christmas is celebrated in Russia, Serbia and in other conservative Orthodox strongholds like the monastery on Mount Athos in Greece on 7th January. These branches of Orthodoxy did not accept the Gregorian reform of 1683 on which our calendars in the West are based and still hold to the Julian calendar, which is 13 days behind the Gregorian.

Later history of Christmas in Europe and America
By the early Middle Ages Christmas had come to mark the beginning of the calendar year and was celebrated as a civil holiday in Europe. On Christmas Day 800, Charlemagne was crowned emperor of the western Christian empire by Pope Leo III at the third Christmas Mass in St Peter's Basilica.

Much folklore, custom and legend grew up around the feast. There were beliefs that at Christmas all creation stopped, evil lost all its power, and animals and plants bowed down to honour the Saviour. Mystery plays based on Luke 2 involving dialogue with the shepherds developed out of the Mass.

In the areas of Europe where the Reformation took hold, Christmas celebration was more muted. It was altogether forbidden in England during the Puritan period until 1660. In North America, especially in the French and Spanish settlements, celebrations were festive and colourful. New England, due to is Puritan ethos, did not celebrate Christmas until the influx of Irish and German immigrants brought a wealth of Christmas customs such as the manger scene, festive lights and the liturgical observance of the feast.

Conclusion
The appropriation of a feast of the sun-god at the winter solstice is today accepted as the more likely hypothesis for the origin of the celebration of Christmas on 25th December. The symbolism and tone this gives to the feast serve to highlight the divinity of Jesus and the saving implications for all human beings of the mystery that God has taken the human form of a baby in a manger.