Hillel II (Hebrew: הלל נשיאה, Hillel the Nasi), also known simply as Hillel held the office of Nasi of the ancient Jewish Sanhedrin between 320 and 385 CE. He was the son and successor of Judah III. He was a Jewish communal and religious authority, circa 330 – 365 CE. He is sometimes confused with Hillel the Elder, as the Talmud sometimes simply uses the name "Hillel".
In two instances his name is quoted in connection with important decisions in Jewish law: in one, Jose ben Abin expounds to him a law; in the other, Hillel cites a mishnah to establish a law (Yer. Ber. ii. 5a; Yer. Ter. i. 41a).
He is traditionally regarded as the creator of the modern fixed Jewish calendar. It first appears in a responsum of R. Hai Gaon (early eleventh century) cited by R. Abraham bar Hiyya in his Sefer Ha'ibbur, written in 1123. The topic of that responsum is the 19-year cycle for leap-year intercalations, so the most that can be inferred from that attribution is that Hillel was responsible for the adoption of that cycle for the regulation of the distribution of leap-years.
Actually there is in fact much more that can be inferred from this citation. The citation explicitly refers to the year that this event happened, 670 of the Seleucid era, which corresponds to 358/9 CE. The Molad of Tishrei for that year 4119 would be Sat 23 hours and 233 parts. Under the Gregorian calendar this would be Sat, Sept 20, 0358 17:12. Rosh Hashanah would have begun Friday evening but not before, according to lunar science, a very bright Old Moon will rise Friday morning at 4:11 AM, an hour and 34 minutes before sunrise. The significance of this can be found in the Talmud Rosh Hashanah 25a.
Scholars who have studied the history of the Jewish calendar are in general agreement (and there is much evidence for this in the Talmud itself and in other rabbinic sources) that in practice, the evolution of the calendar into its present form was a gradual process spanning several centuries from the first to about the eighth or ninth century CE. The champion of the view that the calendar was developed in the eighth or ninth century CE is Sacha Stern. This quote is from page 184-5 of his book Calendar and Community: A History of the Jewish Calendar
“Of far greater importance, however, is a much later document from the Cairo Geniza: a letter of a Babylonian exilarch - one of the main leaders of the Rabbanite community - with detailed calendrical instructions for the year 835/6 CE. The letter reveals that Passover (15 Nisan) in that year was due to occur on a Tuesday; whilst according to the present-day rabbinic calendar, it should have occurred on Thursday. According to the exilarch, the setting of Passover on Tuesday was dictated by a concern to avoid visibility of the new moon before the first day of the month. This concern does not exist in the present-day rabbinic calendar. Once discovered and published in 1922, the exilarch's letter proved beyond doubt that almost five hundred years after R.Yose and 'Hillel the Patriarch', then fixed calendar in its present-day form had still not been instituted."
Rabbinic tradition ascribes to him an enactment which proved of incalculable benefit to his coreligionists of his own and of subsequent generations. The Jewish calendar is lunisolar. That is, its months are synchronized with the phases of the moon, but its average year length approximates the mean length of a solar year. The purpose of the latter is to ensure that the festivals, all of which occur on fixed dates of the lunar months, are also observed each year in the seasons designated for them in the Bible. To ensure the former, occasional intercalations of a day in a month were required; to ensure the latter, occasional intercalations of an extra month in a year were required.
These intercalations were determined at meetings of a special committee of the Sanhedrin. But Constantius II, following the precedents of Hadrian, prohibited the holding of such meetings as well as the vending of articles for distinctly Jewish purposes.
The entire Jewish community outside the land of Israel depended on the calendar sanctioned by the Judean Sanhedrin; this was necessary for the unified observance of the Jewish holidays. However, danger threatened the participants in that sanction and the messengers who communicated their decisions to distant congregations. Temporarily, to relieve the foreign congregations, Huna ben Abin once advised Rava not to wait for the official intercalation: When you are convinced that the winter quarter will extend beyond the sixteenth day of Nisan declare the year a leap year, and do not hesitate (R. H. 21a). But as the religious persecutions continued, Hillel decided to provide an authorized calendar for all time to come, though by doing so he severed the ties which united the Jews of the diaspora to their mother country and to the patriarchate.
The emperor Julian the Apostate was gracious to Hillel, whom he honored on a number of occasions. In an autograph letter to him, Julian assured him of his friendship and promised to ameliorate further the condition of the Jews. Before setting out for the war with Persia, Julian addressed to the Jewish congregations a circular letter in which he informed them that he had "committed the Jewish tax-rolls to the flames," and that, "desiring to show them still greater favors, he has advised his brother, the venerable patriarch "Julos", to abolish what was called the 'send-tax'".