Updated: Update: 2021.01.03
Sham•aiꞋ
A cursory glance at Shamai's anti-Roman orientation has been cause to mistaken him for a Pᵊrush•iꞋ. However, the enmity between the Tzᵊdōq•imꞋ reliance on Antiochus Epiphanes and Syrian Hellenism if conspicuous in Samuels, Ruth (1967). Pathways through Jewish history. Ktav Pub. House. p. 98. OCLC 899113. "Antiochus IV spared no pains to defend his empire against the growing power of Rome. Proud of his Greek ancestry and determined to unite all the peoples of the ancient world under his rule, he had sought to force his subjects to follow the Greek way of life to the exclusion of all others." Antiochus became a political hostage of the Roman Republic following the Treaty of Apamea in 188 BC.
Zugot?
Hileil Sr., the Babylonian
Shimon Ben Gamlieil House of David Maseket-Kilayim 9
1st generation Tanaim:
?? - 80 CE Yokhanan Ben-Zakai ? - 80CE (succeeded as Av Beit Din by Yehoshua Ben-Khananiyah and as Nasi by Gamlieil Jr. c. BCE 10 – 70 CE
argument for Shamai being Perushi solely based on MISconception that Tzedoqim rejected Oral Law--when it's PROVEN that their Oral Law was Hellenist Beit ha-Miqdash Kohanic Oral Law committed to the Tzedoqim "Book of Decrees" in the identical same manner in which the Perushim codified Perushim Oral Law in Talmud.
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https://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/bet-hillel-and-bet-shammai
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Tzedoqim dominated the Sanhedrin until middle 1st century CE; the same is claimed for Shamai
Hileil as descendent of King David:
Wilhelm Bacher, Jacob Zallel Lauterbach, Simeon II. (Ben Gamaliel I.), Jewish Encyclopedia [1]. N.b.: the Jewish Encyclopedia speaks of "his grandfather Hillel", in a generic sense, but the genealogical sequence was Hillel the Elder > Simeon ben Hillel > Gamaliel the Elder > Simeon ben Gamliel.
(Hebrew) "תלמוד ירושלמי - מסכת כלאיים, פרק ט".
Yitzhak Buxbaum (2008), The Life and Teachings of Hillel, Jason Aronson, Incorporated, p. 304, ISBN 978-0742565876, "Ketubot 62b says that Rabbi Judah the Prince, was a descendant of King David on his mother's side, via Shefatiah, David's son by his wife Avital, and Hillel [the Elder]."
(table, bottom of https://en.wikipedia.org/wiki/Yohanan_ben_Zakkai)
Like the first, and all subsequent ZūgꞋōt, Shamai's discipleship under the previous ZūgꞋōt, אַבְטַלְיוֹן and שְׁמַעְיָה, demonstrates that he was taught by both Tzᵊdōq•imꞋ and Pᵊrush•imꞋ leaders. This is no basis to assume that Shamai was a Pᵊrush•iꞋ.
A priori, the Hellenist "Temple" Kohanic—Tzᵊdoq•iꞋ—Complement of the last pair of the ZūgꞋōt could only have been Sham•aiꞋ.
The single worst self-affliction of Jews globally today is the ever-constricting cult-constraints of many rabbis' unwitting Hellenist-Tzᵊdōq•imꞋ-assimilations, propagating the Tzᵊdōq•imꞋ strictures of Beit Sha•maiꞋ on the misconcieved, false assumption that he was a Pᵊrush•iꞋ. Then, simply always requiring adherence to all opinions of the Sages implies requiring adherence to the strictest opinion. As the world progresses, additional rulings generate additional opinions, the strictest of which must be imposed – an endlessly constricting boa; often ignorantly magnifying long-held a•vōd•âhꞋ zâr•âhꞋ of Assyrian, Babylonian and Hellenist assimilations. This process inescapably grows arrogance, intolerance, increasing exclusivity, extremist "We're holier than thou!" cult-fanaticism. This endlessly results in their abuse of Jews, even Orthodox Jews, who reject their cult perceived superior-holiness. The cult then loathes, derides and abuses – both verbally and with physical violence like spitting and stoning – everyone outside their cult, even Israeli-Jews Police and Orthodox Jews, calling them "goyim" idolaters and "Nazis". Such a world view inescapably fragments the Jewish community with internal schisms – which, in modern Israel, routinely produce all of the six things hated by י‑‑ה and defined by Him as to•eiv•otꞋ (Mi•shᵊl•eiꞋ ShᵊlōmꞋōh 6.16-19).
This is why the Sha•maiꞋ mindset not only unavoidably failed in the 1st century CE, but, along with their self-implosion, destroyed YᵊhudꞋâh in its entirety!
It is why those who place tunnel-visioned faith in the precision and strictness of their own exercise of rituals can never find spiritual satisfaction by their own hands; nor can they ever comprehend any other "fix" beyond requiring even stricter precision in their exercise of the rituals in which they place their faith – idolatry/a•vōd•âhꞋ zâr•âhꞋ!
It is also why (in addition to other economic and social factors) there is no possibility that Ultra-Orthodox/Kha•reid•imꞋ, especially in our modern scientific age, can avoid inexorable disillusionment and implosion. The precursor temblors of this implosion are already occurring on an almost daily basis.
The answer is not in the rituals and ceremonies per se at all, no matter how strictly precise one makes the incantations or the proportions of mingled handwavium. These are superstitious, zombie-cult strayings into prohibited Dark Ages magic. It isn't that you're not doing the rituals right. There's no magic in the rituals so you can never get the rituals to work no matter how precise and strict you become! Ultimately, Dark Ages superstition and magic fail.
The answer is in recalling, reliving and celebrating with family and friends the shared events of our history that the rituals – even when the rituals themselves may be imprecise or flawed – commemorate, events in which י‑‑ה has rescued us and brought us to where we are, instilling confidence and rejoicing that י‑‑ה remains with us and continues accompanying us into the future. And that's RibꞋi Hi•leilꞋ. It has never been the endless quest for ever-stricter, ever more minutely-precise quantium of always-constricting vain rituals in the futile hope of getting the prohibited-magic of Sha•maiꞋ bare-rituals to work.
Ironically, even an ignorant "non-Jew" who is doing his best to keep Tor•âhꞋ and goes camping with his family in a geodesic pop-up tent specifically to celebrate Suk•otꞋ can reap the joy and spiritual satisfaction that Ultra-Orthodox, whose faith is in the strictness of their own precision of executing rituals, will never experience.