Was Rav Hai Gaon a kabbalist?

Question

In a recent conversation a friend indicated that Rav Hai Gaon was a well known kabbalist, while another friend pointed to his teshuva [teshuvas ha'geonim 115] to indicate that he was not [and wikipedia seems to agree]. Is there any source that supports the claim that he was in fact a kabbalist?

Answer 1

Shirei Musar Haskel - שירי מוסר השכל - page 39 mentions that in a few locations - (see for example) in the Peirush of Rabbi Moshe Butril to Sefer Yetzira he mentions Rav Hai Gaon as the author of Sefer Hakemitza which is on Kabala.

Answer 2

From Shadal's Vikuach:

The author: And what will you say when you see in sefer haEmunot to the aforementioned Rabbi Shem Tov, and also in the sefer haPardes to Rabbi Moshe Cordevero z"l, many secrets in the wisdom of the kabbalah which Rav Chamai Gaon wrote, and which Rav Hai Gaon wrote to Rav Paltoy Gaon?

The guest: I say that Rav Chamai did not exist and was never created, and no Sage whose name was such is found amongst the Geonim nor amongst the Rabbanan Savorai, and not even amongst the Sages of the Talmud. And I say that Rav Paltoi Gaon died 100 years before Rav Hai Gaon was born. {!!} And therefore I saw that one should not rely much upon the testimony of the sages of kabbalah, for they are established liars.

The author: The mouth of he who speaks falsehood should be shut up! And what will you say when you see with your eyes that Rav Hai Gaon, z"l, in the letter written in sefer Ein Yaakov (masechet Chagiga, perek Ein Doreshin) mentions Heichalot Rabbati and Heichalot Zutrati...

(The conversation then continues.)

It seems that kabbalists ascribed various kabbalistic writings to Rav Hai Gaon. As such, one should take great care before assuming any late ascription to be correct.

To cite Wikipedia:

His attitude toward the Kabbalah is determined by his conservative standpoint. Its elements, as far as they can be traced back to the Talmud, he considered to be true. When the inhabitants of Fez made inquiries regarding the proportions of God,[37] he answered, as one of the signers of the responsum, that God is above any corporeal qualification and that the Talmud forbids the public discussion of these things.[38] His answer to the question regarding the interpretation of the Talmudic tradition that four men entered paradise is interesting, and has caused much discussion.[39] He refers to the opinion of various scholars that specially favored persons could attain, by means of castigation and the reciting of psalms, to an ecstatic state in which they might behold the heavenly halls ("hekalot") as vividly as if they really had entered them. Contrary to his father-in-law, Samuel ben Hofni, gaon of Sura, he followed former scholars in deeming it not impossible that God should reveal the marvels of heaven to the pious while in this state of ecstasy.[40] But all the elements of the later Kabbalah not found in Talmudic tradition, as the belief that miracles could be performed with the names of God, he designated as foolishness not credited by any sensible man.

The best characterization of Hai is given by Steinschneider;[41]: "Certain Kabbalistic pieces were ascribed to him; but in truth he was no mystic in the usual sense of the word. In fact he fought against superstition. He was an orthodox Jew, in possession of general culture, but hostile to deeper philosophical research."

In terms of the Sefer HaKemitza, ascribed to Rav Hai Gaon in the accepted answer, see this thread at Bechadrei Chareidim:

בויקיפדיה מובא כי רב האי גאון חיבר ספר בקבלה הנקרא " ספר הקמיצה " . אך מחיפוש בגוגל מצאתי מאמר בספר היובל לר"ב לוין בו כתוב שציטוטים המובאים אצל ר"מ בוטריל בשם "ספר הקמיצה" הם בדויים.

My translation:

"In Wikipedia is brought that Rav Hai Gaon composed a kabbalah sefer called Sefer HaKemitza. However, from a Google search, I found a statement in the Sefer HaYovel for R"B Lion in which was written that the quotations brought by Rabbi Moshe Butril in the name of the Sefer HaKemitza are made up."