Le-Tacen Olam (עולם לתכן): Establishing the Correct Text in Aleinu
By Mitchell First (firstname.lastname@example.org)
The Jewish obligation of עולם תקון (=improving the world) is widely referred to and it is traditionally assumed that the Aleinu prayer is one of the texts upon which this obligation is based.
This article will show that a very strong case can be made that the original version of Aleinu read עולם לתכן (=to establish the world under God’s sovereignty), and not עולם לתקן (=to perfect/improve the world under God’s sovereignty). If so, the concept of עולם תקון has no connection to the Aleinu prayer.
It is reasonable to assume that Aleinu was already included in the Amidah of Rosh ha-Shanah (=RH) by the time of Rav (early 3rd century C.E.). But no text of Aleinu is included in the Talmud, nor is a text of Aleinu included in any of the classical midrashim. Therefore, we must look to later sources for texts of Aleinu.
When we do, we find that the reading לתכן is found in the text of the RH Amidah in the Siddur Rav Saadiah Gaon (d. 942), and in the text of the RH Amidah in the Mishneh Torah of the Rambam (d. 1204). Moreover, it is found in numerous prayer texts from the Cairo Genizah that include this line of Aleinu. For example, it is found in: 1) a fragment of the RH Amidah first published by Jacob Mann in 1925; 2) a fragment of the RH Amidah first published by Richard Gottheil and William H. Worrell in 1927; 3) a fragment of the RH Amidah first published by Mordecai Margaliot in 1973; and 4) a fragment of Aleinu first published by Mann in 1925. It is found in many other Aleinu prayer texts from the Cairo Genizah as well. (In the fragment of Aleinu first published by Mann in 1925, Aleinu is included in the Pesukei de-Zimra section of the Palestinian shaḥarit ritual.)
Furthermore, the reading לתכן survives in Yemenite siddurim to this day. It was also the reading in the original tradition of the Jews of Persia.
Admittedly, the reading in Europe since the time of the Rishonim has been לתקן. See, for example, the following texts of Aleinu:
- Maḥzor Vitry of R. Simḥah of Vitry (daily shaḥarit and RH);
- Siddur Ḥasidei Ashkenaz (daily shaḥarit and RH);
-Peirush ha-Tefillot ve-ha-Berakhot of R. Judah b. Yakar (RH);
-Peirushei Siddur ha-Tefillah of R. Eleazar b. Judah of Worms (RH); and
-Sefer Arugat ha-Bosem of R. Abraham b. Azriel (RH).
The three main manuscripts of Seder Rav Amram Gaon also read לתקן. But these manuscripts are not from the time of R. Amram (d. 875); they are European manuscripts from the time of the later Rishonim.
Earlier than Maḥzor Vitry, we have circumstantial evidence for the reading לתקן in comments on Aleinu that were probably composed by R. Eliezer b. Nathan of Mainz (c. 1090-1170). Here, in Hamburg MS 153, the following explanatory comment about Aleinu is expressed (without a text of the line itself):
 …בשמך יקראו וכולם מלכותך מתקנים העולם כל ויהיו
Another manuscript also largely composed of the comments of R. Eliezer b. Nathan has essentially this same reading, in two places. Another manuscript, which is probably the Siddur of R. Eliezer b. Nathan, has a similar reading:
 …בשמך יקראו וכולם .במלכותך מתקנים העולם כל ויהיו
Admittedly, it cannot be proven that לתכן was the original reading. But this seems very likely, as לתכן is by far the better reading in the context. This can be seen by looking at all the other scenarios that are longed for in this section:
הארץ מן גילולים להעביר עוזך בתפארת מהרה לראות
י-שד במלכות עולם לתקן /לתכן יכרתון כרות והאלילים
ארץ רשעי כל אליך להפנות בשמך יקראו בשר בני וכל
יכירו וידעו כל יושבי תבל כי לך תכרע כל ברך תשבע כל לשון
ולכבוד שמך יקר יתנו יכרעו ויפולו אלקינו ה׳ לפניך
ותמלוך עליהם מהרה לעולם ועד עול מלכותך את ויקבלו כולם
בכבוד תמלוך עד ולעולמי היא שלך כי המלכות
Beginning with the second line, להעביר, every clause expresses a hope for either the removal of other gods or the universal acceptance of our God. With regard to the first line, properly understood and its mystical and elevated language decoded, it is almost certainly a request for the speedily rebuilding of the Temple. Taken together, this whole section is a prayer for the rebuilding of the Temple and the establishment of God’s kingdom on earth. This fits the reading לתכן perfectly.
It is appropriate that this section of Aleinu is fundmentally a prayer for the establishment of God’s kingdom on earth. Most likely, this section was composed as an introduction to the malkhuyyot section of the RH Amidah.
Moreover, we can easily understand how an original reading of עולם לתכן might have evolved into עולם לתקן, a term related to the familiar term העולם תקון. The term העולם תקון (always with the definite article) is widespread in early rabbinic literature. It is found thirteen times in the Mishnah, and seventeen times in the Babylonian Talmud. The alternative scenario, that the original reading was עולם לתקן and that this evolved in some texts into the unusual reading עולם לתכן, is much less likely.
Finally, the ב of י-שד במלכות seems to fit better in י-שד במלכות עולם לתכן (=to establish the world under God’s sovereignty) than in either of the two ways of understanding י-שד במלכות עולם לתקן. Also, the use of the word עולם instead of העולם and the lack of an את before the object עולם perhaps fit the reading לתכן better. I leave a detailed analysis of these aspects to grammarians.
There is no question that social justice is an important value in Judaism. Moreover, classical rabbinical literature includes many references to the concept of העולם תקון, both in the context of divorce legislation and in other contexts. The purpose of this article was only to show that is almost certainly a mistake to read such a concept into the Aleinu prayer, a prayer most likely composed as an introduction to the malkhuyyot section of the Amidah, and focused primarily on the goal of establishing God’s kingdom on earth. Even if we do not change the text of our siddurim, we should certainly have this alternate and almost certainly original reading in mind as we recite this prayer.
 This essay is a revision of Mitchell First, “Aleinu: Obligation to Fix the World or the Text,” Ḥakirah 11 (Spring 2011), pp. 187-197, available here.
I would like to thank Yehiel Levy for showing me his Yemenite siddur which read לתכן and inspired this research. I would like to thank R. Moshe Yasgur for sharing his thoughts and for always being willing to listen to mine. I would also like to acknowledge the assistance of Dr. Ezra Chwat of the Institute of Microfilmed Hebrew Manuscripts at the Jewish National and Hebrew University Library, and the assistance of Binyamin Goldstein. Finally, I would like to dedicate this article to my beloved wife Sharon, whose name has the gematria of תקון and who needs no improvement.
 The above is how this phrase is usually translated. But The Complete ArtScroll Siddur, p. 161, translates: “to perfect the universe through the Almighty’s sovereignty.” Others adopt this translation as well. See e.g., J. David Bleich, “Tikkun Olam: Jewish Obligations to Non-Jewish Society,” in Tikkun Olam: Social Responsibility in Jewish Thought and Law, eds. David Shatz, Chaim I. Waxman, and Nathan J. Diament, Northvale, N.J.: Jason Aronson, 1997, p. 61.
 One scholar who intuited that the original reading may have been לתכן is Meir Bar-Ilan. See his “Mekorah shel Tefillat ‘Aleinu le-Shabeaḥ,’ ” Daat 43 (1999), p. 20, n. 72.
The articles by Gerald Blidstein and J. David Bleich in Tikkun Olam: Social Responsibility in Jewish Thought and Law assume that the reading is לתקן (see pp. 26, 61 and 98). But the article in this volume by Marc Stern mentions the alternate reading of לתכן, citing R. Saadiah (see p. 165, n. 24).
In 2005, Gilbert S. Rosenthal wrote a detailed article about the concept of tikkun olam throughout the ages and merely assumed that the reading in Aleinu is לתקן. See his “Tikkun ha-Olam: The Metamorphosis of a Concept,” Journal of Religion 85:2 (2005), pp. 214-40.
 The Jerusalem Talmud, at Avodah Zarah 1:2, includes the following passage:
א"ר יוסי בי רבי בון מאן סבר בראש השנה נברא העולם? רב,
דתני בתקיעתא דבי רב זה היום תחילת מעשיך זכרון ליום ראשון וכו'.
A very similar passage is found at J. Talmud Rosh ha-Shanah 1:3 (where the reading is בתקיעתא דרב). The sentence from the liturgy referred to (…זה היום) is from the introductory section to the ten verses of zikhronot. A reasonable inference from these Talmudic passages is that Rav composed (at least) the introductory sections to zikhronot, malkhuyyot and shofarot. Aleinu is part of the introductory section to malkhuyyot. Since the sentence from the introduction to zikhronot quoted corresponds to the present introduction to zikhronot, it is reasonable to assume that their introduction to malkhuyyot corresponded to the present introduction to malkhuyyot, i.e., that it included Aleinu. Admittedly, Rav could have made use of older material in the introductory sections he composed. The fact that Aleinu has been found (in a modified version) in heikhalot literature is some evidence for Aleinu’s existence in this early period, even though the prayer is not specifically mentioned in any Mishnaic or Talmudic source. (Regarding the dating of heikhalot literature, see below.) On the version of Aleinu in heikhalot literature, see Michael D. Swartz,
“ ‘Alay Le-Shabbeaḥ: A Liturgical Prayer in Ma‘aseh Merkabah,” Jewish Quarterly Review 77 (1986-1987), pp. 179-190. See also the article by Bar-Ilan cited above. For parallels in later sources to the two passages from the Jerusalem Talmud, see Swartz, p. 186, n. 20. See also Rosh ha-Shanah 27a.
A statement that Aleinu was composed by Joshua appears in a collection of Geonic responsa known as Shaarei Teshuvah (responsum #44). But the statement was probably a later addition by the thirteenth century kabbalist Moses de Leon. See Elliot R. Wolfson, “Hai Gaon’s Letter and Commentary on ‘Aleynu: Further Evidence of Moses De León’s Pseudepigraphic Activity,” Jewish Quarterly Review 81 (1990-91), pp. 379-380. Statements that Aleinu was composed by Joshua are found in various Ashkenazic Rishonim. This idea seems to have originated with R. Judah he-Hasid (d. 1217). For the references, see Wolfson, pp. 380-381.
There is much evidence that Aleinu could not have been composed by Joshua. For example: 1) Aleinu cites verses from the prophet Isaiah (this will be discussed below); 2) ha-kadosh barukh hu was not an appellation for God in Biblical times; and 3) terms are found in Aleinu that are characteristic of heikhalot literature. Also, for almost the entire Biblical period, the word olam is only a time-related word. It is not until Dan. 12:7 and perhaps Eccles. 3:11 that olam means “world” in the Bible. (Olam definitely means “world” at Ben Sira 3:18.) See Kirsten A. Fudeman and Mayer I. Gruber, “ ‘Eternal King/King of the World’ From the Bronze Age to Modern Times: A Study in Lexical Semantics,” Revue des études juives 166 (2007), pp. 209-242. See also Daat Mikra, comm. to Psalms 89:3 and Eccles. 3:11, and R. Abraham Ibn Ezra, comm. to Ex. 21:6 and Eccles. 3:11. (Based on the language of the book, it is very clear that Ecclesiastes is a late Biblical book See EJ 2:349.)
Regarding the roots תקן and תכן, the root תקן does not appear in Tanakh until the book of Ecclesiastes, and the root תכן probably did not mean “establish” in the period of the Tanakh (see below).
 As noted, Aleinu has been found (in a modified form) in heikhalot literature. There are five manuscripts that include the relevant passage. But four of these only include Aleinu in an abbreviated form and are not long enough to include the phrase עולם לתקן/לתכן. See Peter Schäfer, Synopse zur Hekhalot-Literatur, Tübingen: J.C.B. Mohr, 1981, sec. 551, pp. 206-207. The only manuscript that includes the phrase reads לתקן. But this manuscript, N8128, dates from around 1500. See Ra‘anan S. Boustan, “The Study of Heikhalot Literature: Between Mystical Experience and Textual Artifact,” Currents in Biblical Research 6.1 (2007), p. 137.
Regarding the dating of heikhalot literature, Bar-Ilan (Mekorah, p. 22, n. 85) estimates this literature as dating from the third through fifth centuries. See also more recently his “Shalshelet ha-Kabbalah be-Sifrut ha-Heikhalot,” Daat 56 (2005), pp. 5-37. Moshe Idel, in the second edition of the Encyclopaedia Judaica (11:592) summarizes the subject as follows:
Even though it is quite possible that some of the texts were
not edited until this period [=the geonic era], there is no doubt
that large sections originated in talmudic times, and that the
central ideas, as well as many details, go back as far as the
first and second centuries.
 Siddur Rav Saadiah Gaon, eds. Israel Davidson, Simḥah Assaf, and Yissakhar Joel, Jerusalem: Rubin Mass, 1941, p. 221. Admittedly, the manuscript which forms the basis for this edition was not composed by R. Saadiah himself. It is estimated to date to the twelfth or thirteenth century.
Neither R. Saadiah nor Rambam recited Aleinu in the daily service.
 See the Seder Tefillot Kol ha-Shanah section at the end of Sefer Ahavah. I have looked at the Or ve-Yeshuah edition, the Frankel edition, the Mechon Mamre edition (www.mechon-mamre.org), and the editions published by R. Yitzḥak Sheilat and by R. Yosef Kafaḥ. All print לתכן. (The Frankel edition does note that a small number of manuscripts read לתקן.)
In the standard printed Mishneh Torah, in the al kein nekaveh section of the RH Amidah (Sefer Ahavah, p. 154), only the first ten words were included (up to עוזך), followed by a וכו׳.
 Most of the texts from the Cairo Genizah date from the tenth through the thirteenth centuries. See Robert Brody, The Geonim of Babylonia and the Shaping of Medieval Jewish Culture, New Haven: Yale Univ. Press, 1998, p. 32. All of the texts from the Cairo Genizah that I refer to can be seen at genizah.org.
 See his “Genizah Fragments of the Palestinian Order of Service,” Hebrew Union College Annual 2 (1925), p. 329. The fragment is known as Cambridge Add. 3160, no. 10. When Mann published the fragment, he erroneously printed לתקן.
 See their Fragments from the Cairo Genizah in the Freer Collection, New York: The MacMillan Company, 1927, plate XLIII (opposite p. 194). The fragment is labeled F42 at genizah.org.
 See his Hilkhot Ereẓ Yisrael min ha-Genizah, Jerusalem: Mossad Harav Kook, 1973, p. 148. The fragment is known as Cambridge T-S 8H23.1.
 See above, pp. 324-325. See also, more recently, Ezra Fleischer, Tefillah u-Minhegey Tefillah Ereẓ-Yisre’eliyyim bi-Tekufat ha-Genizah, Jerusalem: Magnes Press, 1988, p. 238. The fragment is known as Cambridge Add. 3160, no. 5. Neither Mann nor Fleischer printed the full text of Aleinu in this fragment.
 See the following fragments: Cambridge Or. 1080 2.46; Cambridge T-S Misc. 10.27, 34.5, and 34.23; Cambridge T-S NS 150.235, 154.19, 155.23, 157.6, 157.37, 157.176, 158.69, 195.55, and 273.38; Cambridge T-S AS 101.64; and New York ENA 1878.8. I was able to find only one fragment that read לתקן: Cambridge T-S NS 122.33. (An interesting fragment is T-S NS 153.64, 8R. Here, only the top line of the letter remains and it is hard to determine if it is the top of a כ or the top of a ק.)
I have been able to examine most of the Aleinu prayer text fragments from the Cairo Genizah. I would like to thank Prof. Uri Ehrlich of Ben Gurion University of the Negev for referring me to them. (Not all of these Aleinu prayer text fragments were long enough to include the relevant passage.)
 Since the second word of the Aleinu prayer is לשבח, it was probably seen as fitting to include this prayer in the Pesukei de-Zimra section. A main theme of both Barukh she-Amar and Yishtabaḥ, as well as of the entire Pesukei de-Zimra, is שבח. See also Ber. 32a: le-olam yesader adam shivḥo shel HKBH ve-aḥar kakh yitpallel.
A Palestinian practice of reciting Aleinu in Pesukei de-Zimra may also explain a statement found in several Rishonim (e.g., Sefer ha-Maḥkim, Kol Bo, and Orḥot Ḥayyim) in the name of Pirkei de-Rabbi Eliezer (a work composed in eighth century Palestine): מעומד לאומרו צריך לכך לשבח בעלינו יש גדול שבח. The statement is obviously not giving an instruction regarding the RH Amidah recited by individuals. Nor does the language of the statement (לאומרו) fit as an instruction to individuals listening to the repetition of the RH Amidah. The recital of Aleinu in a context outside of the Amidah seems to be referred to. (The statement is not found in the surviving texts of Pirkei de-Rabbi Eliezer.)
 See Shelomoh Tal, Nusaḥ ha-Tefillah shel Yehudei Paras, Jerusalem: Makhon Ben Ẓvi, 1981, p. 154 (RH). The Persian-Jewish prayer ritual followed that of R. Saadiah in many respects. At the end of the eighteenth century the Persian Jews were influenced to adopt a Sefardic prayer ritual and their own ritual was forgotten.
 Ed. Aryeh Goldschmidt, Jerusalem: Makhon Oẓar ha-Poskim, 2004, pp. 131 (daily shaḥarit) and 717 (RH). The earliest surviving manuscript of Maḥzor Vitry dates to the first half of the 12th century.
 Ed. Moshe Hirschler, Jerusalem, 1972, p. 125 (daily shaḥarit), and p. 214 (RH). (This work was published by Hirschler together with another work, Siddur Rabbenu Shelomoh; both are integrated into the same volume.) Siddur Ḥasidei Ashkenaz was compiled by the students of R. Judah he-Hasid (d. 1217) and presumably reflects his text of Aleinu. Hirschler’s edition of this siddur is based on several manuscripts.
 Ed. Samuel Yerushalmi, Jerusalem: Meorei Yisrael, 1979, sec. 2, pp. 91-92. R. Judah flourished in Spain and died in the early thirteenth century. Aside from the text of Aleinu in the manuscript published by Yerushalmi including the reading לתקן, it is also clear from the various explanatory comments by R. Judah that he was working with a text that read לתקן.
Ed. Moshe Hirschler, Jerusalem: Makhon Harav Hirschler, 1992, p. 659. R. Eleazar died circa 1230. The text of Aleinu is found in his commentary to the Aleinu of RH. In his commentary on the daily shaḥarit, only the first two words of Aleinu and the last two (timlokh be-kavod) are recorded. In his Sefer ha-Rokeaḥ, his references to Aleinu in both the RH Amidah and the daily shaḥarit are similarly very brief.
 Ed. Ephraim E. Urbach, Jerusalem: Mekiẓei Nirdamim, 1963, vol. 3, pp. 469-470. Sefer Arugat ha-Bosem was composed in 1234, in Bohemia. Aside from the text of Aleinu published here including the word לתקן, it is clear from R. Abraham’s explanatory comment (p. 469, lines 8-9) that he was working with a text that read לתקן.
Other early European texts of Aleinu include the three texts of Aleinu in manuscript Oxford, Corpus Christi College 133 (late twelfth century; daily, RH and one other) and the text of Aleinu in manuscript Cambridge Add. 667.1 (early thirteenth century, daily). The former has לתקן in the first two; the third Aleinu does not include the second paragraph. I have not been able to check the reading in Cambridge Add. 667.1.
 See Seder Rav Amram Gaon, ed. Daniel Goldschmidt, Jerusalem: Mossad Harav Kook, 1971, p. 142.
 Ibid., introduction, pp. 11-13. A few fragments of the Seder Rav Amram Gaon have been found in the Genizah, but these are very short and do not include our passage.
 This manuscript is generally considered to be largely composed of the comments of R. Eliezer b. Nathan. See, e.g., Urbach, Sefer Arugat ha-Bosem, vol. 4, p. 24 and the facsimile edition of this manuscript published by Abraham Naftali Ẓvi Rot, Jerusalem: 1980, pp. 21-30. The manuscript itself is estimated to have been copied in the fourteenth century (Rot, p. 21).
 See Rot, p. 20a (comm. to RH Aleinu).
 See Alter Yehudah Hirschler, “Peirush Siddur ha-Tefillah ve-ha-Maḥzor Meyuḥas le-Rabbi Eliezer ben Natan mi-Magenza (ha-Ravan),” Genuzot vol. 3, Jerusalem:1991, pp. 1-128. In this siddur commentary (pp. 78 and 114), בשמך יקראו וכלם מלכותך ‘מתקני העולם כל ויהיו is found in the commentary to daily Aleinu in shaḥarit, and בשמך יקראו וכלם מלכותך מתקנין העולם כל ויהיו is found in the commentary to RH Aleinu. (One should not deduce from this manuscript that R. Eliezer b. Nathan recited Aleinu daily in shaḥarit.)
 See Siddur Rabbenu Shelomoh, p. 212 (commentary on RH Aleinu). Hirschler published this work as the siddur of Shelomoh b. R. Shimson of Worms (1030-1096), but it is probably that of R. Eliezer b. Nathan. See, e.g., Avraham Grossman, Ḥakhmei Ashkenaz ha-Rishonim, Jerusalem: Magnes Press, 2001, pp. 346-348.
 Gershom Scholem recognized long ago that Aleinu includes several terms that are not only post-Biblical, but are characteristic of heikhalot literature. See his Jewish Gnosticism, Merkabah Mysticism and Talmudic Tradition, New York: Jewish Theological Seminary, 1965 (2d. ed.), pp. 27-28. He points to the terms yoẓer bereshit, moshav yekaro, and shekhinat uzo. Meir Bar-Ilan (Mekorah, p. 8) also points to the term adon ha-kol. All of this suggests that Aleinu was composed by someone with some connection to heikhalot literature, or composed at a time after terms originating in heikhalot literature came to be in normative rabbinic use. This explains how Aleinu easily came to be borrowed into heikhalot literature. Due to the common terms, the authors of this literature probably saw Aleinu as a text “related to their own hymnology.” Scholem, p. 28.
In heikhalot literature, Aleinu is found in the singular form לשבח עלי, as a prayer of gratitude purportedly recited by R. Akiva on return from a safe journey to heaven. See the article by Swartz referred to above. (R. Akiva and R. Ishmael serve as central pillars and chief mouthpieces in this pseudepigraphic literature. See EJ 11:591, 2d. ed.).
Meir Bar-Ilan, Mekorah, pp. 12-24, argues that Aleinu originated in heikhalot literature in the singular, and was then changed to the plural and borrowed into the RH service. I disagree, as do many others. (Bar-Ilan does not claim that Aleinu originated as this prayer of gratitude purportedly recited by R. Akiva. This would be very unlikely. There are too many themes in Aleinu that are out of context and extraneous under the assumption that Aleinu originated as this prayer of gratitude.)
 The idiom is based on verses such as Psalms 78:60-61 (צר ויתן לשבי עזו ותפארתו ביד) and 96:6 (במקדשו ותפארת עז), and Isaiah 60:7 (אפאר תפארתי ובית) and 64:10 (ותפארתנו קדשנו בית). This interpretation is probably implicit in the commentary of R. Judah b. Yakar. On לראות מהרה בתפארת עוזך, he writes:
פני לראות ונזכה ,אתה עוזמו תפארת כי (שם על =) ע״ש
.אפאר תפארתך ובית דכתי׳ המקדש בית בתפארת ולראות שכינה
See the Peirush ha-Tefillot ve-ha-Berakhot of R. Judah b. Yakar, part II, p. 91. R. Judah’s statements are adopted by R. David Abudarham in his commentary to the Aleinu of RH. See also R. Shemtob Gaugine, Keter Shem Tov, Kėdainiai, 1934, p. 104. Unfortunately, this interpretation of the phrase תפארת עוזך has generally been overlooked. Numerous are scholars who have written that the prayer includes no request for the Temple’s rebuilding.
Scholem (p. 28, n. 18) notes the following passage found in other heikhalot texts:
.עזו בתפארת ומבורך הדרו במושב שמו ברוך
The parallel to הדרו מושב strongly suggests that עזו תפארת represents the physical Temple in this passage. For heikhalot texts with this passage, see Mordecai Margaliot, Sefer ha-Razim, Jerusalem, 1966, pp. 107-09, and Martin Samuel Cohen, The Shi‘ur Qomah: Texts and Recensions, Tübingen: J.C.B. Mohr, 1985, pp. 173 and 175.
 The use of the root תכן to mean “establish” does require some explanation. In Tanakh, the root תכן means to “weigh,” “examine,” “measure,” or “place in order.” (At Psalms 75:4, עמודיה תכנתי, the root is commonly translated as “establish,” but even here it probably means something like “properly apportion” or “place in order.” See, e.g., the commentary of S. R. Hirsch.) תכן with the meaning “establish” is not found in the Mishnah or Tosefta. But תכן may mean “establish” in the Dead Sea text 4Q511: שנה למועדי תכן (DJD VII, p. 221), and perhaps in other Dead Sea texts as well.
In paytanic literature, an early use of the root תכן to mean “establish” is found in the piyyut Emet Emunatkha (תכנת עולמך ימים בששת כי). This piyyut is preserved in the Siddur R. Saadiah Gaon (p. 110) and in several Genizah fragments. It has a tetrastichic structure (as does Aleinu), and is generally viewed as a pre-classical piyyut, i.e., a piyyut from the late Tannaitic/early Amoraic period. See, e.g., Ezra Fleischer, Ha-Yotzrot be-Hithavutam ve-Hitpaḥutam, Jerusalem: Magnes, 1984, p. 55, n. 47. The Academy of the Hebrew Language, in its Historical Dictionary Project database (Ma’agarim), estimates the date of composition of this piyyut as the late second century C.E.
In the Musaf Amidah for shabbat, תקנת, not תכנת, may be the original reading. See, e.g., Siddur R. Saadiah Gaon, p. 112 and the Genizah fragment quoted by Fleischer, Tefillah u-Minhegey Tefillah, p. 52. (For more sources on this spelling issue, see Maḥzor Vitry, ed. Goldschmidt, p. 199, n. 1.)
Probably, the use of the root תכן to mean “establish” arose based on the usage of the root at Psalms 75:4, or perhaps from the words תכן and תכון (both from the root כון) found numerous times in the Tanakh (Jer. 30:20; Ps. 89:22, 93:1, 96:10, and 141:2; Prv. 12:19 and 20:18; I Kings 2:12; I Ch. 16:30; and II Ch. 8:16, 29:35, 35:10 and 35:16).
 Aside from the fact that the theme of the section fits as an introduction to verses of malkhuyyot, the section ends with four words from the root מלך:
ותמלוך עליהם מהרה לעולם ועד עול מלכותך את ויקבלו כולם
.בכבוד תמלוך עד ולעולמי היא שלך כי המלכות
I have little doubt that the first section of Aleinu (which includes the words melekh malkhei ha-melakhim and malkeinu) was also composed at the same time. This is contrary to the view of many scholars who point to the two separate themes in the two sections as evidence of different authors. Aleinu is a short prayer, and in the earliest texts of Aleinu there is no division into sections. Therefore, our presumption should be one of unitary authorship. Close analysis of the verses cited shows that both sections quote or paraphrase from the same chapter of Isaiah (45:20: u-mitpallelim el el lo yoshia and 45:23: ki li tikhra kol berekh tishava kol lashon; there are quotes and paraphrases of other verses from chapter 45, and from 44:24 and 46:9 as well.) This strongly suggests that both sections were composed at the same time. (I have not seen anyone else make this point.) Terms characteristic of heikhalot literature are found in both sections as well.
While it cannot be proven that Rav (early third century) was the author of Aleinu, it has been observed that “in some of Rav’s homilies a tendency to a certain mystical thinking is discernible.” See EJ 13:1578 and the citations there, as well as the following statement of Rav at Ber. 55a:
.יודע היה בצלאל לצרף אותיות שנבראו בהן שמים וארץ
Also, several Talmudic passages record Rav’s authorship or contribution to the texts of other prayers. Most of these passages are collected at Ismar Elbogen, Jewish Liturgy: A Comprehensive History, tr. Raymond P. Scheindlin, New York: Jewish Publication Society and Jewish Theological Seminary, 1993, pp. 207-208. Most relevant is Ber.12b where the הקדוש המלך and המשפט המלך changes for the Ten Days of Repentance are recorded in the name of Rav.
Most recently, Ruth Langer is another who believes that the evidence points to authorship of both paragraphs of Aleinu around the period of Rav. She writes:
In literary style, it is consistent with the earliest forms of rabbinic-era
liturgical poetry from the land of Israel…
See Langer, "The Censorship of Aleinu in Ashkenaz and Its Aftermath," in Debra Reed Blank, ed., The Experience of Jewish Liturgy: Studies Dedicated to Menahem Schmelzer, Leiden and Boston: Brill, 2011, pp. 148-149. As Langer points out, although Rav gained prominence in Babylonia, he had also been a student of R. Judah ha-Nasi in Israel.
 העולם תקון was the correct classical term, even though it has now been replaced in popular parlance by
עולם תקון. Rosenthal, p. 214, n. 1.
 Rosenthal, p. 214, n. 1. It is also found eight times in the Jerusalem Talmud and four times in the Tosefta. Most of the time, the term is used in the context of the laws of divorce, but it is found in other contexts as well (e.g., Hillel’s enactment of prozbol at M. Gittin 4:3). Rosenthal suggests that the concept originated in the context of the laws of divorce, and was later expanded into the other contexts. See Rosenthal, pp. 217-219.
 Admittedly, the root תקן can often be translated as “established.” But in many of these cases the context is that of establishing a legal ordinance or procedure, and a better translation would be “instituted.” On the other hand, the musaf Amidah for festivals includes the phrase בתקונו ושמחנו (the subject being the beit ha-mikdash) and this seems to be an example of the root תקן meaning “establish” in a non-legal context. Another such example is the phrase…ממנו לו והתקין found in one of the sheva berakhot (Ketubbot 8a).
Nevertheless, I strongly believe that לתכן was the original reading in Aleinu. It is easily understandable how an original reading of עולם לתכן might have evolved into עולם לתקן; the reverse scenario is much less likely. Moreover, R. Saadiah’s text in the musaf Amidah for shabbat read שבת תקנת. Yet he recorded לתכן in Aleinu.
 As mentioned earlier, in the reading עולם לתקן, there are two ways to translate במלכות: “under the sovereignty” or “through the sovereignty.” If the translation is “under,” establishing a world under the sovereignty of God is a simpler reading than perfecting a world under the sovereignty of God. If one wants to advocate for the translation “through,” it requires investigation whether the prefix ב could have been used to mean “through” in the Tannaitic and Amoraic periods.
 See, e.g., Shatz, Waxman, and Diament, eds., Tikkun Olam: Social Responsibility in Jewish Thought and Law, and Jacob J. Schacter, “Tikkun Olam: Defining the Jewish Obligation,” in Rav Chesed: Essays in Honor of Rabbi Dr. Haskel Lookstein, ed. Rafael Medoff, Jersey City: Ktav, 2009, vol. 2, pp. 183-204. For some citations to Biblical verses on justice, see Rosenthal, p. 215, n. 2.
 R. Chaim Brovender suggested to me that after Aleinu shifted to becoming primarily a daily prayer, reciting a statement about perfecting/improving the world would have been seen as appropriate. By the twelfth century, Aleinu was being recited as a daily prayer in shaḥarit in parts of France (see above, n. 16) and probably in parts of Germany and England as well. (For Germany, see above, n. 17, and for England, see Ms. Oxford, Corpus Christi College 133.)
The recital of Aleinu in the evening prayer in Europe is a slightly later development. For some early references to this practice, see Sefer ha-Minhagot of R. Moshe b. R. Shmuel of Marseilles (early thirteenth cent.), published in Kobeẓ Al Yad 14 (1998), pp. 81-176, at p. 103, and Kol Bo, sec. 11, citing R. Meir of Rothenberg (thirteenth cent.). The recital of Aleinu in the afternoon prayer is a later development.
Regarding the recital of Aleinu as a daily prayer in Palestine, see above, n. 14.