Tikkun Olam is a great idea. It's just not in Aleinu.

Regarding the correct spelling of le-taken olam in the Aleinu prayer, mistakenly translated in this context as "to repair the world," Mitchell First has written convincingly on this topic. The earliest textual evidence certainly points to לתכן ("to establish") instead of the prevalent לתקן ("to repair").

I would add, however, that the strongest proof for לתכן is contextual rather than from textual variants -- that is, from the Musaf prayer itself and from related biblical verses from which Aleinu's author seems to draw.

The expression לתכן עולם appears to allude to the second Ketuvim verse (Ps. 93:1) in the Malkhuyot section of Musaf: 

ה' מָלָךְ גֵּאוּת לָבֵשׁ לָבֵשׁ יְהֹוָה עֹז הִתְאַזָּר אַף־תִּכּוֹן תֵּבֵל בַּל־תִּמּוֹט

More precisely, לתכן עולם במלכות ש-די is a compound phrase constructed from the last words of that verse -- לתכן עולם follows תִּכּוֹן תֵּבֵל -- combined with the biblical usage תכון מלכות (e.g., I Sam. 20:31; I Kings 2:12), the establishment of a permanent dynasty or kingdom. 

But no matter how you spell the word in Aleinu, the current usage of Tikkun Olam represents a noble effort that, in manageable portions, is much more practical to implement than bringing God's kingdom down to earth. Quite possibly, the two programs are effectively the same.

Postscript:

The biblical Hebrew root תקן appears only in Kohelet, where it means “straighten,” “improve," or "repair." 

However, in Daniel 4:33, we find the Aramaic root תקן used in a different sense; that of "establishing a kingdom" -- as it happens, the very same sense used in Aleinu:

בֵּהּ־זִמְנָ֞א מַנְדְּעִ֣י ׀ יְת֣וּב עֲלַ֗י וְלִיקַ֨ר מַלְכוּתִ֜י הַדְרִ֤י וְזִיוִי֙ יְת֣וּב עֲלַ֔י וְלִ֕י הַדָּֽבְרַ֥י וְרַבְרְבָנַ֖י יְבַע֑וֹן וְעַל־מַלְכוּתִ֣י הׇתְקְנַ֔ת וּרְב֥וּ יַתִּירָ֖ה ה֥וּסְפַת לִֽי׃

There and then my reason was restored to me, and my majesty and splendor were restored to me for the glory of my kingdom. My companions and nobles sought me out, and I was reestablished over my kingdom, and added greatness was given me.  

We also see the Targums using the Aramaic root תקן consistently to translate biblical words with the root תכן or כון. See below from Alexander Kohut's Arukh HaShalem:

Simply put, if confusingly, תקן is the Aramaicized Hebrew (later, the rabbinic Hebrew) form of תכן. The Ashkenazic spelling לתקן in Aleinu is based on the Aramaic translation of the Hebrew תכן -- i.e., "establish” rather than “repair.”

I believe this also explains the word metukan in the Emet Ve-Yatziv prayer, which follows the Aramaicized spelling and should be understood as if it were the biblical Hebrew תכן:

וְיַצִּיב וְנָכוֹן וְקַיָּם וְיָשָׁר וְנֶאֱמָן וְאָהוּב וְחָבִיב וְנֶחְמָד וְנָעִים וְנוֹרָא וְאַדִּיר וּמְתֻקָּן וּמְקֻבָּל וְטוֹב וְיָפֶה

Mitchell First further pointed out to me that וְשמְּחֵנוּ בְּתִקּוּנו from the Mussaf Amida of the Three Festivals employs the rabbinic Hebrew usage of תקן, here too with the connotation of "establish."

 

For the Love of God

(Slightly revised version of essay posted on Times of Israel)

 

In a year defined by its compound anxieties — medical, racial, political, environmental, and economic — we are in last days of the most anxious month on the Jewish calendar. Without much of an independent identity, Elul is the final stretch of the religious year and a prelude to the impending Days of Awe. Traditionally, it is a time of increased religious vigilance, including heightened introspection, Selichot (penitential prayers), revisiting personal and communal moral standards, and stricter observance, all in anticipation of Rosh Hashanah and Yom Kippur. 

But there’s more to Elul, even in a year like this one, than brooding over the prior year’s shortcomings or worrying about the weeks and months ahead. For the sensitive religious soul, this season can also be a time of deep spiritual yearning and an intensified love for the divine. A memorable epigram, citing the Song of Songs (6:3), literally spells this out: “’I am for my beloved, and my beloved is for me’ — this is an acronym for ‘Elul.’”

Love and fear often come in tandem. And in Jewish thought, love of God and fear of God are considered opposite but conjoined poles of a unified response to divinity: “And now, Israel, what does the Lord your God demand of you? Only this: to fear the Lord your God, to walk only in His paths, to love him . . .” (Deuteronomy 10:12).

The traditional Siddur for children begins (right after Modeh Ani) with a declaration — “the beginning of wisdom is the fear of God” (Psalms 111:10) — that places awe and reverence for divinity at the epicenter of intellectual achievement. And the second verse of Shema, almost a credo of Jewish faith, is the commandment to love God.

While both mitzvot are somewhat amorphous, fear of God may be the easier of the two to grasp and to implement. But how can the Torah mandate loving God? What does it mean in practice?

In the very first chapters of his Mishneh Torah code, Maimonides lists love and fear of God as distinct but tightly coupled commandments. Characteristically, he intellectualizes the effort required to fulfill them. Maimonides states that love and fear of the divine, properly observed, arises from an appreciation of God’s majesty and man’s humility. And this can only be accomplished by means of study; specifically, training in physics and metaphysics: “One can only love God by the knowledge with which one knows Him. According to the knowledge, will be the love . . . a person ought therefore to devote himself to understanding those sciences and studies which will inform him concerning his Master” (Laws of Repentance 10:6). Such learning, Maimonides assures us, will ultimately result in an obsessive love for God (in an unexpected near-poetic flourish, he compares it to romantic infatuation) and a concomitant feeling of smallness within the vastness of the universe. This sense of humility is what the Torah means by fearing God.

Note that the type of fear that God demands, for Maimonides, is not the fear of punishment (in fact, he rejected the concept of divine retribution by suffering in the afterlife). He has little patience for those who worship exclusively out of fear, as commonly understood, or for the expectation of reward. Rather, he says, one who worships God as intended, out of love, “does what is true because it is true” (ibid., 10:2).

As always, Maimonides sets the bar high -- and in this case, by his own standards, possibly too high. His definition of love and fear of God is so consciously elitist as to be out of reach for most people: “This standard [to worship God from love],” he concedes, “is indeed a very high one; not every sage attained it.” (Note, however: Rather than the conclusion of an intellectual journey, the biblical meaning of “loving” God is to commit to worship Him exclusively, and to observe the mitzvot – in short, “to walk only in His paths”).

On this and many other matters, both philosophical and halakhic, Maimonides had his detractors. It also goes without saying that Maimonidean (unsurprisingly, largely Aristotelian) physics, as summarized in the earliest chapters of Mishneh Torah, is hopelessly out of date.

But the idea that loving God must begin, logically and practically, with a love for the truth, is a timeless one that must be at the foundation of our spiritual lives. In pledging their loyalty and love to God, religious people should never be asked, or ask themselves, to forsake science and fact. And if the beginning of wisdom is the fear of God, human wisdom itself, both secular and divine, is only possible with an irrevocable commitment to the truth.