Rambam’s Shofar: A Call to the Heart, Not to the Heavens

Rambam writes (e.g., Sefer Hamitzvos, Mishneh Torah) that the mitzvah of shofar is to hear the shofar—not to sound it. 

That's to say that men don't have an obligation to blow shofar individually (which is only fulfilled via שומע כתוקע if one is listening to another sound it*) but rather simply to listen to the sound of the shofar (with the caveat that it is blown by someone similarly obligated as well as both the blower and hearer intentionally thinking about connecting with the other). 

The bracha recited prior to mitzvas shofar is formulated in Mishneh Torah to reflect that conceptualization with the nusach לשמוע—not לתקוע. 

Of course there's also Rambam's famous lesson on introspection that the Shofar alludes to which too is about what we hear (and internalize)—not what we project to others (also referenced in the Guide to the Perplexed)**. 

Halachic rationale aside I'd like to suggest that this is (also) Rambam following his philosophical beliefs. 

In Tanach and the Rabbinic literature the mitzvah of Shofar is conceived of as an expression of tefilah—an anguished, unarticulated cry to God.  

(See, e.g., Bamidbar 10:9, Vayikrah 23:24, B RH 16a, 26a, 26b, 33b.)

This is spelled out most clearly in Tosefta RH 1:12:

אמרוּ לְפָנָיו: מַלְכֻיּוֹת, זִכְרוֹנוֹת וְשׁוֹפָרוֹת. מַלְכֻיּוֹת, כְּדֵי שֶׁתַּמְלִיכוּהוּ עֲלֵיהֶם; זִכְרוֹנוֹת, כְּדֵי שֶׁיָּבוֹא זִכְרוֹנְכֶם לְטוֹבָה לְפָנָיו; שׁוֹפָרוֹת, כְּדֵי שֶׁתַּעֲלֶה תְּפִלַּתְכֶם בִּתְרוּעָה לְפָנָיו.

Logically then the mitzvah is to utilize the shofar to emit blasts to beseech God (the opinion adopted by Sheiltos) with the bracha following suit with לתקוע (which is indeed espoused by Rabeinu Tam, cited by Rosh, RH, 4:10). 

For Maimonides tefilah itself isn't about petitioning God to grant us our wishes but rather about keeping us focused on God so that we live a more God-centered life. 

(See here for some sources.)

Ergo, shofar, as a type of tefilah, isn't about appealing to the Deity for mercy, just as tefilah isn't, but rather about self improvement via heightened awareness of God which in turn leads to better living and outcomes. 

Here's R. Yosef ibn Kaspi, a big fan of Maimonides, on Bamidbar 10:9:

"וְנִזְכַּרְתֶּם לִפְנֵי יְיָ אֱלֹהֵיכֶם"— גַּם זֶה, דִּבְּרָה תּוֹרָה כִּלְשׁוֹן בְּנֵי אָדָם, וְהָעִנְיָן כִּי בְּמַעֲשֶׂה הַזֶּה יָעוּרוּ לְבָבוֹתֵינוּ וְנָשׁוּבָה אֶל יְיָ.

*Rambam actually is of the opinion (in a responsum)—and this too may have influenced his opinion—that every male would need to blow the shofar individually if the mitzvah were to blow it.

**R. Nachum Rabinovitch, in his Yad Peshutah, locates a few midrashim in support of Rambam's take on the Shofar's message.