The Gra, in his introduction to the tfilos of Rosh Hashana, notes a powerful and fundamental idea. The mishna in Rosh Hashana (16a) teaches:
"At four times during the year the world is judged ... on Rosh Hashana all of mankind is judged individually, like young sheep who pass through a small opening in the coral."
The seriousness and scope of the judgement is underscored in the Nesaneh Tokef prayer, authored by Rav Amnon of Mayence, wherein we are reminded of the nature of this judgement:
"How many will die, how many will be born, who will be at rest, who will wander about, who will become poor and who will become wealthy."
One would have imagined that in response to such a reference to judgement, one would pray on Rosh Hashana to be pardoned and forgiven, for life for our children and sustenance. Moreover, at first glance the amidah of nineteen brachos that we recite daily would have been most appropriate for Rosh Hashana. The listing of thirteen requests, personal and communal, would precisely articulate the needs of all on Rosh Hashana. Indeed, having offered the specific personal and communal needs on Rosh Hashana, the Shemoneh Esray for the rest of the year could well have been, "Reign over the whole universe in your glory," the theme of all the prayers of Rosh Hashana.
The Rosh Hashana machzor therefore teaches us a very basic principle regarding prayer. As Rav Chaim Volozhiner in Nefesh HaChaim (2:11) teaches, the main thrust and component of all prayer is Hashem, His kingship, glory and honor in this world. The personal needs of man are inconsequential in contrast and hence omitted on Rosh Hashana. Moreover, even during the rest of the year, when we do articulate our needs, one learns from the Rosh Hashana liturgy, that the primary purpose of our asking for health, wealth and religious growth is to serve Hashem. We are to channel these bounties to His service. Only then can we be rewarded.
The Tiferes Yisroel notes that this concept is found in his commentary on the last mishna in the third chapter of Rosh Hashana. The Torah informs us (Shemos 17:11), "And it came to pass when Moshe raised his hand that Israel prevailed." The mishna asks, "Was it Moshe's hands that won or lost the battle against Amalek? Rather, the Torah teaches you: As long as Israel looked heavenly and subjected their heart to their Father in heaven they would prevail, but when they did not, they would fail." Similarly, Hashem instructs Moshe (Bamidbar 21:8): "Go make a fiery serpent, and set it upon a pole, and whoever was bitten looked at it and lived." The mishna rules again that it was not the serpent that killed or gave life. Rather, when Israel looked heavenward, and subjugated their heart to their Father in heaven they were healed, but when they did not, they perished. The Tiferes Yisroel notes that we learn from the above that whether one is praying for success in a new venture such as the war against Amalek, or even a business venture, or whether one is praying to be spared from an impending tragedy such as in the case of the serpents, or sickness, man's prayer is only effective if the primary objective is to serve Hashem. Benei Yisroel's subjugating their hearts to Hashem enabled them to prevail.
In reality, tefillas Chana, which is the haftorah for the first day of Rosh Hashana, teaches us a great deal about prayer, and in particular, highlights the above concept. The gemara in Berachos teaches that the mussaf amidah on Rosh Hashana has nine brachos instead of ten because Chanah used Hashem's name nine times in her prayer. (Instead of the regular seven brachos of the shabbos or yom tov amidah, plus the three extra's- malchuyos, shofaros, and zichronos, we only have six plus three.) She prays for a son and is finally granted one.
The first chapter in Shmuel recounts how Chanah used to accompany her husban Elkanah annually when he went to Shiloh to pray. One would have imagined that once the child was born she would have been the first to go to Shiloh to say thank-you to Hashem. The previous Lubavitcher Rebbe zt"l notes that Chanah does not go, saying: "Until the child is weaned, then I shall bring him; my responsibility is to raise him to best serve Hashem." She asked for a child- l'maancha- for your sake, Hashem.
May we be privileged to have our tefillos answered, and to word them correctly.