Why ask for understanding? Can't I just study?
It would be a shortcut if the prayer replaced studying. The Gemara does not discuss this prayer here, but it does have a rule about who receives wisdom.
Rabbi Yochanan (a sage of the Gemara in the Land of Israel) says that God gives wisdom only to someone who already has wisdom. His proof is a verse in Daniel: God "gives wisdom to the wise." Another sage, Rabbi Abahu, teaches the same rule from a different verse, where God says: "In the heart of every wise-hearted person I have put wisdom" (Shemot 31:6).
Both verses point the same way: wisdom is given to someone who already has some. One way to read that rule is that the gift lands in a mind that is already working. On that reading, asking is not instead of the work.
Why does the blessing call it a favor? The word is chonen, built on the same root as chen, which means favor or grace. Abudarham ties the first line to God's words in Shemot 33:19: "I will be gracious to whom I will be gracious." In the Gemara (Berakhot 7a), Rabbi Meir (a sage of the Mishnah) reads those words as favor "even if he is not worthy." That is one sage's reading of that verse, not a comment on this prayer. It does show how the Gemara can hear the word: a gift, not a payment.
The sources do not say how much you must know first, and none of them speaks about this prayer and studying together. Putting the two side by side is our reading of them.
Berakhot 55a,Shemot 31:6,Abudarham, Weekday Prayers, Amidah,Berakhot 7aWhat does understanding have to do with Havdalah on Saturday night?
On Saturday night, after Shabbat ends, the weekday Amidah gets an extra paragraph inside this blessing. It is Havdalah, which means "separation." The Shulchan Aruch (the main code of Jewish law) rules: "One says Havdalah in Chonen HaDaat." The Rambam (Maimonides, the great medieval codifier) writes out the text. It praises God, who separated holy from ordinary, light from darkness, Israel from the nations, and the seventh day from the six work days. The exact wording differs between traditions.
Why put it here? The Gemara (Berakhot 33a) gives two reasons and records both. Rav Yosef (a sage of the Gemara in Babylonia) says: Havdalah is wisdom, so they put it in the blessing for wisdom. The other sages say: Havdalah is about the ordinary days, so they put it in the first blessing of the ordinary days.
Rashi explains the first reason in one line: the wise person is the one who knows how to tell holy from ordinary, and unclean from clean.
The Talmud Yerushalmi turns it into a question: "If there is no knowledge, where is Havdalah?"
Put simply, the idea behind Rav Yosef's reason, Rashi's line and the Yerushalmi is that you cannot separate two things until you can tell them apart. The other sages give a different reason, and the Gemara leaves both standing.
Berakhot 33a,Rashi on Berakhot 33a,Talmud Yerushalmi, Berakhot 5:2,Shulchan Aruch, Orach Chaim 294:1,Rambam, Order of Prayer 2:22Why is understanding the first thing I ask for, before health or money?
The blessings right after this one ask for things: repentance, forgiveness, rescue, health, a good year. Understanding comes first. Is that a ranking?
The Gemara's own reason for the order (Megillah 17b) is not a ranking. It lines up verses, as the Story section shows: understanding follows holiness, and repentance follows understanding.
Other sages do treat this blessing as special. Rav Ami says (Berakhot 33a): "Great is knowledge, since it was placed at the beginning of the weekday blessing."
The Maharsha (Rabbi Shmuel Eidels, who wrote in Poland around 1600) explains why Havdalah was put in this blessing, at the start of the weekday blessings: it is as if this blessing includes all the others. He supports that with Rav Ami's line and with a teaching he gives from Nedarim 41a: if you have gained knowledge, you have gained everything; if you lack knowledge, you lack everything. The Story section has the Gemara's own words there.
So there are two layers. The Gemara's stated reason for the position is verses. The idea that this blessing holds all the others is a later reading, built on Rav Ami and Nedarim.
Megillah 17b,Berakhot 33a,Maharsha, Berakhot 33a,Nedarim 41a