Gemara

Tana D'Vei Rav Anan: "Chamukei Yerachayich" - Divrei Torah are compared to a thigh, to teach that just like a thigh is hidden, also Divrei Torah. (The verse ends "Ma'aseh Yedei Aman", the handiwork of Hash-m, i.e. the Luchos or the Torah - Rashi here and Mo'ed Katan 16b).

R. Elazar: "V'Hatzne'a Leches Im Elokecha" - this is escorting the dead and bringing a Kalah to Chupah. Even though these are normally done in public, they should be done modestly. All the more so, things normally done in private should be done modestly!

Mo'ed Katan 16a: Once, Rebbi decreed not to teach Talmidim in the market. He learned from "Chamukei Yerachayich" that Divrei Torah should be hidden. R. Chiya taught his nephews in the market. Rebbi asked him why he did so.

R. Chiya: It says "Chachmos ba'Chutz Taronah"!

Rebbi: No, that teaches (like Rava taught,) that if one engages in Torah inside (privately), the Torah proclaims about him outside (publicly).

Question: But it says "Lo me'Rosh b'Seser Dibarti"!

Answer: This refers to Kalah (a Drashah which everyone attends).

Question: How does R. Chiya expound "Chamukei Yerachayich"?

Answer: It teaches that Tzedakah and Chesed should be hidden.

Berachos 8a - Question (Rav Chisda): What do we learn from "Ohev Hash-m Sha'arei Tziyon mi'Kol Mishkenos Yakov"?

Answer: Hash-m loves places where learning leads to conclusive Halachah, more than all the Batei Kenesiyos and Batei Medrash.

R. Chiya bar Ami: After the Churban, these places of Halachah are the only places dear to Hash-m.

Abaye: At first, I used to learn in my house and pray in Beis ha'Keneses. After I heard R. Chiya's teaching, I pray only where I learn.

Even though there were 13 Batei Kenesiyos in Tzipori. R. Ami and R. Asi would pray only where they learned.

61b - Beraisa: The kingdom (Rome) once decreed that the Yisraelim may not learn Torah. Papus ben Yehudah found R. Akiva gathering multitudes and teaching Torah.

Nidah 16b - Sefer Ben Sira: I hate three...one who teaches Talmidim at the city summit.

Rishonim

Rashi (Nidah 16b DH veha'Moshiv): Teaching Talmidim at the city summit is haughty (in order that his voice will be heard for a great distance - Me'iri), and it inconveniences travelers.

Rambam (Hilchos Talmud Torah 3:12): There is a covenant that one who exerts himself in learning in a Beis ha'Keneses will not forget quickly. One who exerts himself b'Tzin'ah (modestly) will grow wise - "V'Es Tzenu'im Chachmah.

Source (Kesef Mishneh): We learn from the Yerushalmi (Berachos 5:1).

R. Chananel (Mo'ed Katan 16b DH Aval): "Chamukei Yerachayich" applies most of the year, but at the time of Kalah, "Chachmos ba'Chutz Taronah ba'Rchovos Titen Kolah"!

Note: This seems to be unlike our text.

Poskim

Shulchan Aruch (246:22): There is a covenant that one who exerts learns in a Beis ha'Keneses will not forget quickly. One who exerts himself b'Tzin'ah will grow wise - "V'Es Tzenu'im Chachmah.

Prishah (49): The text of the Tur (and Shulchan Aruch) says Beis ha'Keneses, but it refers to a Beis Medrash, for its Kedushah is greater. There were 13 Batei Kenesiyos in the city of Abaye and Rava (our text - R. Ami and R. Asi), yet they would pray only where they learned. It does not say that they learned where they prayed!

Taz (8): The Shulchan Aruch discusses when there is no Beis Medrash fixed in the city, and everyone learns in his own. Then, it is better to learn it is not the Beis ha'Keneses; surely, every Tzibur has a Beis ha'Keneses. Surely, if there is a Beis Medrash it is better to learn there than in the Beis ha'Keneses

Keli Yakar (Shemos 28:10 DH v'Hinei Makom): The Torah mentions that the gold inside the Aron is Tahor, but it does not say so regarding the gold outside. This is because there is more Shleimos to Torah learned inside.