Gemara

R. Yochanan ben Zakai saw the daughter of Nakdimon ben Guryon gathering barley amidst the dung of the animals of Arabs.

R. Yochanan ben Zakai: What happened to the money of your father's house? (Her Kesuvah was for more than one million gold Dinarim.)

The girl: This is like people say in Yerushalayim, the way to salt (preserve) money is to deduct (to give to Tzedakah);

Question: Nakdimon ben Guryon gave Tzedakah!

(Beraisa): When Nakdimon ben Guryon walked to the Beis Medrash, they would spread silk garments before him, and the poor would take them!

Answer: He did this for his own honor.

Pesachim 8a (Beraisa): One need not stick his hand into holes and cracks (when checking for Chametz), because it is dangerous.

Question: (Why does danger exempt?) R. Elazar taught that harm will not befall a Shali'ach (someone engaged in a) Mitzvah!

Answer #1 (Rav Ashi): We are concerned lest he lost a needle, and will (also) look for it at the time of Bedikah (so he is not considered a Shali'ach Mitzvah).

Rejection (Beraisa): If one says, 'I give this coin to Tzedakah in order that my son should live', or 'in order that I will merit the world to come', he is a perfect Tzadik!

50b (Rava) Contradiction: It says "Ki Gadol Ad Shomayim Chasdecha", and it says "Ki Gadol me'Al Shomayim Chasdecha"!

Answer: Hash-m's Chesed is above Shomayim for those who serve Him Lishmah. It is up to Shomayim for those who serve Lo Lishmah.

Rav Yehudah: A person should always engage in Torah and Mitzvos even Lo Lishmah, for this will lead him to do them Lishmah.

Sotah 47a - R. Chanina: Because of the 42 sacrifices that Balak brought, 42 youths of Yisrael died (when Elisha incited bears on them).

Question: But Rav Yehudah taught that Balak's reward was that Rus descended from him, and from her Shlomo - "Elef Olos Ya'aleh Shlomo"!

R. Yosi ben Choni: Rus was the (grand)daughter of Eglon Melech Mo'av, who was the son of Balak.

We learn from Balak that a person should always engage in Torah and Mitzvos, even Lo Lishmah, for this will lead to Lishmah!

Answer: Balak's intention was to curse Yisrael (to diminish them).

Berachos 17a - Rava: "Reishis Chachmah Yir'as Hash-m Sechel Tov l'Chol Oseihem" - it does not say 'l'Osim', rather, "l'Chol Oseihem", to those who do Mitzvos Lishmah;

If one learns Lo Lishmah, it would have been better if he had not been created.

Avodah Zarah 19a (R. Elazar): "B'Mitzvosav Chafetz Me'od" - he desires the Mitzvos, not their reward.

(Mishnah): Do not serve Hash-m like servants who serve for the sake of reward, rather, like servants who serve not for the sake of reward.

Rishonim

The Rif and Rosh (Pesachim 16b and 4:2) bring Rava's and Rav Yehudah's teachings.

Question (Rosh): Here, Rava says that Hash-m's Chesed is up to Shomayim for those who serve Lo Lishmah. In Berachos, he says that if one learns Lo Lishmah, it would have been better if he had not been created!

Answer #1A (Rosh): In Berachos he discusses one who learns in order to aggrandize himself and refute others, without intention to fulfill. In Pesachim he refers to one like what discussed above, one who never works, also on Erev Shabbos. He is rewarded for not working on Erev Shabbos.

Korban Nesan'el (3): The Rosh means that here, he learns amidst laziness, i.e. he does not want to work.

Kitzur Piskei ha'Rosh (4:2): Even if one learns without intent for a Mitzvah, since he does not intend for an Aveirah, he is rewarded.

Question: We learn the greatness of Lo Lishmah from Balak, and he served in order to curse Yisrael, which is like in order to quarrel!

Answer (Maharsha Horayos 10b DH she'Mitoch): Balak did so only because he feared Yisrael. This is like serving out of fear, which leads to serving Lishmah.

Answer #1B (Tosfos Berachos 17a DH ha'Oseh): In Pesachim he discusses one who learns in order to be called Rebbi, or to be honored.

Answer #2 (Tosfos Sotah 22b DH l'Olam): In Berachos he discusses one who learns without intent to fulfill the Mitzvos. His learning causes that he transgresses b'Mezid instead of b'Shogeg. In Pesachim he refers to one who learns from fear of punishment or in order to get reward.

Rambam (Hilchos Talmud Torah 3:5): A person is judged first about Divrei Torah, and then about his deeds. Therefore, one should always learn Torah even Lo Lishmah, for this will lead him to learn Lishmah.

Question: Why does the Rambam say therefore? One should always engage in Torah and (all) Mitzvos Lo Lishmah, in order to get to Lishmah!

Answer (Binyan Shlomo, brought in Likutim in Frankel Rambam): The Gemara did not distinguish different kinds of Lo Lishmah. The Rambam infers that all are the same. Other Mitzvos do not normally lead to honor or wealth. The only Lo Lishmah that applies to them is in order to receive reward. Surely, this is permitted. The Rambam needed to teach only about learning Lo Lishmah, which would be forbidden if it did not lead to Lishmah.

Rambam (Hilchos Teshuvah 10:1,5): One should not do Mitzvos and learn in order to receive the Berachos written in the Torah or to get the world to come. One should not refrain from Aveiros to avoid the curses in the Torah or to prevent being cut off from the world to come. This is not how Chachamim serve Hash-m. Rather, this is how we teach children, women and Amei ha'Aretz until they become wiser. Then, we gradually reveal to them this secret that one should serve purely out of love and habituate them to do so.

Rambam (2): This level of serving out of love is very high, and not every Chacham merits it. We are commanded to do so - "V'Ohavta Es Hash-m..."

Rambam (4): Great Chachamim privately taught to their sharp Talmidim not to serve like slaves who anticipate recompense. Rather, serve like slaves who serve without any intent for recompense, rather, because it is fitting to serve the Master, i.e. out of love.

Tosfos (Avodah Zarah 19a DH Al): It is improper to serve for the sake of reward if one will regret doing the Mitzvah if he does not get his request. If not, we say that one who gives Tzedakah in order that his son should live is a perfect Tzadik (Pesachim 8a).

Rashi (Pesachim 8b DH Harei): One who gives Tzedakah in order that his son should live is a perfect Tzadik in this respect. We do not call it Lo Lishmah. Rather, he does the Mitzvah like Hash-m commanded, and also intends for reward.

Poskim

Shulchan Aruch (OC 433:8): If a wall used for Chametz fell, one need not check underneath. Scorpions are common there; we are concerned lest after he finishes checking and is not engaged in a Mitzvah, he will search for a needle that he lost, and be in danger.

Magen Avraham (14): We are not concerned if he looks for it while checking, for he is doing a Mitzvah. One who gives Tzedakah in order that his son should live is a perfect Tzadik.

Shulchan Aruch ha'Rav (Talmud Torah 4:3): One should always engage in Torah and Mitzvos even Lo Lishmah. This is only when he fulfills what he learns, but he does not learn for the sake of the Mitzvah. Rather, he fears punishment or seeks reward in this world or the world to come. "Wealth and honor" is promised for those who learn Lo Lishmah. Even in order to be called Rebbi or be Rosh Yeshiva is permitted. One may not learn without intent to fulfill. This is a Rasha. Any Chacham who disgraces Mitzvos and has no Yir'as Shomayim is like the lowest of the Tzibur. He is worse than an ignoramus, for whom Mezid sins are like Shogeg. The Torah is a lethal poison for him. Some say that in any case, one should always engage in Torah, for from Lo Lishmah he will come to Lishmah, i.e. intent to fulfill. Chachamim expounded 'had they not abandoned My Torah, the light in it would have changed them for the better.' Chachmei ha'Kabalah say that even though Mitzvos done by a Rasha temporarily strengthen Klipos (shells of Tum'ah), when he repents later, in this Gilgul or another (reincarnation), his Torah and Mitzvos will leave their shells and return to Kedushah. Therefore, one should never refrain.