Gemara

(Sefer Ben Sira): I hate three -- a Chacham who frequents (some say - is very talkative or argumentative in) the drinking house, one who teaches Talmidim at the city summit (this is haughty, and it inconveniences travelers) and one who holds his Ever while urinating.

There is a fourth I do not love -- one who enters another's house suddenly. (Perhaps those inside are engaged in something immodest.)

(R. Yochanan): One should not enter even his own house suddenly.

Menachos 99b - Question (Ben Dama, R. Yishmael's nephew): May someone like me, who learned the entire Torah, learn Chachmas Yevanis? (This is Greek wisdom, or a crafty way of speaking.)

Answer (R. Yishmael): "Lo Yamush Sefer ha'Torah ha'Zeh mi'Picha v'Hagisa Bo Yomam va'Laylah." If you find a time that is neither day nor night, at that time you may learn Chachmas Yevanis.

This is unlike R. Shmuel bar Nachmani;

(R. Shmuel bar Nachmani): "Lo Yamush..." is not an obligation or Mitzvah. It is merely a blessing.

Sanhedrin 100b (Mishnah - R. Akiva): Even one who reads foreign Seforim (has no share in the world to come).

(Beraisa): He refers to Sifrei Tzedukim.

(Rav Yosef): It is forbidden to read also Sefer Ben Sira (due to Bitul Torah).

It says worthless things, such as 'if a man's beard is fine and weak, he is a Chacham. If it is thick, he is a fool...

(Rav Yosef): We may expound proper teachings of the Sefer.

Chagigah 14b (Beraisa): Four entered the Pardes (this will be explained) --Ben Azai, Ben Zoma, Acher and R. Akiva. Ben Azai looked and died. Ben Zoma looked and was stricken. Acher cut saplings. R. Akiva came out fine.

15b: When Acher stood up from the Beis Midrash, many Sifrei Minim were detached from his lap.

Shabbos 75a (R. Shimon ben Pazi): It says about one who knows how to calculate Tekufos and Mazalos, but does not, "v'Es Po'al Hash-m Lo Yabitu u'Ma'ase Yadav Lo Ra'u".

(R. Shmuel bar Nachmani): It is a Mitzvah to calculate Tekufos and Mazalos. "Ki Hi Chachmaschem u'Vinaschem l'Einei ha'Amim" - Tekufos and Mazalos is the Chachmah that can be shown to Nochrim.

Rishonim

Rambam (Hilchos Talmud Torah 1:12): The matters called 'Pardes' are included in Gemara.

Drishah (YD 246:2): This is astounding. I say that Pardes is natural science. How can the Rambam say that it is included in Gemara?! He must explain that the four 'entered the Pardes to understand what is above and below', i.e. Divine matters.

Rambam (letter to R. Yehonason ha'Kohen, in Teshuvos ha'Rambam (Blau) p.57): I learned other Chachmos to serve Torah, to be a 'seasoning' for it.

Kovetz Shi'urim (2:47:8): The Rambam intended for a Mitzvah. He relied on 'Sheluchei Mitzvah are not harmed.' Even though we do not say so when damage is common, he estimated that for himself, damage is not common. For people like us, surely damage is common and one may not learn them even for a Mitzvah. This is like a medicine that contains poison. An expert doctor knows the right combination and ingredients to add to weaken the poison. If an amateur prepares it, he will kill people. We find that Shlomo ha'Melech relied on his Chachmah to marry many women, and he stumbled! This is because there was no Mitzvah to marry them.

Ramban (beginning and end of introduction to Bereishis): Every deep secret and Chachmah is hidden in the Torah... They can be attained only from the mouth of a Chacham Mekubal (who has a tradition) to the ear of an understanding receiver. Do not engage in what is beyond you.

Poskim

Rema (YD 246:4): One should learn only Mikra, Mishnah, Gemara and Poskim based on them. Through this one acquires this world and the next. One should not learn other Chachmos. One may learn other Chachmos on occasion, as long as it is not Sifrei Minim (heretics). Chachamim called this 'strolling in the Pardes'.

Shach (6): The 'other Chachmos' are things like philosophy, astronomy and Kabalah. The Rema is not precise. The Rambam says that only Ma'ase Bereishis and Ma'ase Merkavah are called Pardes.

Gra (17): Menachos 99b teaches that one may not learn other Chachmos. The Sifri (va'Eschanan 34) expounds "v'Dibarta Bam" - make them (Divrei Torah) primary, and not secondary. Your engagement should be only in them. Do not mix in other matters. Do not say 'I learned Chachmas Yisrael. I will learn from Chachmos of the (other) nations.' "Laleches Bahem" teaches that we go in Divrei Torah; we do not abandon them.

Teshuvas Rema (7): In a previous letter, I cited a Greek Chacham and the chief philosopher. The questioner said that the Torah girds itself in sackcloth over this. This is an old argument. Chachamim of Provincia wrote to the Rashba (in Teshuvas ha'Rashba 418) to defend their practice. The Rashba objected only to teaching it to children before they learn Talmud. The Rambam wrote Moreh Nevuchim, which is totally based on such Chachmah. Indeed, the Rivash (45) said that he did so only to answer Apikorsim. However, I answer that Chazal were concerned only for Seforim of the cursed Yevanim, lest one be drawn after them. They did not forbid learning Divrei ha'Chachamim and their investigations of nature. Just the contrary! Through this we know the greatness of the Creator! It says about one who knows (how to calculate Tekufos... but does not... "... u'Ma'ase Yadav Lo Ra'u.)" Anyone who says a matter of Chachmah, even a Nochri, is called a Chacham. Many of our Chachamim brought words of (Nochri) researchers, e.g. Moreh Nevuchim, the Akeidah. I merely cited them. Moreh Nevuchim (2:22:4) says that everything Arostotle wrote, up to the sphere of the moon, is true. I see a greater need to flee from Kabalah than from philosophy, based on what the Ramban wrote (that one who is not worthy to understand Kabalah will only err).

R. Yisrael Mishkelov (introduction to Pe'as ha'Shulchan, citing the Gra): All Chachmos are needed for Torah and are included in it - algebra, Meshulashim (geometry), engineering, and music. The Gra praised them very much. He wrote a Sefer "Eil Meshulash" on algebra and geometry.

Ya'aros Devash (2:7 DH Zehu): The seven Neros of the Menorah allude to 'outside' Chachmos. The Ner Ma'aravi alludes to Chachmah of the Torah. The other Chachmos branch off from it. They are maidens that serve the queen. They are needed for Torah. We need geometry and algebra for measuring the closest city for Eglah Arufah and the boundaries of the cities of Leviyim and Techumim. The Chachmah of weights (mechanics) is needed for understanding proper scales. Optics is needed for understanding forgeries of Nochri priests. (They use schemes to show wondrous faces, and one might think that there is Ru'ach in them.) We must be able to interrogate witnesses who say that they saw the new moon. Astronomy is needed for knowing when to make leap years, leap months and the Tekufos (equinoxes and solstices). Astrology is needed for laws of idolatry. (Nochrim offer to heavenly bodies, based on astrology, and people err about this. Witchcraft results from this.) Natural science includes medicine. It is greatly needed for Chachmah of Torah. Great Chachmah is needed to know which Dam Nidah is Tamei, whether a miscarriage was within or after 40 days (from conception), and to distinguish between male and female (on such a tiny fetus) needs. We must know whether a blow was hard enough to kill, and for which sick people we desecrate Shabbos. Agricultural and mineral science is a great Chachmah. For Kil'ayim, we must know how far plants nurture, and when one gives taste to another, and which may be grafted. We must know which animals may be mated, and distinguish between Behemos and Chayos.

Ya'aros Devash: Plato was an expert dietician, and from this developed the Chachmah of compositions needed to understand the reasons for Korbanos, flour-offerings, libations and compositions of Ketores. Chemistry and knowledge of materials is needed for building the Mishkan and Mikdash, to know what should be made from gold, silver, copper and iron, the reasons for the stones of the Efod and their Segulos. Beis Din must know what is natural. What has no source in nature is Darchei ha'Emori. The Chachmah of art and dissection is needed to understand praises of the body in Shir ha'Shirim, and Atah Techezeh in the Zohar. Chachmah of logic and pronunciation helps to understand grammar and metaphors, and (non-literal) expressions in Torah, Nevi'im and Kesuvim. Music helps to understand the cantillation and vowels of songs in the Torah and singing of the Leviyim. Nigunim gladden the heart and remove depression.

Kovetz Shi'urim (2:47): One may not learn from other Chachmos if this will bring to reading Seforim with Apikorsus. The Rambam (Hilchos Avodah Zarah 2:2,3) says that if one reads books of idolatry or that cause one to doubt fundamentals of Judaism, he transgresses "Lo Sasuru Acharei Levavchem" and "Al Tifnu El ha'Elilim." All the more so this applies to one who reads books of heresy, which is more severe. According to the Ramban, who says that the latter Lav is under the umbrella of idolatry, it is forbidden even for Piku'ach Nefesh.

Kovetz Shi'urim (11): Do not say that just like one may learn from witchcraft in order to give rulings about it, the same applies to Sifrei Apikorsus. A verse permits regarding witchcraft, and regarding preparing the Ketores. No verse permits Sifrei Apikorsus. We cannot say that one who is engaged in his work will not be affected, since Apikorsus lures people.