Birkas Shmuel (Kiddushin #27 p.42):
“What emerges is (a) that according to the Torah the obligation of Banim Ubeni Banim means you must make your children into Geonei and Chachmei Torah – and not merely to prepare them for life as a Jew. But rather, you must teach them and get them to learn the entire Torah, and if chas v’sholom you do not, you violate the entire Mitzvah of learning Torah as per Banim Ubnei Banim.
(b) Universities and gymnasiums (i.e. secondary schools) are prohibited because of Apikursus [that they teach]. My Rebbi (i.e. Rav Chaim Soloveichik ZT’L) prohibited them even in war time, and even to save a life, for to avoid violating this, even a Jewish life is to be spent.
(c) To learn secular studies on a regular basis is prohibited, as per the Rama 246:4 …
Brothers, please do Teshuva while there is still time, for the enlightenment (Haskalah) has blinded our eyes and weakened us. For we have no benefit in this world at all – both spiritually and physically – except from Torah. All the strength of Klall Yisroel is from the Torah … we should do Tehsuva and repair the Batei Medrashos that have been broken by the Enlightenment.”
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Kovetz Shiurim II:47
Question:
Under what circumstances is it permitted to learn secular studies?
Answer:
(a) If you must learn books that contain apikursus, it is prohibited … needless to say even to make money or to prevent a loss thereof.
(b) If you must sit in school with Goyim, and it causes someone to befriend the Goyim and their ways, it is prohibited as per the Lo Saseh of Hishomer Lecha etc. for the Torah commanded us to distance ourselves from the Goyim in every way…
(c) If the studies do not cause you to learn Apikursus or to befriend Goyim, and you learn secular studies in order to know a skill to make a living, it is permitted, and it is a Mitzvah. However, this is only in general. But if a person sees that his son wants to learn Torah and he is prepared to be a Gadol B’Torah, in such a case R. Nehuray said: “I will forgo all skills in the world and teach my son only Torah.”…
(d) If you don’t need the studies for Parnasa, and you just want to be involved in them, there is reason to prohibit because of Bitul Torah, as per the Rama in YD 246, who writes that it is forbidden to learn secular studies on a regular basis… perhaps it is not due to Bitul Torah but rather it is an affront to the honor of the Torah… someone who set out to learn secular subjects indicates that he believes that they have a purpose in and of themselves [besides for parnasa], and that is against the Torah’s opinion. [see above]…”