” the frum velt believed that it is inappropriate for a frum yid to study secular sciences and math and that everything you need in life can be obtained from the study of torah”
I dispute that statement. Rambam and Sforno attended secular universities. Were they not frum? The Rema didn’t attend university, but he studied history, astronomy, and philosophy on his own and was friendly with the professors at the university in Krakow (which was one of the great secular intellectual centers of the entire world during his lifetime). The Vilna Gaon wrote on mathematics and directed a student to translate Euclid. Were they not frum?
“there is a branch that believed in studying secular studies lishma”
Rav Hirsch explicitly supports this. I don’t have it in front of me but I think the essay on that is in Volume 7 of his Collected Works.