Is 'learning' non-Jewish topics a prohibited creative process on Shabbat? If so, on what grounds is learning Tanakh exempted? I read that the study non-Jewish subjects is banned or frowned upon, and I wonder why the creative-process ban/frown on the study of non-Jewish topics doesn't apply to Tanakh.
The Mishna Shabbat 148b writes that one may not count the number of guests from a list on Shabbat. Abaye in the Gemara 149a explains that this is a rabbinic restriction so as not to come to read a Shtar Hedyot on Shabbat. What is a Shtar Hedyot which one may not read on Shabbat? Rashi 116b s.v. Shtar explains it to be financial calculations or letters. Rambam (Peirush Mishnayot Shabbat 23:2) also explains Shtar Hedyot to mean letters and the reason for this is that on Shabbat one may only read Navi and it’s explanations and not even a book of wisdom and science. Bet Yosef 307:17 quotes the Baal HaMoer (43a s.v. VeHa) who agrees.
However, the Rashba (149a s.v. VeLeInyan) explains Shtar Hedyot as a business document. This is also the definition of Ri quoted in Tosfot 116b s.v "kol sheken" and Rosh (see there where he writes that reading shtarei hedyotot is a problem of mimtzo cheftzecha from Yishayahu 58:13) Shabbat 23:1. Therefore, Sh”t Rashba 7:288 rules that it’s permitted to read books of wisdom and medicine and quotes Ramban who agreed. [Bet Yosef 307:17 learns this out from another Teshuva of the Rashba 1:772 where he says that one may analyze an astrological tool called the Istrolav.]
Shulcha Aruch 307:17 rules like Rambam who says that on Shabbat one should only learn Torah and not books of other disciplines, however, he mentions that some are lenient. Mishna Brurah 307:65 writes that the minhag is like the Rashba, however, a pious person should be strict. Rav Aviner holds like the Mishna Brurah.
However, Yalkut Yosef (Shabbat vol 2, pg 214, 626) rules like Shulchan Aruch that one should only learn Torah on Shabbat and is only lenient to allow a medical student who has a test after Shabbat and is pressured for time to study medicine (except for the study of surgery) on Shabbat.
Once again, see Rabbi Torczyner's lecture on attending conferences.
While debated by medieval rabbis, it appears that we conclude it is permissible to study science or medicine on Shabbat. (Assuming it's being done for the right reasons, assuming you're not writing, that it's not "business talk", and the like.) There had been a discussion whether an astrolabe (a tool of astronomy from centuries past) could be used on Shabbat, and contemporary authority Rabbi JD Bleich discusses a microscope (again, assuming you're not turning on the light or the like); we tend to rule that this is all permitted.
CAVEAT: Shabbat has two components, the "don't-do" and the "yes do." Don't do creative processes like planting, plowing, burning and the like. Easy enough.
But there's also the "yes-do" of "keep the day sacred." Otherwise, I could come up with 101 loopholes that aren't technically creative processes, but would wind up spending my Shabbat as pretty much just another workday. Isaiah 54:18 talks about keeping Shabbat as a "delight", not trying to do your business or even talk about it.
That's a lot more of the question: is it appropriate and within the spirit to study science? Many believe that as that assists your religious growth, yes. (If you're cramming for an exam the next day, that's a different matter.)
As it says clearly in the Shulchan Aruch (in simon shin-zain, i.e. 307), there are two issues:
(a) reading, even looking at, mundane writings, etc. in Shabbos - a Rabbinic prohibition based on the concern that you might correct them, and,
(b) a prohibition on learning secular subjects in general - which where/if prohibited, is prohibited during the week as well.
As a result, there is a third issue:
(c) muktza - the writings, books, documents etc., forbidden in this way, become muktza in Shabbos
And as is often the case, there is a debated exception:
(d) Books of wisdon, knowledge, medicine - Yesh Omrim, Some say you can read them in Shabbos, which implies that you can read them during the week.
These are the essential concepts. The cases included in the Shulkan Aruch include letters, which may be important or may be muktze for arriving from outside the tehum, history books that a person might read to learn the language, and so forth.
There is a very clear exposition of the topic in the Shulchan Aruch Harav, 307:21-31, which is now available in English.