R' Soloveitchik in "Halachic Mind" proposes a philosophy in which halachic and scientific inquiry are conducted in very similar manners. As he describes it, Jewish sources form a kind of "landscape" which we explore, investigate and categorize, just as we investigate the natural world, in order to develop an approach to running our lives.
R' Soloveitchik's formulation resonates with me, and probably with many other people. It also provides a starting point for recognizing the ways in which scientific and religious inquiry are not alike.
In particular, I see one fundamental difference between Torah knowledge and scientific knowledge. If all the scientific knowledge in the world were forgotten, it would only be a temporary inconvenience for humanity. The same natural world would continue to exist as before. All the experiments performed over the last few thousand years could be re-performed and all the scientific laws and models rediscovered.
The same is not true of Torah knowledge. If the Bible, Talmud, and other traditions were to be forgotten, then barring miracles, they would be forever unrecoverable. Unlike the workings of nature which are forever present and testable, Torah knowledge was introduced into the world through a limited number of revelatory events. If we lose our memory of what happened at those events, the laws of nature do not guarantee us any future revelation.
It seems to me that this is the reason for the great emphasis Judaism places on Torah study. By studying Jewish tradition, and transmitting it to our children (this is an integral part of the mitzvah, see the first paragraph of the Shema), we do our part to ensure that the Torah is accessible to an infinite number of future generations. Unlike every other investment in the world which may pay off for an hour or a year or a thousand years, Torah study is an investment which can pay off literally forever.
This consideration seems to be the basis for the Jewish commitment to Torah study, a commitment which often seems so incomprehensible to outsiders, but can in fact be readily understood in practical terms.
UPDATE: in a sicha by R' Aharon Lichtenstein I saw the following very relevant source:
R' Hoshaya said: Wherever [a Biblical verse] says "morasha", the word is talking about the future.
- But it is written "[Torah tziva lanu Mosheh,] morasha kehilat yaakov"?
- He said: There is nothing more connected to the future than [the Torah].
(Yerushalmi Bava Batra 8:2)