What is the meaning of the word "redundant" in the hadith: "Knowledge is of three things: firm verses, authentic hadiths, and what is derived from these two; anything other than that is redundant." And does this mean that it is impermissible to learn worldly sciences?

The Hadith: "Knowledge is threefold, and anything besides that is a mereفضل (superfluous/additional): a firm (muhkamah) verse, or an established (qa'imah) Sunnah, or a just (adil) fara’id (inheritance)." This Hadith is weak and not authentically attributed to the Prophet, peace and blessings be upon him, due to the presence of two weak narrators, as ruled by a number of imams.

Even assuming its authenticity, the Hadith does not prohibit the study of worldly sciences. Rather, its intent is that the fundamentals of religious sciences and matters of Sharia trace back to these three matters, and anything else is a superfluous addition that is not essential.

"The firm verse" has been interpreted as the abrogated verse, and "the established Sunnah" as the sound, authentic, and transmitted Sunnah, and "the just fara’id" as the ruling derived by analogy (Qiyas) or what Muslims have agreed upon by consensus (Ijma'), or the science of inheritance (fara'id).

Thus, the proofs of Sharia are four: the Quran, the Sunnah, Ijma' (consensus), and Qiyas (analogy).