We see that Chazal learned their science from the Torah. Rav Breil, the Rebbi of the Pachad Yiztchok, teaches us that we do not even entertain the possibility of a scientific statement in Chazal not coming from the Torah. This we see from Rav Briel’s answer to the Pachad Yiztchok’s question regarding the killing of lice on Shabbos. The Gemora permits it, based on a scientific fact. The Pachad Yiztchok asked his Rebbi that due to the possibility that this scientific fact is incorrect, perhaps we should be machmir and not kill lice on Shabbos, just in case.
Once we establish that the scientific knowledge that is incorporated into Torah Shebal Peh is derived form the Torah, it has the same status as all of Chazal’s interpretaitons of the Torah — they are binding:
The Gemora in Sanhedrin (100a) tells that R. Yochanan derived from a posuk that when Moshiach comes, the gates of Jerusalem will be made of jewels 30 amos long and 30 amos high. Some student said that such big jewels do not exist – “we do not even find jewels as big as doves eggs,” he said. Then, one day the student saw angels (!) cutting such big stones, and he asked them what they are for. The angels answered: “They are for the gates of Jerusalem”. When next he saw R. Yochana, he praised his qualifications for expounding the Torah, based on his “scientific observation” that confirmed the Rebbi’s interpretation.
R. Yochanan responded, “Bum! You only believe because of what you see? You dishonor the words of the sages!”, and the student died.
The Ran (Drashos #13) points out that the statemnt of R. Yochana had no halachic relevance at all – it was merely an Agadic interpretation, and the disagreement was regarding a scientific fact, yet the student was punished for not believing in its truth. Therefore, he concludes:
“Just as we are commanded to follow their opinions regarding laws of the Torah, so too are we commanded to follow all of what they say from tradition in Hashkafa (“Deos”), and medrash on Pesukim. And someone who veers from their words, even in something that has no relevance to any Mitzvah, is an Apikores and has no share in the next world.
Particularly interesting is a statement on this topic in the Aruch Hashulchan (EH 13). Quote:
“I will tell you a great principle: Chazal, besides their holiness and wisdom in the Torah, were also greater scholars in the natural sciences those savants (“mischakmim”) who would argue against their pure words. And someone who disagrees with them testifies about himself that he does not believe in Torah shebal peh, even though he would be embarrassed to admit it outright.”
Chasam Sofer (Beshalach) writes that this is the meaning of the posuk “Ki hi chachmascha ubinascha l’einei ha’amim” – Chazal were great experts in the secular sciences and disciplines. In fact, you need to know much secular knowledge in many areas in order to properly understand the Torah – and he gives several simple examples. However, since we are supposed to be busy learning Torah – not secular science – all day and night, and Hashem has no “nachas ruach” from us learning secular studies at all, how would Chazal have known all the secular wisdom that they clearly knew, as we see they did from all of Shas?
Answer: They know it from the Torah, since the entire body of secular wisdom is included in the Torah, for the Torah is the blueprint of the world. And so, when the Goyim see that we do not study the secular science books at all – and we even disagree with them! – yet we derive all the secular knowledge, in the most precisely accurate form – from only the Sefer Torah, they will exclaim, “Am chacham v’navon hagoy hagadol hazeh!”
A similar explanation is given by the Raavad-ibn Daud. He says that the posuk refers to the philosophical truths that it took the nations centuries to develop, we knew all the time via tradition from Har Sinai.