Anyone who ever studied Talmud in depth knows how maddeningly difficult it can be to reach any firm conclusions. Certain proposed solutions are easily enough rejected as nonsense. But even the greatest commentators often reach radically different results, and each of the opposing schools can successfully reconcile its conclusions with every relevant case to be found in the more than 2,700 daf of the Talmud.
The Ramban in the introduction to Milchemes Hashem concedes that there is no such thing as an absolutely irrefutable proof in Talmud, such as we find in geometry and trigonometry. At first glance, it appears that the Ramban is admitting that the study of Torah is in some respect inferior to that of mathematics.
Rav Yitzhak Hutner, zt"l, in one of his most strikingly original ma'amar (Pachad Yitzchak, Chanukah 9), however, explains the difference between Torah study and mathematics in terms of the different nature of the phenomena under investigation. That difference implies no inferiority to Torah study. Mathematics, indeed all science, deals with the investigation of a world in statis. Since the phenomena under investigation are static, or change according to established rules, it is possible to prove or disprove various hypotheses.
The Torah, however, deals with a world in flux, one in the process of coming into being. Our Sages say that there is no mitzva in the Torah that does not contain within it the power of revivifying the dead, i.e., transforming the natural order. Torah study is in a sense the ultimate example of the Heisenberg Uncertainty Principle, which posits that the very act of observation affects that which is being observed. Every bit of Torah study - the greatest of the mitzvos - changes the world. In a world in constant flux, always moving closer to its ultimate goal or retreating from it, there can be no perfect proofs because nothing stays the same.
The difference between the science pioneered by the Greeks and Torah study has its roots, writes Rav Hutner, in two distinct covenants Hashem made with man: the covenant of Noach and the covenant with the Jewish people at Sinai. At the former, Hashem promised Noach that He would never again destroy the world. He established the seasons, and declared that they "shall not cease." The Noachide covenant, then, is one to preserve the status quo "to all generations forever."
At the same time, Hashem imposed seven mitzvos on all of mankind without consulting Noach. Mankind had no part in the creation of the covenant. Afterwards, each person has free will to choose whether or not to follow the Noachide Laws, but they became binding without any human consent. As the sign of this covenant, Hashem pointed to the rainbow. According to the Ramban, the rainbow existed prior to the Flood; only now Hashem specified its role as a reminder of His promise to never utterly wipe out mankind again.
The covenant of the Torah is completely different in nature. Had the Jewish people not declared "we will do and we will listen," the laws of the Torah would never have become binding upon us. Our prior acceptance was the precondition for the giving of Torah. Thus the Jewish people created the covenant of the Torah through a positive act of mental affirmation. (Similarly, in halacha one can create a monetary obligation by affirming the obligation, even where there was no preexisting loan.)
The creative component is what distinguishes the covenant of the Torah. It is that component which is hinted at in the verse, "Behold, I have placed before you good and evil. Choose life." The verse refers to the giving of Torah, and the words "before you" to the Jewish people alone. For while all people have free will to observe or not observe the laws incumbent upon them - the seven Noachide Laws in the case of non-Jews and the 613 commandments of the Torah in the case of Jews - only the Jewish people created the obligation itself through a positive choice.
Unlike the rainbow, an aspect of nature that was appropriated as the symbol of the Noachide covenant, the symbol of the covenant of Torah is bris milah, an act that transforms the natural. The Greeks worshipped the human body, and considered it perfect. The Jews, however, insisted that physical perfection is only achieved through a creative, positive alteration of the natural body. Only after his circumcision, does the Torah refer to Avraham as "tam," complete or perfect.
Because the laws of the Torah only became obligatory upon us by virtue of an act of human creativity, they contain the power to transform the world. They do not merely preserve the world as it is - which is the function of the Noachide covenant; they are designed to bring a new world into being.
That task of transformation is the unique province of the Jewish people. The covenant of the Torah is not given to "all generations" equally, like the Noachide covenant. Through our Torah study and mitzva observance we are constantly changing the world. While there is nothing new under the sun, there is a realm above the stars that governs the Jewish people. (Prior to Bris bein Habesarim, Hashem first elevated Avraham above the stars and showed him that he would have no children in the natural order. Only then did He promise him descendants as numerous as the stars.)
Hashem can be deduced within nature. "Raise your eyes on high and see Who created these ," Yeshaya instructs us. The wisdom revealed within our diurnal world also commands respect. That is why we make a blessing, "Who has given of His wisdom to flesh and blood," upon seeing a wise man of the nations.
Through the Torah, however, Hashem is apprehended directly. Upon seeing a great Torah scholar, we make a different blessing, "Who shares His wisdom with those who fear Him." The difference between the blessing on a great gentile scientist and that made upon seeing a great Torah scholar reflects the difference between scientific knowledge and Torah wisdom. The former is "given" by Hashem to man; once received it does not create an ongoing connection: the latter is "shared"; it forges a lasting bond between Hashem and the one possessing Torah knowledge.
Our unique task as Jews is to connect directly to Hashem through His Torah, and to thereby participate in the creative task of bringing a new, more perfect, world into being. That is why one who breaks off in the midst of his Torah learning to admire a tree or some other aspect of nature is considered as if he has forfeited his life. And that is also why, according to Rav Hutner, we would not recite a blessing upon upon seeing a great Jewish scientist such as Einstein, for his scientific knowledge does not reflect the primary task for which he was created - knowing Hashem directly through the Torah.
The Greeks attempted to subsume the study of Torah within the realm of Greek wisdom. The "darkness" mentioned in the opening verse of the Torah, say Chazal, refers to Greece, in particular to the translation of the Torah into the Septuagint. That very act of translation reduced the Torah to the level of another branch of Greek wisdom, and its study to another form of investigation of natural phenomena.
The Chanukah lights symbolize our victory over the Greeks - the preservation of the unique nature of Torah. When we light Chanukah candles, we recite the words, "these lights are holy, we are forbidden to use them, only to look upon them." That direct looking at the lights reminds us that our task is to apprehend Hashem directly - "by your light shall we see light" - and not through deductions based on investigation of the natural world.
Only if the Jewish people reconnect to the creative realm that is above the stars through Torah and mitzvos, can we hope to escape our current situation and once again celebrate the victory of "the weak over the strong, the few over the many, of the pure over the impure, of the righteous over the wicked."