What evidence is there that the Torah was divinely inspired? Historical evidence, prophecies, etc, for example.
Further reading on this topic would be appreciated.
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This might not directly answer the question. However, I think it is a good starting point, especially what the Rebbe wrote. I will give a short introduction, and then proceed to the words of the Rebbe.
The Torah starts with the letter "beth" בְּ (bold letter, see below), as in Genesis 1:1:
בְּרֵאשִׁ֖ית בָּרָ֣א אֱלֹהִ֑ים אֵ֥ת הַשָּׁמַ֖יִם וְאֵ֥ת הָאָֽרֶץ - IN THE BEGINNING G-d created the heaven and the earth.
The Midrash gives multiple explanations why the Torah starts with a "B" and not with a "A" (Beth and Aleph), as can be read in Bereishis Rabbah 1:10:
Why with a "bet"? Because it is an expression of "blessing."
According to the Midrash, the letter bet symbolises "berachah" - blessing(s).
The same can be read in the commentary of the Shelah (Shenei Luchot HaBerit, Torah Shebikhtav, Toldot, Torah Ohr 10):
The letter ב symbolises ברכה, blessing. The letter א would have been inappropriate, because it is the first letter of the word ארור, cursed. Had the Torah started with א, many would have thought that this was proof that the whole enterprise of Creation was doomed to failure, i.e. cursed. As a result of such considerations, G–d decided to create the universe by using the letter ב first, hoping that the universe would endure.
The Rebbe however, explains something wonderful, yet different than the opinions in the above cited Midrash and Commentary. The Rebbe explains that these explanations share a common meaning, namely "that the study of Torah is predicated on an awareness of its divine source", as Rabbi Yanki Tauber writes, here.
The Rebbe then goes on to explain what exactly the phrase "להשכיחם תורתך" - to make them forget Your Torah means (in the context of the Romans and the Chanukah miracle). The Rebbe explains (Likkutei Sichos, vol. 3, p. 815):
They had no objection to Jews studying the intellect and wisdom of Torah; all they wanted was that this study should be devoid of any sense that this is G‑d’s Torah
The Abarbanel in his commentary to the Pesach Haggadah (Zevach Pesach) explains:
G-d’s teachings are geared to all types of people, answering them “according to each person’s needs.” (Esther 1:8)
The Torah answers every single person, according to their own needs. Does this not prove the divinity of the Torah? That G-ds own essence is clothed in it.
The Shelah learns us the deeper meaning behind the phrase "there are 600.000 words in the Torah":
Kabbalists who are deeply immersed in these esoterics described it in these words: "Torah is the imprint (רושם) of Divinity, whereas אדם is the imprint of Torah. The true revelation of G–d's Divinity is through His holy names, and Torah itself is a string of G–d's holy names. It consists of 600,000 letters which represent the 600,000 souls of Israel. Torah also consists of 248 positive commandments and 365 negative commandments; they represent expressions of G–d's attribute of Mercy and G–d's attribute of Justice respectively. The 365 negative commandments correspond to 365 sinews or tendons in man. Seeing the latter are red, the Kabbalists see in this a symbolism for the attribute of Justice. The 248 positive commandments, however, represent the bones of man, something white, symbolic of the attribute of Mercy.
E.g.: The true revelation of G–d's Divinity is through His holy names, and Torah itself is a string of G–d's holy names.
Similary, Rabbi Yanki Tauber (adapted from the teachings of the Rebbe) explains:
The study of Torah requires its student to engage the faculty that is the crowning glory of the human being—the intellect; yet an equally crucial requirement is that the person empty himself of the arrogance and pretension that a human mind—even the most astute and accomplished of human minds—is capable of apprehending the infinite and supra-rational mind of G‑d. The knowledge of and understanding of Torah is a divine gift, bestowed on those who approach its study with the humility and the commitment to “conceive, understand, listen, learn, teach, keep and do”18 that which G‑d desires of us.
There is the maamid har sinai - what happened by har sinai. 600,000 Jews heard Hashem say the aseres hadibros (10 commandments), and saw the whole event happen. They told their kids, who told their kids, who told their kids... Down to us. There is also the Mesorah from rebbeim - my rebbi's rebbi's rebbi's rebbi's rebbi, all the way back, was taught by Moshe Rabbeinu.