I greatly enjoy your publication, and avidly read it whenever I come across it (I am not a subscriber, but my sister is). I am impressed that the Rebbe’s philosophy is both intellectually stimulating and spiritual at the same time. My question to you is as follows: everything the Rebbe says can be predicated on a single fact: that the Torah is the word of G-d, communicated to the people of Israel at Mount Sinai more than three thousand years ago. I understand that to every believing Jew this is a matter of faith, and that for the believer it makes no difference that there are many others who believe different or even opposite things. My question is: Is there any objective way that this can be proven as a historical fact? Has the Rebbe ever addressed the issue in such terms?
“Proving” the revelation at Sinai, or any of the other fundamentals of the Jewish faith, is not an issue in the Rebbe’s philosophy and teaching, or in chassidic teaching as a whole. Never did the Rebbe deliver an address or write an essay the objective of which is to prove G-d’s existence, the divinity of the Torah, the coming of Moshiach, etc. These are givens, as real and as absolute (indeed, more real and absolute) than the fact that “I am alive,” “I love my children,” “winter will end and spring will come,” and the countless other facts we never even consider the need to prove. Rather, chassidic teaching comes to illuminate these givens and integrate them into our lives. G-d exists; what can we understand of the nature of His existence and His relationship with His creation? G-d gave us the Torah; what is the nature of this “gift” and how do we receive it? Every word of Torah is the revealed wisdom and will of G-d; what is the deeper significance of this particular biblical verse or talmudic saying, and what is its relevance to our daily lives?
However, the Rebbe did address such questions on several occasions, in direct response to individual queries in writing or in person. In these cases, the Rebbe’s answer was usually based on the traditional Torah works that deal with these issues (R. Saadiah Gaon’s Emunot v’De’ot, Maimonides’ Guide for the Perplexed, Rabbi Judah ha-Levi’s Kuzari, etc.), punctuated, of course, with his unique style and approach. What follows is based on four letters  the Rebbe wrote in response to the question you raise: is there any way to “prove” the revelation at Sinai?
The first thing that must be established is what constitutes “proof.” Often, people requiring that something be proven to them (especially if it is something they would rather not accept) employ a double-standard: the degree of proof on which they rely in their daily lives, including their most crucial decisions, is suddenly insufficient.For example, people often say: “I don’t rely on what others tell me; I insist on seeing something with my own eyes before I’ll accept it as true.” But is this, in fact the case? Say you needed to fly from L.A. to London. You walk into a travel agency, pay several hundred dollars, and walk out with a slip of paper in return. How do you know that this slip of paper will get you a seat on the plane? This is the first time you’ve used this agency, but a friend has told you that it is reliable; furthermore, the travel agency has an established office in the center of town, and every day, many people rely on its credibility. Without even thinking twice about it, you have relied on the “hearsay” of a few hundred people, most of whom you have never met and probably never will. This was “proof” enough for you to part with a full week’s salary.
What’s more, you get on the plane! Did you check the engine, the fuel tanks, and the landing gear? Did you test the pilot’s ability, or even ask to see his certification? But this is a well-known airline, which flies thousands of people safely every day. You’re therefore convinced that there’s a qualified team of mechanics somewhere who have checked whatever there needs to be checked, that the pilot is properly trained, etc., etc. On the basis of the fifth or sixth-hand testimony of people you’ve never met, you put your very life on the line.
And what is “history” if not eyewitness accounts by anonymous individuals, passed by word of mouth and eventually set down in writing? A few hundred people saw George Washington crossing the Delaware River on the night of December 25, 1776, and the event’s repercussions were directly experienced by a few thousand others, and two hundred years later no one “in his right mind” would contest that the event indeed took place. But we don’t even require that much evidence: it is enough that an archeologist unearths a tablet describing a battle purported to have occurred thousands of years ago, and that the said battle fits in with other similarly substantiated information we have about that period, for the event to be considered “highly probable”; if another tablet is unearthed in another part of the world in which another eyewitness describes the same battle in the same (or similar) way, it becomes historical fact.
To summarize: In both our daily lives and our knowledge of the past, we rely on the testimony of other people. The greater the number of witnesses, and the greater the consensus among them, the greater the certainty. A historian will devote years of his life to research a certain event, and an airline passenger will allow himself to be lifted 30,000 feet into the air, based on such “proof.”
Now consider the following event: six hundred thousand men between the ages of twenty and sixty, plus an equivalent number of women, plus at least that many children and elders, witnessed, firsthand,  the revelation of G-d at Mount Sinai and heard Him proclaim “I am G-d your G-d…” These included people from all walks of life—simple folk and scholars, rich and poor. They all saw and heard the same thing, and gave a detailed account of the event to their children, who, in turn, related it to their children, and so on to this very day. In the 3,308 years since then, there was never a single moment in which less than several hundred thousand individuals attested to a unanimous version of this event, including many who had been without contact with each other for centuries.
It can therefore be unequivocally stated that there exists not a single event in the whole of human history that is as thoroughly proven and corroborated as the divine revelation at Mount Sinai. 
 . Igrot Kodesh, vol. XVII, pp. 388-393; ibid. pp. 490-492; vol. XVIII, pp. 388-391; vol. XIX, pp. 405-406.
 . See following note.
 . In contrast, the Christian religion is based on events witnessed by no more than a handful of individuals, and Islam is based on a single individual’s account of a revelation he experienced.