@DoubleAA I thought we were talking Talmud and Kabbala (many more to choose from there). Anyway, 1: No. 2: I don't. 3: He didn't, but his brother did (it was finished after his death). 4: I don't know. I merely think that he may have [known enough] to say. 5: Incidentally, I believe it is known that both the Baal HaTanya and the Tzemach Tzedek were accomplished in Talmud, Kabbala, and mathematics.
After spending some time searching, I was able to track down the paper that he wrote, which was finished posthumously by Prof. Paul C. Rosenbloom. It was published in The Journal of Approximation Theory, 1978
^^PDF of the paper. It is published under the pseudonym Mark Gurari, which is the name he used when he escaped the Soviets. (I suppose if he crossed into the west under those papers, that would have become his legal name.)
I would warn all that it's 30 pages of symbols. Enjoy.
Regarding that paper, I found the following written by Prof. Shimon Silman: "It was found that some of the theorems proved in this paper were identical to results obtained by some of the greatest mathematicians of his time (Frobinius and Perron) but which Rabbi Yisroel Aryeh Leib had discovered independently and had proved with his own proofs."
Apparently, the Rebbe had this unpublished manuscript in his possession and he gave it over to Prof. Pesach (Paul) Rosenbloom - a famous Lubavitcher mathematician - so that he should publish it.
