So there I was, first day of calculus class, and the professor, Dr Leon Ehrenpreisz”l hands out a xerox of a page of gemara. The blatt is Sukkah 8a, a conversation of the minimum size of a sukkah, and what it would mean for someone who makes a circular sukkah – do we need to match the diameter of the circle to the length of the smallest square, does the sukkah have to large enough to encompass the smallest square, or a position in the middle, that it be the same in area? In discussing this last position, the gemara explains that the area must be 3*r*r, the limit of approximating πr2 that is “close enough” for halakhah.
Tosafos then set out to prove that given that the circumference of a circle is π times the diameter (2πr), this would be the area of the circle. These diagrams are reproduced from the Tosafos as it appears in the Vilna Shas.
- In the top left, we see the circle filled with co-centric strings. The outer string must be πd = 2πr long, since it’s the outside of the circle.
- We then cut the strings from one edge to the middle, as denoted by the white radius.
- Unwrap the strings, producing the triangle on the right. This triangle’s rightmost string is the old 2πr string.
- Now cut the strings from the obtuse point down the middle, again, as denoted by the white line. This will produce two right triangles, of the same area as the first one. Each triangle has a horizontal side of r, and a vertical side, half that long strong, of πr.
- Rearranging the right triangles, we get the rectangle shown in the bottom left. The rectangle’s short side is the side we already identified as being r wide, and the long side is πr.
- The area of the rectangle is thus r*πr =πr2, and since that’s the string we started with, that means the area of the original circle must be πr2 as well.
However, Dr Ehrenpreis noted, this proof isn’t what a contemporary mathematician would consider rigorous. Rather than strings of finite width, what would happen if we use ever skinnier “strings” and progressively approached the limit of an infinite number of them, each of zero width..
And that’s how Dr Ehrenpreis introduced the notion of limits, with which he began teaching calculus in earnest.
But to the man who also worked as Rabbi Eliezer Ehrenpreis, there was much less value to math without connecting it to Torah. Secular and knowledge as one seamless whole — an example of a life lived with Torah im Derekh Eretz.
He gave a course titled “Modern Scientific and Mathematical Concepts in the Babylonian Talmud”, where we explored topics like how the machloqes about whether Adam was created as a newborn or at the same point of development as a 20 yr old could explain debates about the international date line. (Was the sun created at dawn or at noon over Jerusalem?) How using set theory and the notion of classes might explain the difference between doubts that are resolved by probability, and those considered gavu’ah. (A question that stuck with me so much, I eventually developed the ideas in this post. A different resolution.) Or how the question of the age of the universe is meaningless, since the physical constants — those concepts that divide the quantum uncertain world from the commonsensical one, the relativity that defines time itself and its speed of flow — the constants themselves were being created. And if the one constant called alpha, a ratio of most of the other fundamental constants of physics, was shrinking asymptotically to its current value until the revalation at Sinai (as implied by the medrash linking “the sixth day” to the sixth day of Iyyar, when we reached Mt Sinai), then it’s quite possible the rainbow wasn’t visible to the human eye until after the flood.
Dr Ehrenpreis was one of the five most famous mathematicians of the generation. He not only appeared regularly in the journals at age 77 in a field where you proverbially peak at 27, there were conferences held and journals published in his honor. A chair was inaugurated for him at Temple University. On Dr Claude Chevalley‘s Wikipedia page, his having Dr Ehrenpreis as his PhD student in Princeton is among his listed accomplishments.
But we’re also speaking of a man who embraced Torah observance later in life back in a time when no one spoke of “kiruv“, “baalei teshuvah“, never mind “BTs”. He studied under Rabbi Yehudah Davis and then Rav Moshe Feinstein. Legend around YU had it that he received semikhah from Rav Moshe a mere 5 years after the first time he opened a gemara.
Meeting Rabbi Ehrenpreis might have posed a halachic problem: Do I say the berakah of “שנתן מחכמתו לבשר ודם — … Who gave from His Wisdom to flesh and blood”, the blessing made on meeting a superlative secular scholar? Or do I say the berakhah “שחלק מחכמתו ליראיו — Who apportioned from His Wisdom to those who have yir’ah of Him” being that this is one of the most brilliant minds I ever met who studied Torah? Do I say both — and if so, which comes first?
But in truth, the question wouldn’t have come up even if I thought of it. The berakhah is said when awestruck by someone’s wisdom. And Rabbi Ehrenpreis was too down to earth to leave anyone awestruck. This was also the man who ran in every NY Marathon from its inception in 1970 until he got too ill in 2007. Ran in 37 marathons — and completed all 37, holding a record for the oldest person to complete the marathon by a large margin.
Yes, he enjoyed discussing intellectual pursuits. He leined from the Torah with a precision and meticulousness that showed the same inclinations that made him successful in math. He more than enjoyed teaching, he had a deep-seated need to teach.
And that need to give wasn’t merely the ego of someone who knew he was more intelligent than the others in the room. It extended to his giving tzedaqah; Rabbi Ehrenpreis was the kind of man charities repeatedly honored. His Shabbos table constantly had guests. There was always someone in need of a place to stay borrowing a guest room.
But he would not talk math with another Jewish mathematician (regardless of religious affiliation) without the conversation ending up in both Torah and in catching up on what’s going on in their lives. A world-class genius, yes. But he had no more problem finding what to speak about with his children who inherited that intellect as he did with his son who has Downs. And he could find what to say to the homeless person who sat next to him on the subway. The woman who cleaned the trash in his hospital was struck by how Rabbi Ehrenpreis would remember her son’s name and ask about him. Awestruck by Rabbi Ehrenpreis? Never in his presence.
Rabbi Dr Eliezer Ehrenpreis passed away An exemplar of Torah im Derekh Eretz, of chessed, of “accepting all people with a beautiful expression on the face” regardless of the events in his own life, of connecting to others. A Renaissance Man who was one of my heroes.
תהא נשמתו צרורה בצרור החיים
May his Soul be bound in the bond of life