The most difficult course in the first semester of electrical Engineering at the Technion is, or at least used to be, “Differential and Integral Mathematics 1A”. We called it by its Hebrew acronym, “Chedva”. The letter “A” stood for “Advanced”. I assumed that the course would be an introduction to calculus, a course I had already taken in high school. Calculus was like cooking: We were given a recipe for finding derivatives or limits for all types of functions and then we just followed the recipe. It turns out that Chedva 1A was anything but cooking. Chedva 1A took us under the hood, explaining what makes calculus tick. In the first lesson, the professor got up and started talking about “epsilons” and “deltas” and then he began writing equations on the board, equations that lay at the very heart of calculus. “Where’s the beef?”, I said to myself, thinking that after this lesson was over, maybe we could get down to the business of cooking. No such luck. In each subsequent lesson we were hammered with theorem after theorem: Cauchy-Schwartz, L’Hopital, and some other Europeans whose names I cannot remember. All of these theorems required rigorous proofs. Each time the professor would prove yet another theorem, he would look at us, smile and say “Q.E.D.” – in Hebrew “M.Sh.L.” – Quod Erat Demonstrandum – or “Remember This for the Exam”.
Parashat Chaye Sarah is the only parasha in the Torah that contains a rigorous proof. Abraham sends his trusty slave, Eliezer, to his home town, Padan Aram, in Mesopotamia, to find a wife for his son, Isaac. When Eliezer arrives, he takes his camels to a well for a well-deserved drink. Eliezer turns to G-d and makes a request [Bereishit 24:14]: “Let the maiden to whom I say, ‘Please, lower your jar that I may drink,’ and who replies, ‘Drink, and I will also water your camels’ – let her be the one whom You have decreed for Your servant Isaac. Thereby shall I know that You have dealt graciously with my master.” Rebecca comes to the well, sees Eliezer and his camels, passes the Water Test, and the rest is history. Returning to Eliezer’s request, the word “decreed” is a translation of the Hebrew word “hochachta”. The most popular English translations of the Tanach, including Sefaria, Chabad, and the ArtScroll Stone Chumash, translate this word as “designated”, “appointed” or “decreed”. Nevertheless, the root of the word “hochachta” – “hochiach” – typically means “proved”. Fitting this translation back into the verse is not trivial: “Let her be the one whom You have proved for Your servant Isaac”. What kind of “proof” is this? Eliezer seems to be relying on a character test: a woman who exhibits extreme kindness by means of giving water to me and my camels is worthy of marrying Isaac. To call this a “proof” seems to be a misuse of the word. My Chedva professor would not be pleased.
The Talmud in Tractate Chullin [95b] takes Eliezer to task for his actions, accusing him of overly relying upon superstition. What would have happened, asks the Talmud, had the woman who watered Eliezer’s camels been unworthy of Isaac? What would Eliezer have done had she been physically disfigured or had she come from a disreputable family? Eliezer should have been more pedantic in his words. Rabbi Abraham Ibn Ezra, who lived in Spain in the twelfth century, comes to Eliezer’s rescue by asserting that Eliezer’s test for extreme kindness was what mathematicians call a “necessary but insufficient condition”. The wife that Eliezer would choose for Isaac would have to be extremely kind, physically fit and a family member. Eliezer’s test only covered one of those criteria. The Ibn Ezra proves his point by noting that after Rebecca waters Eliezer’s camels, he asks her [Bereishit 24:23] “Whose daughter are you?”, ensuring that she comes from the right family.
Samuel David Luzzatto, known by his acronym “ShaDaL”, a scholar and a poet who lived in Padua in the nineteenth century, offers an explanation that shines a completely different light on Eliezer’s statement. According to ShaDaL, Eliezer is telling G-d: “I am putting all my cards on the table. G-d, You must be fully aware that the woman who passes my Kindness Test is the woman whom I will choose to be Isaac’s bride, whether or not she comes from the right family and whether or not she is disfigured. I will look for no-one else. I have complete trust that You will ensure that the woman that eventually passes my Water Test will be a fitting woman for Isaac in all other aspects.” Eliezer was telling G-d that passing the Water Test would be sufficient proof that He had approved of the woman. What gave Eliezer that confidence?
Nearly every religious scientist eventually finds himself arguing with a person who cannot believe that an intellectually honest scientist could believe in the existence of G-d. At the core of his argument typically lies something along the lines of “If you can’t prove it then it doesn’t exist” or at least ‘If you can’t prove it then you can’t use it”. The religious scientist will not be flummoxed. He understands that this kind of argument is disingenuous. Gary Marcus, a professor of Cognitive Science at N.Y.U., wrote in the New Yorker in 2013, “In the empirical sciences, almost everything is a matter of weighing evidence; outside of geometry, it is rare for scientists to literally prove anything. Rather, the more typical trajectory is to rule out competing theories, and accumulate more and more evidence in favor of particular hypotheses.” In other words, not everything can be proved mathematically. If the evidence points to something, chances are that that something is true, until new evidence comes along and points to something else. The religious scientist is driven by an axiom, that G-d created this universe and that He continues to actively control it. This axiom cannot be verified or contradicted by experimental evidence. It can only be believed. Belief lies not in the intellect but in the belly. Belief differs from knowledge in that while belief can be challenged, it cannot be proved or disproved. Moreover, belief is not binary concept. It is not possible to divide humans into two categories of “Believers” and “Non-Believers”. Belief is a continuous variable. Some people possess stronger belief than others. Further, we do not maintain the same level of belief at all times. Certain events can reinforce our belief that G-d manages the world while other events can make believing in G-d more difficult. But make no mistake, a religious scientist’s belief in G-d is no less real and no less valid than an atheist physicist’s acceptance of String Theory.
In all of history, there were three exceptions to the analysis in the previous paragraph: our forefathers, Abraham, Isaac, and Jacob. These men held beliefs that were as bulletproof as if they were mathematical theorems. Our Sages in the Kabballah refer to our forefathers as “Chariots of G-d’s Holy Presence”. They were so close to G-d that to them, belief was synonymous with absolute truth. Rabbi Naphtali Tzvi Yehuda Berlin, known as the Netziv, who served as the Dean of the prestigious Yeshiva of Volozhn during the nineteenth century, notes a subtlety in Eliezer’s request from G-d [Bereishit 24:14]: “let her be the one whom You have proved for Your servant Isaac.” You will not have proved anything to me because the best I can do is to believe that You have helped me make the correct choice. My Master Isaac, on the other hand, is a man with perfect unconditional belief. He knows that You would not allow me to bring home anyone but the perfect bride. He will see her success in the Water Test as unequivocal proof. He will know, the same way he knows that 1+1=2, the same way he knows that the limit of sin(x)/x as x tends to zero equals one, that “You have dealt graciously with my master”. To believe anything else would be mathematically false.
Ari Sacher, Moreshet, 5780
Please daven for a Refu’a Shelema for Yechiel ben Shprintza and David ben Sarah.
 “Ma SheTzarich LeHochiach” – [this is] what we need to prove.
 This is the translation of the two most prominent Aramaic translations of the Torah: the Targum of Onkelos and of Yonatan ben Uziel.
 We in an earlier lesson (Chaye Sarah 5777) that this is a feat of herculean proportions.
 When Eliezer later tells the story of the events at the well to Rebecca’s family, he tells them that Abraham commanded him to take a wife [Bereishit 24:40] “from my family and from my father’s household”.
 “Can Science Lead to Faith?” at this link: https://www.newyorker.com/tech/annals-of-technology/can-science-lead-to-faith