I am constantly reminded here that the Western philosophy and scientific tradition which is based on ancient Greek wisdom is not the right way to view Judaism. On the other hand when I say that I am a mathematician people keep asking me if I had a chance to study Talmud, because Talmud is supposedly “very mathematical”.
First, what is Talmud? The Talmud is the central text of Rabbinic Judaism and the primary source of Jewish religious law and Jewish theology. It was composed between 2000 and 1500 years ago.
Here is my first impression of Talmud.
When I first studied Talmud under the supervision of a senior student, I think I had the same experience as a first-year mathematics student has during my lecture of mathematical analysis. The teacher presents weird symbols, uses alien type of reasoning and finally concludes that the theorem is proved – leaving the student dumbfounded and full of doubts. In the case of mathematics these are mathematical symbols, a mathematical theorem and a mathematical proof. In the case of Talmud, there is a page full of Hebrew alephbeth writing part of which is written in a different script (so-called “Rashi script”), part of which is Aramaic and part of which is biblical Hebrew. Instead of the theorem there is a question, e.g. “Does one drop of non-kosher oil in a soup render the entire soup non-kosher?”, and instead of the proof there is a recorded dialogue between ancient Rabbis who lived more or less 1700 years ago who usually end up with a conclusion. Additionally there is a large page worth of commentary. Here is a comparison:
A page from Babylonian Talmud.
A page from my PhD thesis
Similarities between Talmud and math.
As explained above, the structure of reasoning and appearance is somewhat similar. There is more to it. Talmudic discussion proceeds according to established principles and rules. One can metaphorically say that the Torah and the Oral Torah (or its parts) have the status of axioms. There are also rules on how these axioms should be applied and what to do in the case of a contradiction, say, two different sources provide principles whose application contradict each other. It does not look like formal mathematics, but I would be willing to see it as proper mathematics, because it was written more than a thousand years ago.
Euclid wrote his Elements hundreds of years earlier, but mathematics hardly developed for 2000 years after Euclid, so mathematically we are speaking of the same era.
Euclid’s Elements is not written in modern formal mathematical notation either. Like the Talmud, it is also a form of discussion. Euclid’s “axioms” resemble more Talmudic principles than modern mathematical axioms. And Euclid’s “proofs” resemble more Talmudic discussion than modern day mathematical proofs. However, there is a fundamental difference between Talmud and mathematics. If we find a mistake in Euclid’s proof, we will correct it without a second thought.
Similarities between Talmud and poetry.
The fundamental difference between Talmud and mathematics is that the conclusions drawn in Talmud are fixed. This is also the reason why people actually readoriginal Talmud!! Do mathematicians read original texts by Euclid? Hell no! Have they even seen it? Maybe in a museum or out of curiosity, or maybe they have seen a photo of one page while studying history of mathematics. The religious belief is that Talmud was written with divine inspiration. So from the point of view of mathematics it is kinda funny: On the one hand there is argumentation, but on the other hand you are not allowed to come up with better arguments, or spot mistakes in the original arguments. What’s the point of the arguments then? This question results in a misconception and the wrong metaphor (mathematics). In fact, while studying Talmud, you can, and are even invited to find problems, contradictions and apparent inaccuracies in the text. You are supposed to apply as much of your own intellect as you can when reading it. Unlike in mathematics, if you find a “problem” in Talmudic “proof”, your job is not to correct Talmud, but rather try to figure out why is the problem there, how can we learn something from it, or which Rabbi should we ask for help. The end result is always that Talmud remains intact, but you have learned something.
Mathematics: The more recent is more accurate. Mathematics improves with time.
Talmud: The original text is perfect. We can exercise our mind by reading and analyzing it.
It seems that the comparison to mathematics is losing its power. But now we can compare Talmud to poetry. If you are reading a poem by Shakespeare, your goal is not to improve it. Even if you are a scholar of English literature and you are analysing Shakespeare’s poems, the last thing you want to do is to say “This poem is imperfect. Changing the second-to-last-line will make it better” and then publish the new “revised” poem. That sounds ridiculous, because it is. It seems that this is very much the attitude towards Talmud.