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Once upon a time, I was a strong math student. My specialty was mental calculation, and while my days of lightning quick computation are behind me at this point, my brain moves at a well above-average speed when crunching a series of numbers. Is this still a useful skill? In an age where cell phones have built-in calculators, its main utility is for winning an occasional dinner-party bet.
Can you learn math from traditional Jewish sources? Not exactly, although we do see calculations here and there in the Talmud – for example, in calculating the area of a sukkah – and even, occasionally, helpful drawings which are found in the commentary of Rashi (1040-1105). You also shouldn’t learn animal behavior from the Talmud, or botany, or medicine or astronomy or a host of other subjects.
That should not be taken as a declaration that our sages were disinterested in mathematics. On the contrary, they tried to be as accurate as possible, and clearly they did have a reasonable working knowledge of the basics.
Take for example, Jacob’s promise that if G-d brought him one day back to his home safely, he would donate a tenth of his “income”. This leads our sages to observe the following (Braishit Rabbah, 70:7):
- Rabbi Yehoshua of Sikhnin said in the name of Rabbi Levi: A certain Samaritan asked Rabbi Meir, ‘Do you not say that Jacob is truthful, as the verse says “Give truth to Jacob”?’ (Micah 7:20). He said to him: ‘Yes.’ He said to him: ‘But did he not say: “Everything that You will give me I will give a tenth to You”?’ He said to him: ‘Yes.’ He said to him: ‘He separated the tribe of Levi as a tenth of his inheritance. Why did he not separate one for the other two tribes?’ He said to him: ‘Were they twelve? Were they not fourteen? “Ephraim and Manasseh will be for me like Reuben and Simeon”’ (Genesis 48:5). He said to him: ‘All the more so – if you add water, add flour.’ (In other words, if giving one “tribe” out of twelve is too little, all the more so if it’s one out of fourteen). He said to him: ‘Do you not concede to me that there were four first born sons that were exempt from the requirement? The firstborn is sacred, and sacred does not produce sacred.’ (In other words, we deduct Reuven, the first born of Leah, and Joseph, the first born of Rachel. Then we deduct Joseph’s two sons, Ephraim and Manasseh, as the sacred does not produce sacred). He said to him: ‘Happy are you, and happy is your nation, that you are found in its midst.’
Of course, I know what you’re thinking – rabbinic math isn’t that precise, as there are other ways to “solve” this “problem.” It is, nevertheless, a clever and plausible solution. And hey, it’s not like the sages were worried about winning a bet at a dinner party.
- Rabbi Scott Hoffman
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