Rabbinic Attitudes towards Mathematics
A D'var Torah on Avot 3:23
by Jonathan Baker
23 Ap 94
Mishnah: Rabbi Eliezer ben Chisma omer kinin u-pitchei niddah
hen hen gufey halakhot, tekufot u-gematriot parparaot l'chochmah.
Mishnah: Rabbi Eliezer ben Chisma says: Bird-offerings and the
commencement of menstruation; these are the body of the halakhot.
Astronomy and geometry are condiments to wisdom.
At first glance, this seems fairly straightforward: sacrifices
and the laws of ritual purity are examples of the sort of
halakhot one should study, even if they are not necessarily
interesting. Mathematics and natural philosophy should only be
studied as peripheral elements of one's learning.
This is essentially how the Artscroll siddur reads it. One
should only progress to gematria and calendar calculations after
one has sated themselves on standard halakhic materials.
The peshat-oriented commentators support this reading. Rashi,
for example, reads "gematriot" as we would, that is, as
numerological linkages between different Torah passages.
"Tekufot" are planetary orbital mechanics, which are
mathematically complex. While these areas of study appear
interesting and tempting, they yield no reward. The regular
halakhot, however, while initally seeming dull, conceal great
depths and important ideas, which will be revealed the serious
student.
Rabbi Ovadiah of Bertinoro similarly reads "parpara'ot" as
"dessert". Only after the main course of the central halakhot,
may one delve into natural philosophy and mathematics.
This attitude raises a serious question, however. Much Talmudic
material, the core of halakhic study, requires a fair amount of
mathematics. The laws governing round sukkot, surveying Sabbath
limits, the calculations for the fixed calendar: all of these
require mathematical and astronomical knowledge. How can the
Mishnah relegate mathematics to the periphery of halakha?
Let us look at the author of this mishnaic statement, R' Eliezer
Chisma.
The major story concerning R' Eliezer Chisma emphasizes his
prowess as a mathematician and the high regard in which his
teachers held him, partly for his mathematical skill.
The Talmud in Horayot 10b tells us that R' Gamaliel and R' Joshua
were traveling together on a ship. R' Gamliel had brought bread,
while R' Joshua had brought flour as well as bread. This turned
out to be necessary, as the trip took longer than expected. R'
Joshua explained why he had brought the extra flour: There is a
star which appears once in 70 years, which draws navigators off
course. [Some have seen this as Halley's Comet] I brought extra
flour in case this happened. R' Gamliel exclaimed: You are so
smart, yet here you are on this ship going abroad to earn a
living! R' Joshua replied: You think I'm in a bad situation?
Consider my students R' Eliezer ben Chisma and R' Yochanan of
Gudgoda, who can calculate the number of drops in the ocean, yet
they have no food nor place to work!
This story indicates that R' Joshua knew astronomy (tekufot), and
that his students were even greater mathematicians than he. This
mathematical knowledge was important enough for R' Gamliel to
offer them jobs at his academy or yeshiva.