The Vilna Gaon’s Theorem – Fact or Urban Legend?

In the Yeshiva world some people like to attribute the Vilna Gaon’s mathematical expertise (from his publication of a Trigonometry book Ayil Meshulash) and giving him credit to Cramer’s Theorem (his grandfather’s last name was Kremer, hence the derivative). I would like to debunk the bunk.

Firstly, while the Vilna Gaon wrote amendations and corrections on the Talmud based on Mathemics and likely was well-versed, the Ayil Meshulash book was a basic “intro” book to Trigonometry. Most high-school textbooks today cover much more (thanks, Reb Micha Berger) – see here.

Secondly, Cramer’s theorem/rule has two authors. Both were Gentiles, forget Rabbis with a secular name corresponding with Eliyahu.

  • Cramer’s Theorem (the result that if X and Y are independent real-valued random variables whose sum X + Y is a normal random variable, then both X and Y must be normal as well) has been attributed to Harald Cramer (September 25, 1893 – October 5, 1985), a Swedish statistician and probabilist, and
  • Cramer’s Rule (an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution) was attributed to Gabriel Cramer (1704–1752).

This of course is not to say that the Vilna Gaon was not well-rounded in the Maths and Sciences. This is more of a matter of getting the facts straight.

Any questions?