[Avodah] The Gaon's Theorem

[Prof. Levine]

Until I came across this I was not aware that there was something 
called the Gaon's Theorem.

Note that the Gaon apparently felt that knowledge of mathematics was 
important, because "Gaon was
putting the notes and explanations in book form to preserve them for 
generations to come.


I do not understand why the Gaon's sefer Ayil Meshulash is not used 
as a mathematics text during the last year of math in Yeshiva High 
Schools.  Perhaps it is because it would be most difficult to find 
someone who could teach it. >:-} YL

The following is from 
http://www2.hmc.edu/www_common/hmnj/journal/26/pdf/articles/26.pdf

UNIQUE TOPICS

Some extremely interesting topics arose in this course
following the students' extensive searching for knowledge
sources. Before I compiled the course, I discovered
the book Ayil Meshulash (Stature of the Triangle)
(1960), written in the 19th century by a student of the
Jewish Torah scholar the Vilna Gaon (Genius from
Vilna). It was based upon notes found after the Gaon's
death, that derived from his oral mathematics teaching.
In this book, subtitled "On the wisdom of triangles
and geometry and some rules of qualities and algebra
author Shmuel Lukenik notes that the Gaon was
putting the notes and explanations in book form to
preserve them for generations to come.

The Vilna Gaon, or Rabbi Eliyahu was a master of
Torah, Talmud, Jewish philosophy, Halacha (Jewish
religious law), and Kabbalah (Jewish mysticism). The
bulk of his written work concerns corrections and
emendations of Talmudic texts, and interpretations of
the Shulchan Aruch (code of Jewish law). In the academic
field, the Vilna Gaon wrote on geography (The
Form of the Earth) and grammar (Eliyahu Grammar).
He was also interested in music, claiming that most
of the arguments of the Torah would be incomprehensible
without it (On-line Resources, 2001). According
to some sources, the Vilna Gaon is the author of
"The Gaon's Theorem," a principle of the mathematics
of infinity (Feldman, A., 1999). Other sources
claimed that this theorem was called "Kramer's Theorem,"
Kramer being the Vilna Gaon's family name.
Gerver (1993), however, stated that this supposition
was unlikely, as the author of this article did not
present proof for these two opinions.

After reading Ayil Meshulash, I had the idea of including
in the course Jewish and Islamic sources of
mathematics history and integrating them in mathematics
teaching. The result was a collection of materials
included in a chapter entitled "Mathematics in
Judaism and Islam," unique to this course. Every year,
a number of student pairs, both heterogeneous (Jewish
and Bedouin) or homogeneous, work on this chapter.

Ayil Hameshulash was frequently chosen for investigation
by these students, as it is both a mathematical
work including mathematical explanations and geometrical
definitions, theorems, and proofs as well as
selected topics in algebra, and an historical document.
Although the book was written 200 years ago, it still
contains explanations that cannot be found today in
any other mathematical work. The students in the
course maintain that this book offers better explanations
than those used today, and often say that they
find it exciting to study such a venerable work. In one
of the lectures, the students compared the Vilna Gaon's
presentation of the right-angle triangle with that of
Israeli mathematics teacher Benny Goren in his book
Plane Geometry - a text currently in wide use in Israeli
schools. Most of the students in the class announced
that they would adopt the former method
in teaching this topic in their classes.


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