Volume 7 Number 54

Subjects Discussed In This Issue: 

Cramer vs. the GR"A
         [Mike Gerver]
GR"A's Mathroom Bathroom (3)
         [Danny Skaist, Andy Jacobs, Frank Silbermann]
Orthodox? (4)
         [Bob Werman, Janice Gelb, Dov Ettner, Yaakov Kayman]


From: <GERVER@...> (Mike Gerver)
Date: Fri, 21 May 1993 3:26:31 -0400 (EDT)
Subject: Cramer vs. the GR"A

Several people, starting I think with Michael Allen in v7n21, have mentioned
the story, which I had heard before, that the GR"A was the first person
to prove a well-known mathematical theorem called Kramer's theorem, and
that Kramer was, in fact, the GR"A's family name. I thought that this was
a sort of frummie urban legend when I first heard it, an implausible story
which remains alive because it is repeated by people who don't know much
about math. Since it was repeated several times in mail-jewish, and no one
debunked it, I decided to look into it further, and I asked my brother
Joseph Gerver, a mathematician, what he knew about Kramer's theorem. He

>     Cramer's rule (I've never seen it spelled with a K) states that if Ax=b
>(where A is a matrix, and x and b are vectors), then x_i = det(A_i)/det(A),
>where x_i is the ith component of x, and A_i is A with b substituted for column
>i.  It is actually the fastest way to solve a system of three equations,
>especially if you are doing it by hand and all the coefficients are integers,
>and I gather that it was the method recommended to math students before the
>appearance of computers for solving any system of equations, but it has fallen
>out of favor in recent years because it requires n! operations to solve n
>equations (assuming the determinants are computed by minors), whereas Gaussian
>elimination requires n^3 operations.  It was named for the Swiss mathematician
>Gabriel Cramer (1704-1752), although Maclaurin apparently published it first.

I think it is clear from this that Cramer's rule is in fact the "Kramer's
theorem" that appears in the story. There was a mathematician or physicist
named Kramers who lived, I think, in the early 20th century, who was, among
other things, the "K" of the "WKB approximation" familiar to physicists.
But is not plausible that the GR"A would be credited with a theorem that
is generally considered to have been first proven in the 20th century. And
since the story claims that "Kramer's theorem" is well known, it is not
likely to refer to some obscure Kramer that most mathematician would not
think of when asked about "Kramer's theorem." That would be especially unlikely
if you require this obscure Kramer to have lived at the time of the GR"A
(1720-1797), since the great majority of mathematicians lived after the GR"A.

Assuming, then, that "Kramer's theorem" in the story is really Cramer's rule,
it is also pretty certain that it was not named after the GR"A's family name.
In fact, I don't think the GR"A had a family name. Most Jews in those days
didn't, and Cecil Roth's New Standard Jewish Encyclopedia does not give a
family name for the GR"A, although it generally lists famous rabbis under
their family names even if their family names are not well known. If the
GR"A did not have a family name, this could explain how the story could
persist, since no one could say "But that can't be true, the GR"A's family
name was really such-and-such."

How could the story have gotten started? If there is any basis in truth
to it, I would guess that the GR"A mentioned Cramer's rule in something he
wrote, or mentioned it to a contemporary of his who wrote about the fact
that the GR"A knew of it. Since there is some ambiguity about whether it was
first discovered by Cramer or Maclaurin, it seems that it was spread around
informally for some time before it was published, something that is more
plausible in the 18th century than it would be in the mathematical world
today. Or it could have been discovered independently by two or more
people before anyone published it. If the GR"A mentioned it to someone
before it was published, or before it was generally attributed to Cramer,
that person, if he was an admirer of the GR"A, might naturally assume
that the GR"A had discovered it himself. Alternatively, the GR"A might
really have discovered it independently of Cramer, and possibly even
before Cramer. He was acquainted with the mathematics of the day, and was
certainly smart enough to come up with Cramer's rule, if he found enough
time to work on it. And we all know where he could have found the time!

If anyone knows of any original source material that would throw light
on the question of whether the GR"A knew Cramer's rule, and particularly
whether he knew it early enough that he could have discovered it first,
or independently, I would be interested in hearing about it. By original
source material, I mean something published by the GR"A, or something
published about the GR"A by a contemporary of his, not just a recent
publication repeating the story with no substantiation.

Mike Gerver, <gerver@...>


From: DANNY%<ILNCRD@...> (Danny Skaist)
Date: Wed, 12 May 93 08:38:19 -0400
Subject: GR"A's Mathroom Bathroom

The Gra"s mathroom is being discussed interspersed with the Rav's Torah

Is it that difficult to conceive of the Gra learning mathmatics in the
same attitude that the Rav learned philosophy ?

You don't have to believe that all mathmatics was learned in the
bathroom, even though all bathroom time was spent on math. The math
would have been assigned to the bathroom merely for convenience sake and
would also serve the purpose of keeping his mind busy on permitted


From: dca/G=Andy/S=Jacobs/O=CCGATE/OU=<DCAALPTS@...> (Andy Jacobs)
Date: 12 May 93 05:40:03 GMT
Subject: GR"A's Mathroom Bathroom

I have two questions on this issue:

1) Did the GR"A write his Mathematical safer entirely in the bathroom?

2) Is it possible that the GR"A (or the story author) considered the
   study of Torah to include Mathematics?

 - Andy

From: Frank Silbermann <fs@...>
Date: Tue, 11 May 93 16:25:20 -0400
Subject: GR"A's Mathroom Bathroom

In Vol.7 #32 Reuven Bell expressed skepticism about the legend that the
GR"A would only contemplate mathematics and other secular topics at a
time when he was not permitted to learn Torah, thus in the bathroom.

Could this legend be just another instance of historical revisionism,
this time by those who wish to promote the relatively recent Halachic
innovation of forbidding secular learning?

	Frank Silbermann	<fs@...>
	Tulane University	New Orleans, Louisiana  USA


From: <RWERMAN@...> (Bob Werman)
Date: Tue, 18 May 93 03:52:13 -0400
Subject: Orthodox?

Norman Miller points out the drawbacks of using the word "orthodox," in
view of its shady origins and other uses.  He also suggests a Hebrew
word be substituted.

There are some more positive associations to the word "orthodox" than
Norman (Noyekh to readers of _Mendele_) mentions.  For example, Bishop
Newman's "I do not know who your doxy is but mine is Orthodoxy."

But even granting Noyekh's point, as a minor expert in Hebrew, may I
suggest that the best word is the Yiddish FRUM.

__Bob Werman    <rwerman@...>    rwerman@vms.huji.ac.il

From: <Janice.Gelb@...> (Janice Gelb)
Date: Tue, 18 May 93 18:12:34 -0400
Subject: Re: Orthodox?

How bout "cipah sruga" and "shachor"? Both are terms I heard used when 
I was living in Israel.

Janice Gelb                  | (415) 336-7075     
<janiceg@...>   | "A silly message but mine own" (not Sun's!) 

From: <dovle@...> (Dov Ettner)
Date: Tue, 18 May 93 13:43:35 +0300
Subject: Orthodox?

In reply to Norman Miller`s request, I would like to suggest using the
term  "Observant" in place of "Orthodox" and for Hebrew, "Shomrei Mitzvot"
or "Yirat Hashamayim".

Dov Ettner

From: Yaakov Kayman <YZKCU@...>
Date: Tue, 18 May 93 12:14:31 -0400
Subject: Re: Orthodox?

Re Norman Miller's "Modern Orthodox:" Since the term "Orthodox" as it
applies to Jews was coined by those NOT of that persuasion, and a (pre-
sumably accurate) Hebrew name is desired (by mr. Miller, at any rate),
why not "shomrei Torah umitzvot?"

Yaakov Kayman      (212) 903-3666       City University of New York
BITNET:   YZKCU@CUNYVM                  Internet: <YZKCU@...>


End of Volume 7 Issue 54