Gra's knowledge of mathematics - correction?

rabbi sedley comments to "Gra's derech in Halacha & Hashkofa I - not mainst...":

Sorry to jump in to your conversation about halacha with a trivial point, but it is highly unlikely that the Gaon wrote a mathematical formula. The mathematics that is contained within Ayal Meshulash (which allegedly the Gra had translated from the Greek) is pre-Newton, which was way behind the times by the 18th century. There is no evidence to suggest that he knew modern mathematics.
Also Kramers' Law was only derived in 1923, which would have been a bit difficult even for the Gra.
I've checked wikipedia and the rest of the web and haven't found any scientific sites which give any evidence of the Gra's contribution to mathematics.
(Ralbag on the other hand .... )
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D.T. replied:

Apparently what is being referenced is Cramer's rule - not Kramer's Law. I still don't know of any evidence that links the Gra to this

From Wikipedia, the free encyclopedia

Cramer's rule is a theorem in linear algebra, which gives the solution of a system of linear equations in terms of determinants. It is named after Gabriel Cramer (1704 - 1752), who published the rule in his 1750 Introduction à l'analyse des lignes courbes algébriques, although Colin Maclaurin also published the method in his 1748 Treatise of Algebra (and probably knew of the method as early as 1729).^[1]

Computationally, it is inefficient for large matrices and thus not used in practical applications which may involve many equations. However, as no pivoting is needed, it is more efficient than Gaussian elimination for small matrices, particularly when SIMD operations are used.

Cramer's rule is of theoretical importance in that it gives an explicit expression for the solution of the system.

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RaP has made a lengthy comment which is published below. Unfortunately he has totally missed the simple valid point that Rabbi Sedley has made concerning historical reality. Rabbi Sedley did not comment on the validity of secular studies at all. Neverthess I am publishing RaP's comment simply because he does make some valid observations - even though they are the result of a total misunderstanding of Rabbi Sedley's comment.

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Recipients and Publicity responded:

The present day Haredi world is very insular. It is still fighting the cultural wars against the Haskala of past centuries. Secular studies and those who study it are despised and banned. Many children in many Haredi yeshivas and Bais Yaakov are barely taught the 3Rs, if at all.

So is it any wonder then that when the very simple idea is brought up that the Vilna Gaon valued the study of mathematics, that those closest to the Haredi mindset simply short-circuit and resort to that all-time favorite psychological mechanism of denial and lying.

When someone says they have "searched the web" and makes it sound so authoritative I get very suspicious because the web consists of tens of billions of web pages, more than even Goggle can handle, so how on earth can anyone claim definitive results on a web search alone?

For example just a simple search on Google for "Vilna Gaon secular learning" yields many interesting articles worth further research (yes it takes time, lots of it, to get good results) but in this case, here's an article by Dr. Yitzchok Levine from the Jewish Press (and of course he is grinding his own axe) but he starts his article of "The Case for Secular Studies in Yeshivas" (November 17, 2004) with:

"When I was in the illustrious city of Vilna in the presence of the Rav, the light, the great Gaon, my master and teacher, the light of the eyes of the exile, the renowned pious one (may Hashem protect and save him) Rav Eliyahu, in the month of Teves 5538 [January 1778], I heard from his holy mouth that according to what a person is lacking in knowledge of the "other wisdoms," correspondingly he will be lacking one hundred portions in the wisdom of the Torah, because the Torah and the 'other wisdoms' are inextricably linked together ..."
(From the Introduction to the Hebrew translation of Euclid's book on geometry, Sefer Uklidos [The Hague, 1780] by R. Barukh Schick of Shklov, one of the main talmidim of the Vilna Gaon.)"

and while I do not agree with Dr. Levine's hysteria and advice to yeshivas, but he does point out that R. Barukh Schick of Shklov was into mathematics because of the GRA.

So do we all have to freak out and launch into revisionistic denial, projecting our own fears about Haskala and secularization onto the GRA's life?

No doubt this is what happens, instead of thinking, well, if the GRA taught one talmid the importance of math, he surely taught it to a number of others, and with that the GRA was not passive, he was mechedesh in whatever he studied.

In any case, the private life and secretiveness of the GRA is a two-edged sword that while it allows for some "plausible deniability" theories by narrow-minded yeshivish revisionists who are stuck in their mental ghettos (afetr all there are no gedolim nor "da'as Torah" today that tells people in the yeshiva and Chasidik world to study mathematics as a pure science in depth), there is another side to the coin that may just be too frightening to contemplate and that is that Vilna Gaon was truly a real GAON (peshuto kemashma'o) who had mastery over ALL spheres of knowledge, secular and holy, and in those days secular knowledge was centered on the "queen of science" which was mathematics and the study of philosophy which was more related to theology than to anything else. That is why university granted doctorates are still called a "PhD" meaning a "doctor in/of philosophy" and the GRA's penetrating mind grasped it all including nigleh and nistar -- and I can see some bright spark standing up and saying that GRA was not really a mekubal either because not too much is known about what he taught about that subject either except by a rare few talmidei chachomim.

The GRA lived by the maxims of "dai lechochom beremiza" and "yishma chochem veyosif lekach" and given the times he lived in, with oppression from the Cathlic Church and being surrounded by enemies, much of what he said was in whispers and was known to few, but it does make it an excuse to come up with theories that the GRA was just another narrow-minded Charedi rabbi!

One thing all know, is that the GRA opposed Chasidism. But as for what he held about most other subjects in life, it is much tougher to discern his position and policies and pesakim.