domingo, 26 de enero de 2014

El reporte de Coxeter sobre el caso de Matusalén

H. S. M. Coxeter hacía notar en su artículo An ancient tragedy (Math. Gaz., 55 393 (1971), pág. 312) lo siguiente:

«En Genésis 5: 25-29 se lee que:

"... Vivió Matusalén ciento ochenta y siete años, y engendró a Lamec. Y vivió Matusalén, después que engendró a Lamec, setecientos ochenta y dos años... Fueron, pues, todos los días de Matusalén novecientos sesenta y nueve años; y murió. Vivió Lamec ciento ochenta y dos años, y engendró un hijo; y llamó su nombre Noé...".

Por otro lado, en Genésis 7: 6 se lee esto:

"Era Noé de seiscientos años cuando el diluvio de las aguas vino sobre la tierra...".

Por consiguiente, Matusalén murió en el año del diluvio pues en tal año su edad era de

187 + 182 + 600 = 969.
años...»

Después de revisar la cuentas, es posible que algún lector por ahí se pregunte: ¿Murió Matusalén en el diluvio? O en otras palabras, ¿permitió Noé que su abuelo pereciera en el diluvio?

En The magic numbers of Dr. Matrix (Prometheus Books, NY, 1985, pág. 176.), Martin Gardner menciona que, de acuerdo al rabino Shlomo Yitzchaki (1040-1105), la respuesta a esta cuestión es negativa: según Yitzchaki, Matusalén murió unos días antes del inicio del diluvio; Dios envió el diluvio una vez que pasaron los siete días de duelo por el fallecimiento de Matusalén. Al parecer, Yitzchaki basaba su hipótesis en Genésis 7: 4 ("Porque pasados aún siete días, yo haré llover sobre la tierra cuarenta días y cuarenta noches...").

domingo, 12 de enero de 2014

Una anécdota retomada del "muro" de Ken Ribet


«There's a long story about this page, and I might as well tell it here. I uploaded this image because one of my facebook friends asked me about it yesterday [9/11/2009]; she had heard mention of it at the MSRI, but the story that she heard was—how shall I put it—not completely accurate.

Best to tell it as I remember it...

I took a graduate algebra course at Brown when I was an undergraduate. I bought a copy of Lang's "Algebra (3rd edition)" around that time. It was the bible of graduate algebra, and I suppose that it still is. When I was at Harvard, I studied very hard for the written qualifying exam that we sat for at the end of our first year of graduate work. I spent months mastering the core material in algebra, topology and analysis. I got a little frustrated by Lang's style and wrote the comment that you see in black ink. Years later, Serge had my office in Princeton while I was away in Paris. As usual, he consulted his own books, and he found my comment. He added his own (bottom of the page) and told me about it when I returned to the US. We both had a good laugh.

I was amazed, years later, when a German mathematician asked me about this page when we were at the Canadian number theory meeting in Vancouver—this must have been 20 years ago. How did the guy know? Serge or I must have talked, and word had gotten around.

I made this image in July, 2001 by pointing my first digital camera at the page and pressing the shutter. Serge was in town, and I told him that I wanted to link this image to the web page for the graduate algebra course (Math 250A) that I was about to teach. That way the students could see it. "Of course!" As the semester progressed, mathematicians around the world found out about the link on my web page and began forwarding the URL to their friends. One day Serge phoned me in my office: "You mean anyone in the world can see this? Take it down!" So I did.»