Mes: diciembre 2012

Aprenda un poco de inglés con… Gian-Carlo Rota (7/11)

(Sigue de las entradas Aprenda un poco de inglés con… Gian-Carlo Rota (1/11), (2/11), (3/11), (4/11),  (5/11) y (6/11))

6 Do not worry about your mistakes

Once more let me begin with Hilbert. When the Germans were planning to publish Hilbert’s collected papers and to present him with a set on the occasion of one of his later birthdays, they realized that they could not publish the papers in their original versions because they were full of errors, some of them quite serious. Thereupon they hired a young unemployed mathematician, Olga Taussky-Todd, to go over Hilbert’s papers and correct all mistakes. Olga labored for three years; it turned out that all mistake scould be corrected without any major changes in the statement of the theorems. There was one exception, a paper Hilbert wrote in his old age, which could not be fixed; it was a purported proof of the continuum hypothesis, you will find it in a volume of the Mathematische Annalen of the early thirties. At last, on Hilbert’s birthday, a freshly printed set of Hilbert’s collected papers was presented to the Geheimrat. Hilbert leafed through them carefully and did not notice anything.

Now let us shift to the other end of the spectrum, and allow me to relate another personal anecdote. In the summer of 1979, while attending a philosophy meeting in Pittsburgh, I was struck with a case of detached retinas. Thanks to Joni’s prompt intervention, I managed to be operated on in the nick of time and my eyesight was saved.

On the morning after the operation, while I was lying on a hospital bed with my eyes bandaged, Joni dropped in to visit. Since I was to remain in that Pittsburgh hospital for at least a week, we decided to write a paper. Joni fished a manuscript out of my suitcase, and I mentioned to her that the text had a few mistakes which she could help me fix.

There followed twenty minutes of silence while she went through the draft. “Why, it is all wrong!” she finally remarked in her youthful voice. She was right. Every statement in the manuscript had something wrong. Nevertheless, after laboring for a while, she managed to correct every mistake, and the paper was eventually published.

There are two kinds of mistakes. There are fatal mistakes that destroy a theory; but there are also contingent ones, which are useful in testing the stability of a theory.

El enredo de la bolsa y la vida

Visto en divulgaMAT

[El abuelo Siau habla con el protagonista de esta novela…]

Suspiró, hizo una profunda pausa y siguió hablando con la mirada perdida en el vacio. como si estuviera dialogando con sus propios ancestros.

– Nos dijeron: nada más grande que Emperador, porque Emperador es hijo de cielo. A fuerza de oír cantinela, algunos pensaban: será verdad. Otros pensaban: será mentira. Por causa de estas conclusiones vino guerra. Luego Larga Marcha y Libro Rojo. Y ya ve cómo hemos acabado. Adaptándonos a tiempos modernos. Durante siglos tuvimos dominación extranjera y pasamos hambre que te cagas. Ahora hemos aprendido lección, hemos sabido aprovechar oportunidad y nos hemos hecho amos de medio mundo. Ha sido triunfo de realismo sobre fantasías, de humildad sobre arrogancia. Occidente está en crisis y causa de crisis no es otra que arrogancia. Mire Europa. Por arrogancia quiso dejar de ser conjunto de provincias en guerra y convertirse en gran imperio. Cambió moneda nacional por euro y ahí empezó decadencia y ruina. Occidentales son malos matemáticos. Buenos juristas. buenos filósofos, mentalidad lógica. Pero números no son lógicos. Lógica está supeditada a criterios morales: bueno, malo, regular. En cambio números son sólo números. Ahora europeos no saben cuánto dinero tienen en banco ni cuánto valen cosas. Gastan sin ton ni son, se hacen lio y piden crédito a Caixa. Nosotros, por nuestra parte, no somos lógicos. Nuestra filosofia y nuestras leyes no tienen pies ni cabeza. Sólo mandarines entendían leyes y ya no quedan mandarines. Sin embargo, números son nuestra especialidad, quizá porque somos muchos.

El enredo de la bolsa y la vida, Eduardo Mendoza, Seix barral, 2012.

Aprenda un poco de inglés con… Gian-Carlo Rota (6/11)

(Sigue de las entradas Aprenda un poco de inglés con… Gian-Carlo Rota (1/11), (2/11), (3/11), (4/11) y (5/11))

5 Every mathematician has only a few tricks

A long time ago an older and well known number theorist made some disparaging remarks about Paul Erdos’ work. You admire contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdos’ work could be reduced to a few tricks which Erdos repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten. But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert’s proofs relied on the same few tricks. Even Hilbert had only a few tricks!