Angel "Java" Lopez en Blog

Publicado el 7 de Junio, 2011, 12:04

De vez en cuando se alza la pregunta ¿qué utilidad tienen las matemáticas? Parece que sentarse a pensar, hacer garabatos y escribir teoremas no es una "actividad útil". Pero cualquiera que se sumerja un poco en la historia de las matemáticas, pronto caerá en la cuenta de una verdad evidente: el avance del conocimiento humano ha sido acompañado por el avance de las matemáticas. No es casual que nuestras primeras actividades en ciencia (buscar explicación a la realidad, por medio de leyes y mecanismos) nacieran en la antigua Grecia, mano a mano con el sistema axiomático y deductivo y a la formalización de las matemáticas de la mano de Euclides y muchos otros.

Hay un excelente libro de física cuántica, que estoy consultando para mi serie: Física cuántica. Es "Lectures On Quantum Mechanics" de Jean-Louis Basdevant, que recomiendo sin dudar. Ahí Basdevant recuerda a Laurent Schwartz (1915-2002) matemático francés:

Laurent Schwartz, the man I admired most, liked the question: what"s the use of doing mathematics? "It"s very simple," he said, mathematicians study Lp spaces, negligible sets, and representable functors. One must certainly do mathematics. Because mathematics allows to do physics. Physics allows to make refrigerators. Refrigerators allow to keep lobsters, and lobsters are useful for mathematicians who can eat them and therefore be in a good mood to do Lp spaces, negligible sets, and representable functors. It is obviously useful to do mathematics.

;-) Me sirve de excusa para presentar a Laurent Schwartz. ¿Por qué Basdevant escribe "el hombre que más admiro"? No solo por el caracter afable y capacidad matemática de Schwartz, sino por su claridad en sus posiciones políticas, su compromiso con ellas, en una Francia de la segunda guerra y después. La foto de este post la tomé de:

Laurent Schwartz in Math.info

Ahí leo:

The intellectual ferment of these years was paralleled by political engagement. Though from a traditionally right-wing background, he was a strong supporter of Leon Blum's Popular Front Government until he became disillusioned by its failure to support the Spanish Republicans. Similarly, his sympathies for communism were soon dampened by Stalin's show trials, though he then spent ten years as a Trotskyite, up to 1947. He claimed never to regret this, even though it almost prevented him travelling to America to receive the Fields Medal .

During the war his political activities and Jewish background put him in all manner of delicate situations.

Por ejemplo, fue uno de los que protestaron por la invasión de Rusia a Hungría. Muchos matemáticos franceses reaccionaron a los abusos del gobierno francés y el ejército en el caso de Argelia. El caso Audin lo tuvo de protagonista:

Audin, a mathematician and communist based in Algiers, was writing his thesis under Schwartz's supervision. But in June 1957 the 25-year-old father of three and opponent of French rule in Algeria was abducted by paratroopers, tortured and killed. Schwartz was tireless in his calls for justice, and organised a presentation of the young man's thesis in his absence.

Vocal in his opposition to the French campaign, he signed the famous "Declaration des 121" in favour of military insubordination. The riposte of Pierre Messmer, the Minister for the French Army (and, by the same token, of the École), was to strip him of his position at the Polytechnique, for reasons of "common sense and honour". To which Schwartz replied that since the Army commanded by Messmer had sanctioned torture and promoted torturers, such remarks were absurd.

After a brief exile in New York, he regained his post two years later ...

Se opuso también a la intervención americana en Vietnam, a la rusa en Afganistán, y la guerra en Chechenia.

En matemáticas, yo lo conocí (poco) por su trabajo en distribuciones. Sigo leyendo en la página mencionada, la descripción de su trabajo en la Enciclopedia Británica, artículo sobre Análisis, de Francois Treves:

    ... Schwartz's idea (in 1947) was to give a unified interpretation of all the generalized functions that had infiltrated analysis as (continuous) linear functionals on the space Cç of infinitely differentiable functions vanishing outside compact sets. He provided a systematic and rigorous description, entirely based on abstract functional analysis and on duality. It is noteworthy that such an approach had a precedent, in the presentation by André Weil of the integration of locally compact groups ... Because of the demands of differentiability in distribution theory, the spaces of test-functions and their duals are somewhat more complicated. This has led to extensive studies of topological vector spaces beyond the familiar categories of Hilbert and Banach spaces, studies that, in turn, have provided useful new insights in some areas of analysis proper, such as partial differential equations or functions of several complex variables. Schwartz's ideas can be applied to many other spaces of test-functions beside Cç, as he himself and others have shown ...

Por ejemplo, estableció en bases firmes las propiedades de la delta de Dirac, como mencioné en Recordando a Beppo Levi.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
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