Sofía Vasilyevna Kovalevskaya
Cuando en la facultad estudié el teorema de Cauchy-Kovalevskaya sobre ecuaciones en derivadas parciales, alguien me contó que Kovalevskaya no era autora del teorema, que fue un regalo de amor de Weierstrass. En su momento no sólo me lo creí, sino que encima me pareció romántico. Ahora veo ese comentario como la falsa deducción que seguramente vivió Sofía por ser guapa, inteligente… y mujer. Aún hoy en día he escuchado a licenciados en matemáticas achacar a su belleza el hecho de que no haya premio Nobel de Matemáticas.
Siendo muy niña escuchaba hablar de matemáticas a su tío. Según cuenta ella misma en su autobiografía:
No entendía el significado de los conceptos, pero actuaban sobre mi imaginación, inspirándome un respeto por las matemáticas como una ciencia excitante y misteriosa que abría las puertas a sus iniciados a un mundo de maravillas, inaccesible al resto de los mortales.
Cuando tenía 11 años su padre empapeló su habitación con los apuntes de un curso de Cálculo Diferencial e Integral: pudo visualizar las maravillas que contaba su tío y así relegó todos sus estudios por el de Cálculo, lo que obligó a su padre a quitarle su profesor de matemáticas, aunque ella siguió estudiando por las noches. Un día el profesor Tyrtov regaló a su familia su libro de Física y Sofía lo devoró, pero no entendía las fórmulas trigonométricas y las dedujo. Tyrtov convenció a sus padres para que la permitieran volver a estudiar.
Pero Sofía no podía acceder a la enseñanza reglada: la universidad rusa estaba prohibida para las mujeres y no podía salir del hogar paterno sin autorización paterna, así que para poder salir de Rusia se casó con el paleontólogo Vladimir Kovalevski. Estudió en Heidelberg como oyente: sólo podía asistir a las clases si el profesor lo autorizara.
En 1871 se fue a Berlín para estudiar con Weierstrass, un hombre de 50 años que, al recibir la petición de Sofía, le puso una serie de problemas que tenía preparados para sus alumnos más avanzados. Pensaba que era una forma diplomática de librarse de esa mujer. Al cabo de una semana le devolvió todos los problemas hermosa y originalmente resueltos. A partir de ese momento Weierstrass fue su mayor apoyo.
Durante la etapa de Berlín realizó tres trabajos de investigación: “Sobre la teoría de ecuaciones en derivadas parciales, Suplementos y observaciones a las investigaciones de Laplace sobre la forma de los anillos de Saturno y sobre la reducción de una determinada clase de integrales abelianas de tercer orden a las integrales elípticas”. Uno solo hubiera valido un doctorado, pero Weierstrass no consiguió que Berlín lo apoyara y Sofía defendió sus trabajos en Göttingen, consiguiendo el doctorado summa cum laude.
Doctora… pero mujer. Imposible dar clases. Volvió a Rusia con su marido y su familia y pidió permiso para presentarse a una prueba para impartir docencia, siendo rechazada. Eso unido a la muerte de su padre hizo que Sofía tirara la toalla matemática durante seis largos años, en los que tuvo a su hija y se separó definitivamente de su marido. En 1882 volvió a la carga: realizó estudios sobre la refracción de la luz y con el apoyo de Mittag-Leffl er consiguió un puesto no remunerado en la universidad de Estocolmo; el único salario que recibía se lo pagaban sus alumnos mediante colecta. Por fin, en 1889 consiguió ser profesora de pleno derecho.
Muchos consideran la estancia sueca de Sofía como su etapa más fructífera: fue editora del Acta Matemática y consiguió el premio Bordin de la Academia de las Ciencias de Francia con su trabajo Mémoire sur un cas particulier du problème de le rotation d’un corps pesant autour d’un point fixe, où l’intégration s’effectue à l’aide des fonctions ultraelliptiques du temps. Este premio era de 3.000 francos, pero se incrementó a 5.000 por la extraordinaria calidad del estudio. También ganó un premio de 1.500 coronas de la Academia Sueca de las Ciencias en 1889 y, por iniciativa de Chebychef, la Academia Imperial de las Ciencias cambió sus leyes para admitir a Sofía. Cuando por fi n iba a impartir clases con pleno derecho, una gripe derivó en neumonía y murió con tan solo 41 años.
¿Qué es una ecuación diferencial?
En una ecuación funcional, el resultado que desconocemos no es un número, es una función. Como las ecuaciones habituales,
pueden tener una o varias incógnitas.
Por ejemplo, una ecuación funcional sencilla podría ser f(x)+2f(x)-x=3. Se puede resolver como resolvemos las ecuaciones
sencillas, sólo hay que tener en cuenta que f(x) es la incógnita y x es la variable que tiene la función.
Una ecuación diferencial es una ecuación funcional en la que aparece la derivada de la función. En términos sencillos, la derivada de una función es otra función que indica cómo cambia la que teníamos; es decir, si aumenta o si disminuye y a qué velocidad. Se suele representar por f´(x). Vamos a ver un ejemplo con la gráfica de f(x)=x
Está claro que la función crece, el cambio es positivo (la derivada será positiva) pero ¿cambia la velocidad del cambio? No, cuando avanzamos un paso a la derecha subimos uno. El cambio es siempre así, constante. Por lo tanto la derivada será una función constante (horizontal) y positiva ( por encima del eje de las X ).
Para saber más…
Sobre su vida
Si te ha parecido interesante la vida y obra de Sofía, no dejes de visitar los tres artículos del blog “En Diálogo con la Ciencia” sobre ella
Sobre homenajes a ella
¿Sabías que se han dedicado sellos a esta fantástica mujer?. Aquí podrás ver uno de ellos de la serie “análisis matemático“. Además de sellos, se ha dedicado una moneda que puedes ver en la imagen siguiente junto con otro de los sellos de ella.
Sobre Saturno
Como se puede leer en su biografía, escribió sobre la configuración de los anillos de Saturno, probablemente el más bello de los planetas vistos desde el telescopio, pero ¿tú lo has visto?. A continuación te enlazamos con vídeos, animaciones e imágenes de este planeta para que puedas comprender de primera mano la atracción de muchos hacia él.
Aproximación de una sonda espacial a Saturno (fuente: NASA)
Dos años en Saturno. Montaje de la NASA con fotografías de Saturno, sus anillos y sus satélites recogidas con la sonda espacial Cassini
Sofia Kovalevskaya fue una mujer matemática con la que se cometió una gran injusticia,porque era doctora, pero por el hecho de ser mujer no pudo dar clase remunerda y se tenia que buscar la vida de otra manera. Cuando por fin iba a empezar a impartir clases remuneradas murió con tan solo 41 años.
Sofia fue una gran matemática,pero a pesar de todo por lo que pasó a la historia y por lo que hoy es recordada es por su afan de superación. Tenia un sueño y no dejo que la sociedad en la que vivia lo destruyera; era mujer y no se sentía diferente por ello, es más enseñó algo más valioso que cualquier cálculo matemático, y es que esa diferencia entre hombres y mujeres que todos veían no existía, ¿NO MERECE LA PENA SEGUIR SU EJEMPLO….?
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