• Matemáticos reconocidos poco conocidos

    Karl Weierstraß
    (1815 - 1897)

    Maestro de Cantor, Runge,  Schwarz  y de toda una generación de matemáticos alemanes, Weierstrass es el responsable de uno de los métodos más efectivos en Cálculo: el método épsilon (nombrado así pues su notación utiliza la letra griega ε). Gracias a este método se pudieron probar varios teoremas fundamentales para el fundamento de la matemática infinitesimal lo que a la postre permitió varios de los desarrollos tecnológicos de la actualidad.

    Nacido en Ostenfelde, Westphalia (ahora parte de Alemania) , en 1828, al establecerse su familia en Paderborn, ingresó al Gimnasio Católico (institución equivalente a la educación media superior) y paso mucho de su tiempo leyendo el Journal of Pure and Applied Mathematics,  que era la revista matemática líder en Europa.  

    Mientras era profesor en el Instituto Industrial de Berlín, Weierstrass desarrollo una de las más grandes ideas matemáticas hasta el momento.  En su “Introducción al Análisis” druante los años 1859-1860, dio al mundo una rigurosa metodología para que los matemáticos trabajaran con la noción de secuencias infinitas o series que alcanzaban un límite. 

    Hasta ese momento, mucho del desarrollo del cálculo Newtoniano se basaba en ideas, nociones que se sabían verdad pero no se habían demostrado rigurosamente. El concepto de “límite infinito” aplicado a variables fijas, como en la expresión “n tiende a infinito” no se sabía realmente su significado formal.  El método épsilon resolvió esto.

    Weierstrass razonó: En lugar de que el límite estuviera definido para n como el proceso de alcanzar el infinito, por qué no definimos una secuencia infinita que tenga un límite si para cualquier épsilon  ε, siempre puedes encontrar un entero n tal que para todos los enteros m>=n, el emésimo término de la secuencia siempre estuviera a ε del límite.

    Entre los conceptos que gracias al método épsilon se pudieron formalizar se encuentran:
    + El concepto de continuidad , pieza clave para el desarrollo de la ciencia
    + El teorema de Weierstraß que trata sobre máximos y mínimos locales, y
    + Teorema de Bolzano-Weierstrass , otra pieza fundamental en la construcción de los ladrillos fundamentales del cálculo: los números Reales.

    Mucho le debe la humanidad a este gigante Alemán de las matemáticas.

  • Ansiedad



    María Márquez es redactora en jefe de un prestigioso periódico de tiraje internacional. Su puesto en la empresa le reporta buenos beneficios económicos, pero también le endosa una gran responsabilidad. Tiene tres hijos de 5, 7 y 14 años, que aun siendo lo mejor que le ha ocurrido en su vida, cierto es también que le proporcionan una responsabilidad adicional, que unida a la de su trabajo le causan un estrés constante. Por si fuese poco, su padre hace más de un año sufre de Alzheimer. María apenas tiene tiempo para sí misma, y vive en un estado de alerta constante e indefinido. Su marido es un buen hombre y le ayuda en lo que puede, pero es poco hábil en el hogar y su ayuda es insuficiente en la mayoría de las ocasiones, y un verdadero lastre en otras.

    Es lunes y María se ha incorporado a su puesto en el periódico sin haber descansado lo suficiente durante el fin de semana, una cierta tristeza e irritación le embarga. Frente a la pantalla de la computadora trabaja en la nueva portada semanal del periódico. Comienza a sentir que un malestar impreciso y poco definido le invade. Una extraña y desagradable sensación la envuelve y no la deja estar. Su ritmo cardíaco está ligeramente acelerado, y de vez en cuando siente alguna palpitación. Le duele la cabeza y su espalda está rígida. Apenas ha comido en la mañana, se había levantado con un hoyo en la boca del estómago que le impedía ingerir los alimentos.



    María se levanta de la silla, toma su bolso y saca una caja de paracetamol buscando aliviar su malestar. Súbitamente siente que no entra aire en su pecho. Su respiración se acelera vertiginosamente, pero cuanto más aire inspira, más se ahoga. Siente mucho miedo y piensa que morirá, en su cabeza se aglutinan fantasías fatalistas: “Esto es un infarto, creo que me viene un paro respiratorio, y si me muero, ¿qué pasará con mis hijos?” Presa del pánico comienza a llorar y gritar. Sus compañeros, alarmados, rápidamente acuden a prestarle ayuda, llaman una ambulancia que la lleva al hospital.

    Más tarde, el diagnóstico: Crisis de ansiedad. O lo que es lo mismo: ataque de nervios. María ha sufrido su primera crisis de ansiedad. Obviamente, no todas las crisis de ansiedad son tan aparatosas. Existen grados intermedios, pero está demostrado que para llegar al cenit de la ansiedad, ésta, con toda seguridad, debió haber aparecido tiempo atrás, en principio de maneras casi imperceptibles, y más tarde se fue incrementando y retroalimentando hasta alcanzar paulatinamente unos niveles insoportables.

    Las crisis de ansiedad son comúnmente confundidas por quienes las sufren –y en ocasiones hasta por los médicos que las atienden- con cuadros de cardiopatías, problemas gastrointestinales o con síntomas consecuentes de trastornos hormonales, por ello deben ser descartadas otras enfermedades y/o patologías.

    La ansiedad es una emoción connatural del ser humano, tal y como lo es el miedo, la tristeza, la alegría y tantas otras, y cumple una función muy interesante relacionada con nuestra supervivencia. Un nivel “óptimo” de ansiedad nos lleva a esforzarnos, a resolver el o los problemas que la generan, incluso nos puede llevar a ser creativos, pero cuando la sensación de ansiedad sobrepasa los límites de tolerancia de la persona y alcanza niveles patológicos, puede llegar a ser muy preocupante, y si esto se convierte en algo sostenido, crónico, permanente, puede ser de proporciones fatales. Un nivel alto y sostenido de ansiedad puede desencadenar problemas físicos graves. Y si a ellos se le aúnan cosas como dieta alta en grasas y carbohidratos, vida sedentaria, colesterol alto, antecedentes genéticos de problemas cardiovasculares y/o cáncer, el desenlace no será bueno. En otros casos la reaparición de la ansiedad puede ocasionar el desarrollo de trastornos mayores como fobias, neurosis de ansiedad generalizada (en la que ataques como el antes descrito se vuelven un martirio cotidiano) o incluso enfermedades graves como la depresión, que requieren un tratamiento largo psicoterapéutico, psiquiátrico y posiblemente no ambulatorio. En todo caso, siempre es necesario acudir con un especialista con el fin de evitar que el trastorno reaparezca y se haga crónico.



    CONCLUSIÓN: La ansiedad en sí misma no es mala, sino por el contrario es beneficiosa siempre que se desarrolle dentro de parámetros moderados y estables. Se vuelve patológica cuando sus niveles dejan de ser normales y se incrementan y exacerban. Para que esto no ocurra debemos aprender a pedir ayuda cuando la necesitamos o a decir con sabiduría y autoconocimiento “no puedo más” a pesar de las heridas narcicísticas que esto pueda causarnos. Si es de nuestro conocimiento alguna situación conflictiva y/o dolorosa, ya sea del pasado o del presente, ignorarla no la resolverá y tampoco lo hará el hecho de intelectualizarlo, hacerse cargo de las cosas implica un proceso de conciencia y un trabajo de elaboración que nos tomarán también un poco de tiempo. Adoptemos una forma de vida sana, dediquémonos más tiempo a nosotros mismos, afrontemos nuestros problemas a su debido tiempo sin permitir que se prolonguen indefinidamente, organicemos bien nuestro tiempo y nuestra vida, no aspiremos nunca a todo aquello que no podamos alcanzar, sepamos delegar, seamos felices con las pequeñas cosas de la vida y, sobre todo, aprendamos a conocer y a interpretar nuestro cuerpo y nuestras sensaciones, para de esta forma poder entender y saber manejar nuestra ansiedad con el fin de que nunca sea ella la que nos maneje a nosotros, y así evitaremos en la medida de lo posible el consiguiente sufrimiento y perjuicio.


    ¿Sabías que...?

    La ansiedad es llamada la epidemia silenciosa del siglo XXI. En 2001 un sondeo realizado por la OMS arrojó que aproximadamente 450 millones de personas se han visto aquejadas por algún tipo de ansiedad y, según la revista PsicologiaCientifica.com, la mujeres son dos veces más propensas a padecer esta clase de trastornos psicológicos.


    Ilustrado por Engendro
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