Angel "Java" Lopez en Blog

11 de Septiembre, 2013

Publicado el 11 de Septiembre, 2013, 12:38

En estos días, estoy estudiando y leyendo bastante sobre matemáticas, y sobre la historia de las matemáticas. Pueden ver mi actividad en Twitter o en los posts que escribo cada mes. Ayer, en mis lecturas, me encuentro con

The Elements of the Theory of Algebraic Numbers
por Leigh Wilber Reid (Professor of Mathematics in Haverford College)

publicado en Nueva York, 1910, que notablemente tiene una introducción escrita por el mismísimo David Hilbert (en alemán, traducida al inglés). No quiero olvidarme de este dato, así que hoy lo comparto con este post:

The theory of numbers is a magnificent structure, created and developed by men who belong among the most brilliant investigators in the domain of the mathematical sciences: Fermat, Euler, Lagrange, Legendre, Gauss, Jacobi, Dirichlet, Hermite, Kummer, Dedekind, and Kronecker. All these men have expressed their high opinion respecting the theory of numbers in the most enthusiastic words and up to the present there is indeed no science so highly praised by its devotees as is the theory of numbers. In the theory of numbers, we value the simplicity of its foundations, the exactness of its conceptions and the purity of its truths; we extol it as the pattern for the other sciences, as the deepest, the inexhaustible source of all mathematical knowledge, prodigal of incitements to investigatiion in other department of mathematics, such as algebra, the theory of functions, analysis and geometry.

Moreover, the theory of numbers is independent of the change of fashion and in it we do not see, as is often the case in other departments of knowledge,  a conception or method at one time given undue prominence, at another suffering undeserved neglect; in the theory of numbers the oldest problema is often to-day modern, like a genuine work of art from the past. Nevertheless it is true now as formerly, a fact which Gauss and Dirichlet lamented, that only a small number of mathematicians busy themselves deeply with the theory of numbers and attain to a full enjoyment of its beauty. Especially outside of Germany and among young mathematicians arithmetical knowledge is little disseminated. Every devotee of the theory of numbers will desire that it shall be equally a possession of all nations and be cultivated and spread abroad, especially among the younger generation to whom the future belongs. Such is the aim of this book. May it reach this goal, not only by helping to make the elements of the theory of numbers the common property of all mathematicians, but also by serving as an introduction to the original works to which reference is made, and by inciting to independent activity in the field of the theory of numbers. On account of the devoted absorption of the author in the theory of numbers and the comprehensive understanding with which he has presented into its nature, we may rely upon the fulfilment of this wish.

Vean que menciona que la teoría de números no está muy difundida fuera de Alemania, como era el caso entonces. Para Hilbert, teoría de números es teoría de números algebraicos, en gran medida. Tengo que averiguar cómo conoció al profesor Reid. No parece que haya relación con Constance Reid, la biógrafa de Hilbert (y hermana de Julia Robinson, que tuvo su participación en la resolución de uno de los problemas de Hilbert).

Nos leemos!

Angel "Java" Lopez