Ricardo Riaza

Departamento de Matemática Aplicada a las TIC

ETSI Telecomunicación, Universidad Politécnica de Madrid


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History and Philosophy of Mathematics

I have always had an intellectual interest towards historical and philosophical aspects of mathematics. My only written contribution in this regard can be found below (in Spanish).

R. Riaza, Aspectos culturales en la historia de las matemáticas, Boletín de la Sociedad Española de Matemática Aplicada, Vol. 35, pp. 143-157, 2006.

This amateur paper was inspired by E. Lizcano's book Imaginario colectivo y creación matemática, Gedisa, 1993, 2009 (in Spanish). Have a look also at the ancient Chinese book The Nine Chapters on the Mathematical Art.

Some other (unrelated) links:

  • M. Kline, Mathematical Thought From Ancient to Modern Times (3 volumes). In Spanish: El Pensamiento Matemático de la Antigüedad a Nuestros Días, Alianza, 1992

  • N. Bourbaki, Elements of the History of Mathematics, Springer. In French: Éléments d'Histoire des Mathématiques, Hermann, 1960. In Spanish: Elementos de Historia de las Matemáticas, Alianza

  • Historia Mathematica

  • Analysis by its History (Hairer and Wanner)

  • An English translation of Gauss' Doctoral Thesis

  • Felix Klein and the Erlanger Programm

  • Georg Cantor

  • Hilbert's problems

  • Set theory from Cantor to Cohen (A. Kanamori). Gödel on the Continuum problem

  • The collected works of Kurt Gödel. In Spanish: Kurt Gödel. Obras completas, Alianza, 1981, 2006

  • An interesting paper on the history (and historiography) of dynamical systems and chaos

  • Andrew Wiles' proof of Fermat's Last Theorem

  • Mathematics: Frontiers and Perspectives, IMU/AMS, 2000. This book includes Smale's list of mathematical problems for the 21st century

  • Millennium problems (Clay Mathematics Institute)

  • Philosophy of mathematics: an overview (Stanford Encyclopedia of Philosophy)

  • Principia Mathematica (Whitehead and Russell) in PDF: Vol I, Vol II, Vol III. More readable is Russell's Introduction to Mathematical Philosophy

  • Hilbert's Program

  • Several writings by members of the Vienna Circle can be found in English here

  • A must: Philosophy of Mathematics: Selected Readings, P. Benacerraf and H. Putnam (eds.), Prentice-Hall, 1964. 2nd ed., Cambridge University Press, 1983

  • G. H. Hardy, A Mathematician's Apology, Cambridge, 1967. Find it also in Spanish

  • "Not to threaten visiting lecturers with pokers" - Finally, a nice literary introduction to some key ideas, people (Wittgenstein, Popper) and conflicts in the 20th century philosophy of science can be found in the book Wittgenstein’s Poker. In Spanish: El Atizador de Wittgenstein, Península, 2001.

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    Literature and more

    My father, Luis Riaza, was a playwright. If you are interested in his literature, some of his main plays can be found (open access) at the Biblioteca Virtual Cervantes.

    In a completely different context, let me drive your attention to the ancient game of go. Take a look at its history. In 2016 and 2017, two Go computer programs, namely AlphaGo and AlphaZero, became major breakthroughs in Artificial Intelligence.