Ricardo Riaza

Departamento de Matemática Aplicada a las TIC

ETSI Telecomunicación, Universidad Politécnica de Madrid


ricardo.riaza(at)upm.es

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Miscellanea

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:
 
  • Take a look at José Ferreirós works on the history and philosophy of matematics.
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  • M. Kline, Mathematical Thought From Ancient to Modern Times (3 volumes). In Spanish: El Pensamiento Matemático de la Antigüedad a Nuestros Días, Alianza, 1992
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  • 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
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  • Historia Mathematica
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  • An English translation of Gauss' Doctoral Thesis
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  • Felix Klein and the Erlanger Programm
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  • Georg Cantor. Gödel on the Continuum problem
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  • The collected works of Kurt Gödel. In Spanish: Kurt Gödel. Obras completas, Alianza, 1981, 2006
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  • Andrew Wiles' proof of Fermat's Last Theorem
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  • Millennium problems (Clay Mathematics Institute)
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  • Philosophy of mathematics: an overview (Stanford Encyclopedia of Philosophy)
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  • Principia Mathematica (Whitehead and Russell) in PDF: Vol I, Vol II, Vol III. More readable is Russell's Introduction to Mathematical Philosophy
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  • Hilbert's Program
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  • Several writings by members of the Vienna Circle can be found in English here
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  • A must: Philosophy of Mathematics: Selected Readings, P. Benacerraf and H. Putnam (eds.), Prentice-Hall, 1964. 2nd ed., Cambridge University Press, 1983
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  • G. H. Hardy, A Mathematician's Apology, Cambridge, 1967. Find it also in Spanish
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  • "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 curious about his work, his plays can be found (open access) at Biblioteca Virtual Miguel de Cervantes. I wrote this when he passed away (online version).

    Like many people, I am truly excited about some aspects of technology but deeply worried about others. Here are some of my thoughts on this topic:

  • R. Riaza, Revolución digital, tecnooptimismo y educación, Revista Diecisiete, 4, 2021. PDF.
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  • R. Riaza, Tecnologías educativas: ¿la revolución que nunca llega?, The Conversation, 2021.

    • On a different note, let me draw your attention to the ancient game of Go. Take a look at its history here. In 2016 and 2017, two Go computer programs, AlphaGo and AlphaZero, represented major breakthroughs in Artificial Intelligence. The AlphaGo vs. Lee Sedol documentary is worth watching. Some humans, such as Shin Jin-seo, are still doing well in the AI era.