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. 143157, 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.), PrenticeHall, 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.
Back
to top
of page.
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.
