History of Mathematics. Specialized Topics
Cryptography:

 Decrypted Secrets
 F. C. Bauer. History and some technical description. $28
 Algebraic aspects of Cryptography, Chapter 1
 Neal Koblitz. $60.
 Elementary Cryptanalysis
 Helen Fouché Gaines $6:50.
Indian Mathematics:

 B. Datta and A. N. Singh, Hindu Mathematics
 Available from Firestone Library, Princeton
 I have a xerox copy
 Colebrooke, Hindu Algebra and Mensuration
 Available from Firestone Library, Princeton
 I have extensive extracts
The notion of Proof

General views

 Imre Lakatos, Proofs and Refutations
 See the biography of
Lakatos
(with references) at the St. Andrews site.
Euclid, and the Parallel Postulate

 Hilbert, Foundations of Geometry
 Proclos, Saccheri, Bolyai, Lobachevski, NonEuclidean geometry
Logic

 Nagel and Newman, Godel's Proof

Proofs of impossibility

 Classic Greek problems
 Quadrature of the circle, trisection of the angle, duplication of
the cube
Proof by computer

 Peter L. Renz, Mathematical Proof: what it is and what it ought to be,
TwoYear Coll. Math. J. 12 (1981), 83103
 Doron Zeilberger
Medieval European Mathematics
 Some suggestions by Teresa Kuo


A website with links and references focussed on this topic.
 A mixed bag
 Books by Suppes/Moravcsik/Mendell, Pearl Kibre, and Marshall Clagett
 (Iris search).
Descartes
 Selections from the St. Andrews site reference list
 Books

 Descartes: Philosophy, Mathematics, and Physics
 S. Gaukroger, editor
 The Scientific Work of René Descartes
 J. F. Scott (1987)
 Articles

 Descartes and the philosophy of mathematics
 A. LoBello, Math. Intelligencer 13 (1991), 3539
 Descartes and the geometrization of algebra
 C. Boyer, Amer. Math. Monthly 66 (1959), 390393
 Fermat and Descartes
 C. Boyer, Scripta Mathematica 18 (1952), 189217.
 Descartes and the birth of analytic geometry
 E. Forbes, Historia Mathematica 4 (1977), 141151
 Descartes' "Geometry" and the classical tradition
 E. Grosholz, in Revolution and Continuity 183196 (1991).
 Mathematics, Descartes, and the rise of modernity
 R. Harris, Philos. Math. 3 (1988), 120
 Descartes and the geometrization of thought: the methodological
background of Descartes' "Geometrie"
 T. Lenoir, Historia Mathematica 6 (1979).
 Shifting the foundations: Descartes' transformation of ancient geometry
 A. Molland, Historia Mathematica 3 (1976), 2149
 The influence of mathematics on the philosophy of Descartes
 R. Moorman, Nat. Math. Magazine 17 (1943)
Operations Research
 Two links
Back to resource
page for History of Algebra
Back to
History of Algebra Seminar Home
Back to
Professor Cherlin's Home Page.
Back to
Department of Mathematics
...
File date: Spring 2002