Jean-Luc Chabert, et al.: A History of Algorithms: From the Pebble to the Microchip (1994–) [French, English]

A source book for the history of mathematics, but one which offers a different perspective by focusing on algorithms. With the development of computing has come an awakening of interest in algorithms. Often neglegted by historians and modern scientists, more concerned with the nature of concepts, algorithmic procedures turn out to have been instrumental in the development of fundamental ideas: practice led to theory just as much as the other way round. The purpose of this book is to offer a historical background to contemporary algorithmic practice. Each chapter centres around a theme, more or less in chronological order, and the story is told through the reading of over 200 original texts, faithfully reproduced. This provides an opportunity for the reader to sit alongside such mathematicians as Archimedes, Omar Khayyam, Newton, Euler and Gauss as they explain their techniques. The book ends with an account of the development of the modern concept of algorithm.

With Évelyne Barbin, Michel Guillemot, Anne Michel-Pajus, Jacques Borowczyk, Ahmed Djebbar, and Jean-Claude Martzloff
Publisher Belin, Paris, 1994
ISBN 2701113466, 9782701113463
591 pages

English edition
Translated by Chris Weeks
Publisher Springer, 1999
ISBN 3540633693
524 pages

Publisher (FR, new edition)
Publisher (EN)

Histoire d’algorithmes: du caillou à la puce (French, DJVU, 10 MB)
A History of Algorithms: From the Pebble to the Microchip (English, DJVU, 6 MB)

See also Algomation.com, a platform for viewing, creating and sharing algorithms.

David Aubin: A Cultural History of Catastrophes and Chaos: Around the Institut des Hautes Études Scientifiques, France 1958-1980 (1998)

“This is the story of a group of scientists who, in the local context of the Institut des Hautes Études Scientifiques (IHÉS), France, contributed to the elaboration of catastrophe theory and deterministic chaos theory. Starting with a study of the role of Bourbaki’s mathematics on the French intellectual scene (and especially with respect to structuralism), this dissertation examines the resources from topology, embryology, and linguistics used by René Thom to construct catastrophe theory.

It describes the foundation of the IHÉS by Léon Motchane in 1958 and the ideology of fundamental research that shaped it. It reviews the history of structural stability for differential equations, focusing on the work of Aleksandr Andronov and Solomon Lefschetz, among others, and the synthesis achieved in the 1960s by Stephen Smale at the University of California, Berkeley. These mathematical developments were used by Thom to develop new modeling practices. The IHÉS, which welcomed topologists such as E. Christopher Zeeman and Ralph Abraham, played a role in developing modeling practices based on recent advances in topology. A physics professor at the IHÉS, David Ruelle, together with Dutch mathematician Floris Takens, adapted the modeling practices of these ‘applied topologists’ and proposed a mechanism for the onset of turbulence, thereby introducing the concept of strange attractors. Looking at the history of fluid mechanics, I argue that Ruelle’s work displaced earlier emphases on fundamental laws, like the Navier-Stokes equations, and focused on the modes of representation rather than representations themselves. A certain Bourbakization of physics and the advent of the computer shaped this evolution.

Finally, focusing on convention, and taking the Rayleigh-Bénard system as a boundary system, various communities’ responses to the Ruelle-Takens model are examined, in particular hydrodynamic stability theorists, phase transition physicists and Pierre-Gilles de Gennes’s group, and chemical physicists orbiting Ilya Prigogine. Prior interest in developing interdisciplinary approaches for the study of turbulence helped the adaptation of a dynamical systems approach for the study of natural phenomena, greatly inspired by the work of Smale, Thom, and Ruelle.” (Abstract)

Ph. D. thesis
Princeton University
782 pages

single PDF (final section “Sources and Bibliography” missing; no OCR)
PDF chapters (from the author’s website)

Martin Davis: The Universal Computer: The Road from Leibniz to Turing (2000–) [EN, IT, CR]

“Martin Davis, a fluent interpreter of mathematics and philosophy, locates the source of this knowledge in the work of the remarkable German thinker G. W. Leibniz, who, among other accomplishments, was a distinguished jurist, mining engineer, and diplomat but found time to invent a contraption called the “Leibniz wheel,” a sort of calculator that could carry out the four basic operations of arithmetic. Leibniz subsequently developed a method of calculation called the calculus raciocinator, an innovation his successor George Boole extended by, in Davis’s words, “turning logic into algebra.” (Boole emerges as a deeply sympathetic character in Davis’s pages, rather than as the dry-as-dust figure of other histories. He explained, Davis reports, that he had turned to mathematics because he had so little money as a student to buy books, and mathematics books provided more value for the money because they took so long to work through.) Davis traces the development of this logic, essential to the advent of “thinking machines,” through the workshops and studies of such thinkers as Georg Cantor, Kurt Gödel, and Alan Turing, each of whom puzzled out just a little bit more of the workings of the world–and who, in the bargain, made the present possible.”

The paperback edition was retitled Engines of Logic: Mathematicians and the Origin of the Computer.

Publisher W. W. Norton, 2000
ISBN 0393047857, 9780393047851
257 pages

Review (Mark Johnson, Mathematical Association of America)
Review (Georges Ifrah, The American Mathematical Monthly)

The Universal Computer. The Road from Leibniz to Turing (English, 2001)
Il calcolatore universale: da Leibniz a Turing (Italian, trans. Gianni Rigamonti, 2003)
Na logički pogon: podrijetlo ideje računala (Croatian, trans. Ljerka Vukić and Ognjen Strpić, 2003)