Palle Yourgrau: A World Without Time: The Forgotten Legacy of Gödel and Einstein (2005)

In 1942, the logician Kurt Gödel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics, and the lost world of German science. By 1949, Gödel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Gödel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

Publisher Basic Books, New York, 2005
ISBN 0465092934
210 pages

review (Kelley L. Ross)

publisher
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PDF (83 MB)

Andrew Hodges: The Alan Turing: Enigma (1983/2012)

The full story behind the persecuted genius of wartime codebreaking and the computer revolution.

A new edition to celebrate Alan Turing’s centenary, includes a new foreword by the author and a preface by Douglas Hofstadter.

Alan Turing was the extraordinary Cambridge mathematician who masterminded the cracking of the German Enigma ciphers and transformed the Second World War. But his vision went far beyond this crucial achievement. Before the war he had formulated the concept of the universal machine, and in 1945 he turned this into the first design for a digital computer.

Turing’s far-sighted plans for the digital era forged ahead into a vision for Artificial Intelligence. However, in 1952 his homosexuality rendered him a criminal and he was subjected to humiliating treatment. In 1954, aged 41, Alan Turing committed suicide and one of Britain’s greatest scientific minds was lost.

First published in 1983, Burnett Books
Centenary edition
With Foreword by Douglas Hofstadter
Publisher Vintage, Random House, 2012
ISBN 1448137810, 9781448137817
624 pages

notes by the author
publisher
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Niccolò Guicciardini: Isaac Newton on Mathematical Certainty and Method (2009)

Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton’s work that has not been tightly connected to Newton’s actual practice: his philosophy of mathematics.

Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’s Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity’s legitimate heir, thereby distancing himself from the moderns.

Guicciardini reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton’s works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton’s understanding of method and his mathematical work then reveal themselves through Guicciardini’s careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

Publisher MIT Press, 2009
Transformations: Studies in the History of Science and Technology Series
ISBN 0262013177, 9780262013178
422 pages

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