Ivor Grattan-Guinness

He spent much of his career at Middlesex University Business School. He has been a fellow at the Institute for Advanced Study in Princeton, and is a member of the Academie Internationale d'Histoire des Sciences.

The work of Grattan-Guinness touches on all historical periods, but he is particularly interested in Euclid, and in the rise of functional analysis and mathematical logic. He has been especially interested in characterising how past thinkers far removed from us in time view their findings differently from the way we see them now, and has emphasised the importance of ignorance in this task. He has done extensive research with original sources, thanks to his reading knowledge of the main European languages.

Grattan-Guinness (2000) is a sweeping study of the rise of mathematical logic during the critical period 1870-1940. The central theme of the book is the rise of logicism, thanks to the efforts of Frege, Bertrand Russell, and Whitehead, and its demise due to Gödel and indifference. Whole chapters are devoted to the emergence of algebraic logic in the 19th century UK, Cantor and the emergence of set theory, the emergence of mathematical logic in Germany told in a way that downplays Frege's importance, and to Peano and his followers. There follow four chapters devoted to the ideas of the young Bertrand Russell, the writing of Principia Mathematica, and to the mixed reception its ideas and methods encountered over the period 1910-40. The book touches on the rise of model theory as well as proof theory, and on the emergence of American research on the foundation of mathematics, especially in the hands of Eliakim Hastings Moore and his students, of the postulate theorists, and of Quine. While Polish logic is often mentioned, it is not covered systematically. Finally, the book is a contribution to the history of philosophy as well as of mathematics..

Selected publications

Books written

• 1970. The Development of the Foundations of Mathematical Analysis from Euler to Riemann. MIT Press (1970).
• 1980. From the Calculus to Set Theory, 1630-1910: An Introductory History. Duckworth (1980).
• 1997. The Rainbow of Mathematics: A History of the Mathematical Sciences. Fontana (1997) ISBN 978-000-686179-9 (pbk). W. W. Norton and Company (1999) ISBN 978-0393-04650-2 (hbk) ISBN 0-393-32030-8 (pbk).
• 2000. From the Calculus to Set Theory 1630-1910: An Introductory History. Princeton Univ. Press. ISBN 0-691-07082-2.
• 2000. The Search for Mathematical Roots 1870-1940: Logics, Set Theories, and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton Univ. Press. ISBN 0-691-05858-X. Enormous bibliography.

Books edited

• 2003. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, 2 vols. Johns Hopkins Univ. Press. ISBN 0801873967
• 2005. Landmark Writings in Western Mathematics. Elsevier.

Articles

• 2002. "A Sideways Look at Hilbert's Twenty-Three Problems of 1900," Notices of the American Mathematical Society 47: 752-57.

External links

• Academic home page.
• Encomium at Mathematical Sciences Foundation