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He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He has gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He is Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.
He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission for the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. In 2010, he was elected an Honorary Member of the Bertrand Russell Society.
He spent much of his career at Middlesex University. He has been a fellow at the Institute for Advanced Study in Princeton, New Jersey, and is a member of the Académie Internationale d'Histoire des Sciences.
From 1974 to 1981, he was editor of the history of science journal Annals of Science. In 1979 he founded the journal History and Philosophy of Logic, and edited it until 1992. He was an associate editor of Historia Mathematica for twenty years from its inception in 1974, and again from 1996.
He also acts as advisory editor to the editions of the writings of C.S. Peirce and Bertrand Russell, and to several other journals and book series. He was a member of the Executive Committee of the International Commission on the History of Mathematics from 1977 to 1993.
He has given over 570 invited lectures to organisations and societies, or to conferences and congresses, in over 20 countries around the world. These lectures include tours undertaken in Australia, New Zealand, Italy, South Africa and Portugal.
From 1986 to 1988, he was the President of the British Society for the History of Mathematics, and for 1992 the Vice-President. In 1991, he was elected an effective member of the Académie Internationale d'Histoire des Sciences. He was the Associate Editor for mathematicians and statisticians for the Oxford Dictionary of National Biography (2004).
Grattan-Guinness has also taken an interest in the phenomenon of coincidence and has written on it for The Society For Psychical Research. He claims to have a rerurrent affinity with one particular number; the square of 15: 225, even recounting one occasion when a car was in front of him with the number plate IGG225, i.e. his very initials and that number.
The work of Grattan-Guinness touches on all historical periods, but he specialises in the development of the calculus and mathematical analysis, and their applications to mechanics and mathematical physics, and in the rise of set theory 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 (for example, Euclid). He has emphasised the importance of ignorance as an epistemological notion in this task. He has done extensive research with original sources both published and unpublished, thanks to his reading and spoken knowledge of the main European languages.
- 1970. The Development of the Foundations of Mathematical Analysis from Euler to Riemann. MIT Press.
- 1972. 'Joseph Fourier, 1768–1830' (In collaboration with J.R. Ravetz). MIT Press.
- 1977. Dear Russell—Dear Jourdain: a Commentary on Russell's Logic, Based on His Correspondence with Philip Jourdain. Duckworth.
- 1980. From the Calculus to Set Theory, 1630–1910: An Introductory History (with chapters written by H. J. M. Bos). Duckworth.
- 1982. Psychical Research: A Guide to Its History, Principles & Practices - in celebration of 100 years of the Society for Psychical Research, Aquarian Press, ISBN 0-85030-316-8 .
- 1990. 'Convolutions in French Mathematics, 1800–1840' in 3 Vols. Birkhauser.
- 1997. The Rainbow of Mathematics: A History of the Mathematical Sciences. Fontana. ISBN 978-0-00-686179-9 (pbk). W. W. Norton and Company (1999). ISBN 978-0-393-04650-2 (hbk), ISBN 0-393-32030-8 (pbk).
- 2000. (Reprint) From the Calculus to Set Theory 1630–1910: An Introductory History (with chapters written by H. J. M. Bos). Princeton University 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 University Press. ISBN 0-691-05858-X. Bibliography. (For research on this book he held a Leverhulme Fellowship from 1995 to 1997.)
- 2009 Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics. Johns Hopkins University Press. ISBN 0-8018-9248-1.
- W.H. and G.C. Young, The theory of sets of points, 2nd edition (ed. with R.C.H. Tanner; 1972, New York: Chelsea). [Introduction and appendix.]
- E.L. Post, ‘The modern paradoxes’, History and philosophy of logic, 11 (1990), 85–91.
- Philip E. B. Jourdain, Selected essays on the history of set theory and logics (1906–1918) (1991, Bologna: CLUEB), xlii + 352 pages. [Introduction and indexes.]
- George Boole, Selected manuscripts on logic and its philosophy (ed. with G. Bornet, 1997, Basel: Birkhäuser), lxvi + 236 pages.[Part Introduction and editorial material.]
- Grattan-Guinness' The Search for Mathematical Roots 1870–1940 is a sweeping study of the rise of mathematical logic during that critical period. The central theme of the book is the rise of logicism, thanks to the efforts of Frege, Bertrand Russell, and Alfred 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 both The Principles of Mathematics and Principia Mathematica, and to the mixed reception the 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 E. H. 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.
- 2003. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, 2 vols. Johns Hopkins University Press. ISBN 0-8018-7396-7
- 2005. Landmark Writings in Western Mathematics. Elsevier.
- 2000. "Christianity and Mathematics: Kinds of Link and the Rare Occurrences after 1750." Physis: Rivista Internazionale di Storia della Scienza XXXVII. Nuova Serie. Fasc. 2. 2000: 467-500.
- 2001. "Manifestations of Mathematics in and around the Christianities: Some Examples and Issues." Historia Scientiarum 11-1. July 2001: 48-84.
- 2002. "A Sideways Look at Hilbert's Twenty-Three Problems of 1900," Notices of the American Mathematical Society 47: 752–57.
- "Editor Profile: Professor Ivor Grattan-Guinness". Taylor & Francis. March 2005. Retrieved 11 January 2012.
- "Academic Staff Profile: Prof Ivor Grattan-Guinness". Middlesex University. Archive.org. 1999–2004. Retrieved 11 January 2012.
- Waterhouse, William C. (1972). "Review: Lebesgue's Theory of Integration, by Thomas Hawkins; A History of Vector Analysis, by Michael J. Crowe; The Development of the Foundations of Mathematical Analysis from Euler to Riemann, by I. Grattan-Guinness; and Die Genesis des abstrakten Gruppenbegriffes, by Hans Wussing". Bull. Amer. Math. Soc. 78 (3): 385–391.
- Gillmor, G. Stewart (July 1973). "Review: Joseph Fourier, 1768–1830, by I. Grattan-Guinness". Technology and Culture 14 (3): 501–503.
- Sainsbury, R. M. (Oct 1979). "Review: Dear Russell—Dear Jourdain, by I. Grattan-Guinness". Mind. New Series 88 (352): 604–607.
- Ewald, William (2003). "Review: The search for mathematical roots, 1870–1940: Logics, set theories, and the foundations of mathematics from Cantor through Russell to Gödel, by I. Grattan-Guinness". Bull. Amer. Math. Soc. (N.S.) 40 (1): 125–129.
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