Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

Life

Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. 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 gained both the doctorate (PhD) in 1969, and higher doctorate ( D.Sc.) in 1978, in the History of Science at the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...

. He was

Emeritus Professor ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

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 on the History of Mathematics (ICHM) on 31 July 2009, at

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, on the occasion of the 23rd International Congress for the History of Science.Awarding of the K.O. May Prize
from International Mathematical Union In 2010, he was elected an Honorary Member of the

Bertrand Russell Society Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

. Grattan-Guinness spent much of his career at Middlesex University. He was a fellow at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

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, United States, and a member of the International Academy of the History of Science. From 1974 to 1981, Grattan-Guinness was editor of the

history of science The history of science covers the development of science from ancient history, ancient times to the present. It encompasses all three major branches of science: natural science, natural, social science, social, and formal science, formal. Pr ...

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 acted as advisory editor to the editions of the writings of C.S. Peirce and

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

, 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. Grattan-Guinness gave 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, Grattan-Guinness 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 The ''Dictionary of National Biography'' (''DNB'') is a standard work of reference on notable figures from History of the British Isles, British history, published since 1885. The updated ''Oxford Dictionary of National Biography'' (''ODNB'') ...

(2004). Grattan-Guinness took an interest in the phenomenon of coincidence and has written on it for the Society for Psychical Research. He claimed to have a recurrent affinity with one particular number, namely 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. He died of heart failure on 12 December 2014, aged 73, survived by his wife Enid Grattan-Guinness. The personal papers of Grattan-Guinness are preserved at the Archives of American Mathematics. His offprint collection is held by the American Institute of Mathematics.

Work

The work of Grattan-Guinness touched on all historical periods, but he specialised in the development of the calculus and mathematical analysis, and their applications to mechanics and mathematical physics, and in the rise of

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

and

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

. He was 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 Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

). He has emphasised the importance of ignorance as an epistemological notion in this task. He did extensive research with original sources both published and unpublished, thanks to his reading and spoken knowledge of the main European languages.

Selected publications

Books written

* 1970. ''The Development of the Foundations of Mathematical Analysis from Euler to Riemann''.

MIT Press The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Ac ...

. * 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 ''et al.''). Duckworth. * 1982. ''Psychical Research: A Guide to Its History, Principles & Practices - in celebration of 100 years of the Society for Psychical Research'', Aquarian Press, . * 1990. ''Convolutions in French Mathematics, 1800–1840'' in 3 Vols. Birkhauser. * 1997. ''The Fontana History of the Mathematical Sciences: The Rainbow of Mathematics''. Fontana Press. (pbk). ''Norton History of the Mathematical Sciences''. W. W. Norton and Company (1998). (hbk), (pbk). * 2000. ''(Reprint
''From the Calculus to Set Theory 1630–1910: An Introductory History''
(ed. by I. Grattan-Guiness with chapters written by H. J. M. Bos, R. Bunn, J. W. Dauben, I. Grattan-Guinness, T. W. Hawkins, & K. Møller Pederson).

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

. . * 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. . 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 Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University. It was founded in 1878 and is the oldest continuously running university press in the United States. The press publi ...

. .

Editions

* W.H. and G.C. Young, ''The theory of sets of points'', 2nd edition (ed. with R.C.H. Tanner; 1972, New York: Chelsea). ntroduction 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. ntroduction and indexes.*

George Boole George Boole ( ; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. H ...

, ''Selected manuscripts on logic and its philosophy'' (ed. with G. Bornet, 1997, Basel: Birkhäuser), lxvi + 236 pages. art Introduction and editorial material.* Grattan-Guinness' ''The Search for Mathematical Roots 1870–1940'' is a sweeping study of the rise of

during that critical period. The central theme of the book is the rise of logicism, thanks to the efforts of Frege,

, 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

, 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 In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

as well as

proof theory Proof theory is a major branchAccording to , proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. consists of four corresponding parts, with part D being about "Proof The ...

, and on the emergence of American research on the

foundation of mathematics Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particul ...

, 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.

Books edited

* 2003. ''Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences'', 2 vols. Johns Hopkins University Press. * 2005
''Landmark Writings in Western Mathematics 1640-1940''

Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell (journal), Cell'', the ScienceDirect collection of electronic journals, ...

Articles

* 1975. "Mathematical Bibliography for W. H. and G. C. Young." ''Historia Mathematica'', Vol. 2, No. 1, February 1975, pp. 43-58. * 1978. "How Bertrand Russell Discovered His Paradox." ''Historia Mathematica'', Vol. 5, No. 2, May 1978, pp. 127-137. * 1989. "The Earliest Contribution to Location Theory? Spatio-economic Equilibrium with Lamé and Clapeyron, 1829." ''Mathematics and Computers in Simulation'', Vol. 31, No. 3, July 1986, pp. 195-220. * 1990. "The Varieties of Mechanics by 1800." ''Historia Mathematica'', Vol. 17, No. 4, November 1990, pp. 313-338. * 1992. "A Note on The Educational Times and Mathematical Questions" ''Historia Mathematica'', Vol. 19, No. 1, February 1992, pp. 76-78. * 1994. "Contributing to the Educational Times: Letters to W.J.C. Miller." ''Historia Mathematica'', Vol. 21, No. 2, May 1994, pp. 204-205. * 1996. "Mozart 18, Beethoven 32: Hidden Shadows of Integers in Classical Music", pages 29 to 48 in ''History of Mathematics: States of the Art'', edited by Joseph W. Dauben, Menso Folkerts, Eberhard Knobloch and Hans Wussing, Academic Press * 1996. "Numbers, Magnitudes, Ratios, and Proportions in Euclid's Elements: How Did He Handle Them?" ''Historia Mathematica'', Vol. 23, No. 4, November 1996, pp. 355-375. * 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. * 2002. "Algebras, Projective Geometry, Mathematical Logic, and Constructing the World: Intersections in the Philosophy of Mathematics of A. N. Whitehead." ''Historia Mathematica'', Vol. 29, No. 4, November 2002, pp. 427-462. * 2004. "The Mathematics of the Past: Distinguishing Its History From Our Heritage." ''Historia Mathematica'', Vol. 31, No. 2, May 2004, pp. 163-185. * 2008. "Foundations of Mathematics and Logicism," in Michel Weber and Will Desmond (eds.)
Handbook of Whiteheadian Process Thought
Frankfurt / Lancaster, Ontos Verlag: 97-104. Cf. Michel Weber, �
Ivor Grattan-Guinness, "Algebras, Projective Geometry, Mathematical Logic, and Constructing the World. Intersections in the Philosophy of Mathematics of A.N. Whitehead", Historia Mathematica 29, N° 4, 2002, pp. 427-462
», ''Zentralblatt MATH'', European Mathematical Society, Fachinformationszentrum Karlsruhe & Springer-Verlag, 1046.00003. * 2014. "From Anomaly to Fundament: Louis Poinsot's Theories of the Couple in Mechanics." ''Historia Mathematica'', Vol. 41, No. 1, February 2014, pp. 82-102.

References

External links

Encomium
at Mathematical Sciences Foundation * *
Hommage à I. Grattan-Guinness
December 2014. * {{DEFAULTSORT:Grattan-Guinness, Ivor 1941 births 2014 deaths People from Bakewell Alumni of Wadham College, Oxford Alumni of the London School of Economics Alumni of the University of London Academics of Middlesex University Academics of the London School of Economics Institute for Advanced Study visiting scholars British parapsychologists English mathematicians English logicians English historians 20th-century English philosophers 21st-century English philosophers British historians of mathematics British academic journal editors