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Ivor Grattan-Guinness | |
---|---|

Ivor Grattan-Guinness in 2003. | |

Born | Bakewell, England | 23 June 1941

Died | 12 December 2014 73) England | (aged

Residence | England |

Nationality | British |

Alma mater | Wadham College, Oxford London School of Economics University of London |

Known for | History of mathematics, history of logic |

Awards | Kenneth O. May Medal |

Scientific career | |

Fields | Mathematician, historian, logician |

Institutions | Middlesex University London School of Economics |

Doctoral students | Niccolò Guicciardini |

Notes | |

He shared a birthday with the mathematician Alan Turing, born 29 years earlier. |

**Ivor Owen Grattan-Guinness** (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.^{ [1] }^{ [2] }

The area of study known as the **history of mathematics** is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, together with Ancient Egypt and Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy and to formulate calendars and record time.

The **history of logic** deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the *Organon*, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.

Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator.^{ [1] } 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.^{ [1] }^{ [3] } 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. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.

**Bakewell** is a small market town and civil parish in the Derbyshire Dales district of Derbyshire, England, well known for the local confection Bakewell pudding. It is located on the River Wye, about thirteen miles (21 km) southwest of Sheffield. In the 2011 census the civil parish of Bakewell had a population of 3,949. The town is close to the tourist attractions of Chatsworth House and Haddon Hall.

**Wadham College** is one of the constituent colleges of the University of Oxford in the United Kingdom. It is located in the centre of Oxford, at the intersection of Broad Street and Parks Road.

The **London School of Economics** is a public research university located in London, England, and a constituent college of the federal University of London. Founded in 1895 by Fabian Society members Sidney Webb, Beatrice Webb, Graham Wallas, and George Bernard Shaw for the betterment of society, LSE joined the University of London in 1900 and established its first degree courses under the auspices of the University in 1901. The LSE started awarding its own degrees in 2008, prior to which it awarded degrees of the University of London.

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 Budapest, on the occasion of the 23rd International Congress for the History of Science.^{ [4] } In 2010, he was elected an Honorary Member of the Bertrand Russell Society.

**Kenneth O. May Prize** and **Medal** in history of mathematics is an award of the International Commission on the History of Mathematics (ICHM) "for the encouragement and promotion of the history of mathematics internationally". It was established in 1989 and is named in honor of Kenneth O. May, the founder of ICHM. Since then, the award is given every four years, at the ICHM congress.

The **International Commission on the History of Mathematics** was established in 1971 to promote the study of history of mathematics. Kenneth O. May provided its initial impetus. In 1974 its official journal Historia Mathematica began publishing. Every four years the Commission bestows the Kenneth O. May Medal upon a deserving historian of mathematics.

**Budapest** is the capital and the most populous city of Hungary, and the tenth-largest city in the European Union by population within city limits. The city had an estimated population of 1,752,704 in 2016 distributed over a land area of about 525 square kilometres. Budapest is both a city and county, and forms the centre of the Budapest metropolitan area, which has an area of 7,626 square kilometres and a population of 3,303,786, comprising 33 percent of the population of Hungary.

Grattan-Guinness spent much of his career at Middlesex University.^{ [5] } He was a fellow at the Institute for Advanced Study in Princeton, New Jersey, United States, and a member of the International Academy of the History of Science.^{ [6] }

The **Institute for Advanced Study** (**IAS**) located 1 Einstein Drive, Princeton, New Jersey, in the United States, is an independent, postdoctoral research center for theoretical research and intellectual inquiry founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld.

**Princeton** is a municipality with a borough form of government in Mercer County, New Jersey, United States, that was established in its current form on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township. As of the 2010 United States Census, the municipality's population was 28,572, reflecting the former township's population of 16,265, along with the 12,307 in the former borough.

The **International Academy of the History of Science** is a membership organization for historians of science. The academy was founded on 17 August 1928 at the Congress of Historical Science by Aldo Mieli, Abel Rey, George Sarton, Henry E. Sigerist, Charles Singer, Karl Sudhoff, and Lynn Thorndike.

From 1974 to 1981, Grattan-Guinness was editor of the history of science journal * Annals of Science *.^{ [3] } In 1979 he founded the journal * History and Philosophy of Logic *,^{ [1] } 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.

The **history of science** is the study of the development of science and scientific knowledge, including both the natural and social sciences. Science is a body of empirical, theoretical, and practical knowledge about the natural world, produced by scientists who emphasize the observation, explanation, and prediction of real-world phenomena. Historiography of science, in contrast, studies the methods employed by historians of science.

* Annals of Science* is a peer-reviewed academic journal covering the history of science and technology. It is published by Taylor & Francis and was established in 1936. The founding editor-in-chief was the Canadian historian of science Harcourt Brown.

* Historia Mathematica: International Journal of History of Mathematics* is an academic journal on the history of mathematics published by Elsevier. It was established by Kenneth O. May in 1971 as the free newsletter

He also acted 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.

**Bertrand Arthur William Russell, 3rd Earl Russell**, was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he also confessed that his skeptical nature had led him to feel that he had "never been any of these things, in any profound sense." Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.

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 (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.^{ [2] }

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 and mathematical logic.^{ [1] } 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). 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.

- 1970.
*The Development of the Foundations of Mathematical Analysis from Euler to Riemann*. MIT Press.^{ [7] } - 1972.
*Joseph Fourier, 1768–1830*(In collaboration with J.R. Ravetz). MIT Press.^{ [8] } - 1977.
*Dear Russell—Dear Jourdain: a Commentary on Russell's Logic, Based on His Correspondence with Philip Jourdain*. Duckworth.^{ [9] } - 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.^{ [10] }(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.
- 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.

**Georg Ferdinand Ludwig Philipp Cantor** was a German mathematician. He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of.

**Kurt Friedrich Gödel** was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle, Alfred Tarski and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.

**Mathematics** includes the study of such topics as quantity, structure, space, and change.

In the philosophy of mathematics, **intuitionism**, or **neointuitionism**, is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.

**Mathematical logic** is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

The * Principia Mathematica* is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–27, it appeared in a second edition with an important

**Ernst Friedrich Ferdinand Zermelo** was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.

**Metamathematics** is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic". An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.

**Friedrich Wilhelm Karl Ernst Schröder** was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic, by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental *Vorlesungen über die Algebra der Logik*, in three volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day.

In his work on set theory, Georg Cantor denoted the collection of all cardinal numbers by the last letter of the Hebrew alphabet, **ת** As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the Burali-Forti type. Cantor instead said that it was an "inconsistent" collection which was absolutely infinite.

**Paul Isaac Bernays** was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert.

**Cassius Jackson Keyser** was an American mathematician of pronounced philosophical inclinations.

**Philip Edward Bertrand Jourdain** was a British logician and follower of Bertrand Russell.

**Logic** is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.

**Part–whole theory** is the name of a loose collection of historical theories, all informal and nearly all unwitting, relating wholes to their parts via inclusion. Part–whole theory has been overtaken by mereology.

* The Principles of Mathematics* (

The aspects of **Bertrand Russell's views on philosophy** cover the changing viewpoints of philosopher and mathematician Bertrand Russell (1872–1970), from his early writings in 1896 until his death in February 1970.

The mathematical concept of a function emerged in the 17th century in connection with the development of the calculus; for example, the slope of a graph at a point was regarded as a function of the *x*-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme.

- 1 2 3 4 5 Grilly, Tony (31 December 2014). "Ivor Grattan-Guinness obituary: Energetic historian of mathematics and logic".
*The Guardian*. - 1 2 Reisz, Matthew (8 January 2015). "Obituaries: Ivor Grattan-Guinness, 1941–2014".
*Times Higher Education*. - 1 2 "Editor Profile: Professor Ivor Grattan-Guinness" (PDF). Taylor & Francis. March 2005. Retrieved 11 January 2012.
- ↑ Report on the Awarding of the Kenneth O. May Prize to Ivor Grattan-Guinness and Rhada Charan Gupta on the Occasion of the 23rd International Congress of History of Science and Technology, Craig Fraser, ICHM, retrieved 2015-02-04.
- ↑ "Academic Staff Profile: Prof Ivor Grattan-Guinness".
*Middlesex University*. Archive.org. 1999–2004. Archived from the original on 29 September 2007. Retrieved 11 January 2012. - ↑ Member profile, IAHS, retrieved 2015-02-04.
- ↑ 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" (PDF).*Bull. Amer. Math. Soc*.**78**(3): 385–391. doi:10.1090/S0002-9904-1972-12909-4. - ↑ Gillmor, G. Stewart (July 1973). "Review:
*Joseph Fourier, 1768–1830*, by I. Grattan-Guinness".*Technology and Culture*.**14**(3): 501–503. doi:10.2307/3102345. JSTOR 3102345. - ↑ Sainsbury, R. M. (Oct 1979). "Review:
*Dear Russell—Dear Jourdain*, by I. Grattan-Guinness".*Mind*. New Series.**88**(352): 604–607. JSTOR 2253463. - ↑ 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" (PDF).*Bull. Amer. Math. Soc. (N.S.)*.**40**(1): 125–129. doi:10.1090/s0273-0979-02-00959-x.

Wikiquote has quotations related to: Ivor Grattan-Guinness |

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