Ivor Grattan-Guinness in 2003.
|Born||23 June 1941|
|Died|| 12 December 2014 73) (aged|
|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|
|Fields||Mathematician, historian, logician|
|Institutions|| Middlesex University |
London School of Economics
|Doctoral students||Niccolò Guicciardini|
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.
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.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. 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.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.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.
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 .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.
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 Notae de Historia Mathematica, but by its sixth issue in 1974 had turned into a full journal.
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.
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.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.
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 Introduction to the Second Edition, an Appendix A that replaced ✸9 and all-new Appendix B and Appendix C. PM is not to be confused with Russell's 1903 The Principles of Mathematics. PM was originally conceived as a sequel volume to Russell's 1903 Principles, but as PM states, this became an unworkable suggestion for practical and philosophical reasons: "The present work was originally intended by us to be comprised in a second volume of Principles of Mathematics... But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions."
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 (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.
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.
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