{{italic title
''Revolutions in Mathematics'' is a 1992 collection of essays in the history and philosophy of mathematics.
Contents
*
Michael J. Crowe Michael J. Crowe (b. 1936) is Rev. John J. Cavanaugh Professor Emeritus in the Program of Liberal Studies and
Graduate Program in History and Philosophy of Science at the University of Notre Dame. He is best known for writing the influential book '' ...
, Ten "laws" concerning patterns of change in the history of mathematics (1975) (15–20);
*Herbert Mehrtens, T. S. Kuhn's theories and mathematics: a discussion paper on the "new historiography" of mathematics (1976) (21–41);
*Herbert Mehrtens, Appendix (1992): revolutions reconsidered (42–48);
*
Joseph Dauben
Joseph Warren Dauben (born 29 December 1944, Santa Monica) is a Herbert H. Lehman Distinguished Professor of History at the CUNY Graduate Center, Graduate Center of the City University of New York. He obtained his PhD from Harvard University.
H ...
, Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984) (49–71);
*Joseph Dauben, Appendix (1992): revolutions revisited (72–82);
* Paolo Mancosu, Descartes's Géométrie and revolutions in mathematics (83–116);
* Emily Grosholz, Was Leibniz a mathematical revolutionary? (117–133);
*
Giulio Giorello
Giulio Giorello (; 14 May 1945 – 15 June 2020) was an Italian philosopher, mathematician, and epistemologist.
Biography
Giorello graduated with a degree in philosophy in 1968 and in mathematics in 1971 at the University of Milan. While the ...
, The "fine structure" of mathematical revolutions: metaphysics, legitimacy, and rigour. The case of the calculus from Newton to Berkeley and Maclaurin (134–168);
*Yu Xin Zheng, Non-Euclidean geometry and revolutions in mathematics (169–182);
*Luciano Boi, The "revolution" in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics (183–208);
*Caroline Dunmore, Meta-level revolutions in mathematics (209–225);
*
Jeremy Gray
Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics.
Biography
Gray studied mathematics at Oxford University from 1966 to 1969, and then at Warwick University, obtaining his Ph.D ...
, The nineteenth-century revolution in mathematical ontology (226–248);
*Herbert Breger, A restoration that failed: Paul Finsler's theory of sets (249–264);
* Donald A. Gillies, The Fregean revolution in logic (265–305);
*Michael Crowe, Afterword (1992): a revolution in the historiography of mathematics? (306–316).
Reviews
The book was reviewed by Pierre Kerszberg for ''
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science.
The AMS also pu ...
'' and by
Michael S. Mahoney
Michael Sean Mahoney (June 30, 1939 – July 23, 2008) was a historian of science.
Mahoney was born in New York City, and did his undergraduate studies at Harvard University, graduating in 1960. He earned a Ph.D. in history and history of scienc ...
for ''
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an e ...
''. Mahoney says "The title should have a question mark." He sets the context by referring to
paradigm shift
A paradigm shift, a concept brought into the common lexicon by the American physicist and philosopher Thomas Kuhn, is a fundamental change in the basic concepts and experimental practices of a scientific discipline. Even though Kuhn restricted t ...
s that characterize scientific revolutions as described by
Thomas Kuhn
Thomas Samuel Kuhn (; July 18, 1922 – June 17, 1996) was an American philosopher of science whose 1962 book ''The Structure of Scientific Revolutions'' was influential in both academic and popular circles, introducing the term '' paradigm ...
in his book ''
The Structure of Scientific Revolutions
''The Structure of Scientific Revolutions'' (1962; second edition 1970; third edition 1996; fourth edition 2012) is a book about the history of science by philosopher Thomas S. Kuhn. Its publication was a landmark event in the history, philosophy ...
''. According to Michael Crowe in chapter one, revolutions never occur in mathematics. Mahoney explains how mathematics grows upon itself and does not discard earlier gains in understanding with new ones, such as happens in biology, physics, or other sciences. A nuanced version of revolution in mathematics is described by Caroline Dunmore who sees change at the level of "meta-mathematical values of the community that define the telos and methods of the subject, and encapsulate general beliefs about its value." On the other hand, reaction to innovation in mathematics is noted, resulting in "clashes of intellectual and social values".
Editions
* Gillies, Donald (1992) ''Revolutions in Mathematics'', Oxford Science Publications, The Clarendon Press,
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books ...
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science.
The AMS also pu ...
.
* Michael S. Mahoney (1994) "Review of ''Revolutions in Mathematics''",
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an e ...