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The origins and development of the ACE project

B. Jack Copeland

in Alan Turing's Automatic Computing Engine: The Master Codebreaker's Struggle to build the Modern Computer

Published in print:
2005
Published Online:
January 2008
ISBN:
9780198565932
eISBN:
9780191714016
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198565932.003.0004
Subject:
Mathematics, History of Mathematics

This chapter details the history of the Automatic Computing Engine (ACE) project. The story of the ACE begins with John Womersley's appointment as superintendent of the newly created Mathematics ... More


Amsterdam, Breda, 1643–1652

Noel Malcolm

in John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish: The Mental World of an Early Modern Mathematician

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198564843
eISBN:
9780191713750
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564843.003.0004
Subject:
Mathematics, History of Mathematics

This chapter chronicles the life of John Pell in Amsterdam and Breda from 1643 to 1652. John Pell had little idea of what awaited him in Amsterdam; apparently he thought his trip was to be a brief ... More


GENERALIZED INDUCTIVE DEFINITIONS IN CONSTRUCTIVE SET THEORY

Michael Rathjen

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0002
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies generalized inductive definitions on the basis of constructive Zermelo-Fraenkel set theory, CZF. In theories such as classical Zermelo-Fraenkel set theory, it can be shown that ... More


Nathaniel Bowditch and the Power of Numbers: "How a Nineteenth-Century Man of Business, Science, and the Sea Changed American Life"

Tamara Plakins Thornton

Published in print:
2016
Published Online:
September 2016
ISBN:
9781469626932
eISBN:
9781469628110
Item type:
book
Publisher:
University of North Carolina Press
DOI:
10.5149/northcarolina/9781469626932.001.0001
Subject:
History, American History: 19th Century

Nathaniel Bowditch (1773-1838) was a mathematician, astronomer, navigator, seafarer, and business executive whose Enlightenment-inspired perspectives shaped nineteenth-century capitalism while ... More


Parameterisation

Graham Priest

in Beyond the Limits of Thought

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199254057
eISBN:
9780191698194
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199254057.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter examines the relevance of mathematician Frank Ramsey's essay The Foundations of Mathematics to the contradictions in the limits of thought. Ramsey has provided the most acute early ... More


The Mathematical A Priori

David Webb

in Foucault's Archaeology: Science and Transformation

Published in print:
2012
Published Online:
May 2013
ISBN:
9780748624218
eISBN:
9780748684472
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748624218.003.0007
Subject:
Philosophy, Metaphysics/Epistemology

In The Order of Things, Foucault writes that the interest in formal languages opens up ‘the possibility, and the task, of applying a second critique of pure reason on the basis of new forms of the ... More


Wittgenstein and Intuitionism

Robert J. Fogelin

in Philosophical Interpretations

Published in print:
1992
Published Online:
November 2003
ISBN:
9780195071627
eISBN:
9780199833221
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019507162X.003.0015
Subject:
Philosophy, General

This essay explores one important strain that runs through Wittgenstein's Remarks on the Foundations of Mathematics: his commitment to themes characteristic of the intuitionist movement in logic and ... More


The Office of Mathematics: foundation and staff

Catherine Jami

in The Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign (1662-1722)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199601400
eISBN:
9780191729218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199601400.003.0013
Subject:
Mathematics, History of Mathematics

This chapter discusses the creation, in 1713, of an Office of Mathematics where a group of selected young scholars, both Chinese and Bannermen, started to work on the treatises commissioned by the ... More


The Jesuits and innovation in imperial science: Jean-François Foucquet's treatises

Catherine Jami

in The Emperor's New Mathematics: Western Learning and Imperial Authority During the Kangxi Reign (1662-1722)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199601400
eISBN:
9780191729218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199601400.003.0014
Subject:
Mathematics, History of Mathematics

This chapter focuses on Jean-François Foucquet, the French Jesuit in charge of drafting the new astronomical treatise, and analyzes the conflicts that arose among his confreres following his proposal ... More


The New Math: A Political History

Christopher J. Phillips

Published in print:
2014
Published Online:
May 2015
ISBN:
9780226184968
eISBN:
9780226185019
Item type:
book
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226185019.001.0001
Subject:
History, History of Science, Technology, and Medicine

The new math changed the way Americans think about mathematics. The mathematicians and teachers who designed the novel and controversial curriculum in the late 1950s--generously supported by the ... More


The Logical Must: Wittgenstein on Logic

Penelope Maddy

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199391752
eISBN:
9780199391776
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199391752.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, General

This book is an examination of Wittgenstein’s philosophy of logic, early and late, undertaken from an austere naturalistic perspective called ‘‘Second Philosophy’’. On a generally metaphysical ... More


Chalk: Materials and Concepts in Mathematics Research

Michael J. Barany and Donald MacKenzie

in Representation in Scientific Practice Revisited

Published in print:
2014
Published Online:
May 2014
ISBN:
9780262525381
eISBN:
9780262319157
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262525381.003.0006
Subject:
Society and Culture, Technology and Society

This chapter devotes close empirical attention to the social and material achievement of proofs, theorems, and other mathematical constructions. Mathematics is often treated as the most abstract and ... More


Theory

Massimiliano Di Ventra

in The Scientific Method: Reflections from a Practitioner

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198825623
eISBN:
9780191864605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198825623.003.0009
Subject:
Physics, History of Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the role of a theory: to describe (preferably mathematically) observations and to make new predictions that are testable. Theories, as the hypotheses they build upon, are not ... More


Including Students with Learning Disabilities

Fuk Chuen Ho

in Learning Diversity in the Chinese Classroom: Contexts and Practice for Students with Special Needs

Published in print:
2007
Published Online:
May 2013
ISBN:
9789622098725
eISBN:
9789882207134
Item type:
chapter
Publisher:
Hong Kong University Press
DOI:
10.5790/hongkong/9789622098725.003.0011
Subject:
Education, Secondary Education

This chapter discusses the learning difficulties of Chinese students in regular classroom contexts. Since disabilities in the subject areas of reading and mathematics influence all areas of school ... More


Dueling Standards

Suzanne M. Wilson

in California Dreaming: Reforming Mathematics Education

Published in print:
2002
Published Online:
October 2013
ISBN:
9780300094329
eISBN:
9780300127539
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300094329.003.0008
Subject:
Sociology, Education

This chapter explores the back-to-basics move promoted by a pair of bills—the ABCs bills—with the aim of arriving at a more balanced curriculum. At roughly the same time, Governor Wilson signed a ... More


Parsnips and Orchids Side by Side: A View from the Classroom

Suzanne M. Wilson

in California Dreaming: Reforming Mathematics Education

Published in print:
2002
Published Online:
October 2013
ISBN:
9780300094329
eISBN:
9780300127539
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300094329.003.0009
Subject:
Sociology, Education

This chapter focuses mostly on the activities inside the classroom. In the late 1980s, for example, Andrew Porter and his colleagues at Michigan State University conducted a large-scale study of ... More


Gaston Bachelard: Construction and Temporal Discontinuity

David Webb

in Foucault's Archaeology: Science and Transformation

Published in print:
2012
Published Online:
May 2013
ISBN:
9780748624218
eISBN:
9780748684472
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748624218.003.0003
Subject:
Philosophy, Metaphysics/Epistemology

For Bachelard, science is not the direct formalisation of experience, but the modification of the conditions of existing experience. The laws that give form even to phenomena as they present ... More


Jean Cavaillès: Grounding Thought in its Own History

David Webb

in Foucault's Archaeology: Science and Transformation

Published in print:
2012
Published Online:
May 2013
ISBN:
9780748624218
eISBN:
9780748684472
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748624218.003.0004
Subject:
Philosophy, Metaphysics/Epistemology

The philosopher of mathematics, Jean Cavaillès, developed a conception of mathematics that rejected Hilbert's programme of an axiomatic foundation, intuitionism, logicism, and the idea of placing ... More


Michel Serres: Mathematics, Epistemology, History

David Webb

in Foucault's Archaeology: Science and Transformation

Published in print:
2012
Published Online:
May 2013
ISBN:
9780748624218
eISBN:
9780748684472
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9780748624218.003.0005
Subject:
Philosophy, Metaphysics/Epistemology

Michel Serres’ early work was concerned with forms of thought proper to mathematics, and with the possibility of their adoption by branches of critical thought outside the sciences. Serres describes ... More


The New New Math in California

David K. Cohen and Heather C. Hill

in Learning Policy: When State Education Reform Works

Published in print:
2001
Published Online:
October 2013
ISBN:
9780300089479
eISBN:
9780300133349
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300089479.003.0002
Subject:
Sociology, Education

The 1985 Mathematics Framework for California Public Schools was an early product of a national movement for school reform. It was a useful piece but offered little help in recommending specific ... More


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