## 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