## Circles Disturbed: The Interplay of Mathematics and Narrative

*Apostolos Doxiadis and Barry Mazur (eds)*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.001.0001
- Subject:
- Mathematics, History of Mathematics

This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of ... More

## Moving the Alps: uncovering the mathematics of John Pell

*Jacqueline A. Stedall*

### in A Discourse Concerning Algebra: English Algebra to 1685

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198524953
- eISBN:
- 9780191711886
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198524953.003.0005
- Subject:
- Mathematics, History of Mathematics

John Pell (1611-1685) has long been considered the most enigmatic of the 17th-century mathematicians. He was well read in both Classical and contemporary mathematics, and there is no doubt that he ... More

## Why Spin Glasses?

*Daniel L. Stein and Charles M. Newman*

### in Spin Glasses and Complexity

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.003.0001
- Subject:
- Sociology, Science, Technology and Environment

Spin glasses are disordered magnetic materials, and it is hard to find a less promising candidate to serve as a focal point of complexity studies, much less as the object of thousands of ... More

## From Voyagers to Martyrs: Toward a Storied History of Mathematics

*Amir Alexander*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0001
- Subject:
- Mathematics, History of Mathematics

This chapter traces the history of mathematics, from the late sixteenth century to the present, through the lens of mathematical stories. The period is divided into three main epochs and a possible ... More

## Narrative and the Rationality of Mathematical Practice

*David Corfield*

*Apostolos Doxiadis and Barry Mazur (eds)*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0009
- Subject:
- Mathematics, History of Mathematics

This chapter examines the rationality of mathematical practice in relation to narrative. It begins with a discussion of Alasdair MacIntyre's account of rational enquiry, Three Rival Versions of Moral ... More

## Mathematics and Narrative: An Aristotelian Perspective

*G. E. R. Lloyd*

*Apostolos Doxiadis and Barry Mazur (eds)*

### in Circles Disturbed: The Interplay of Mathematics and Narrative

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0011
- Subject:
- Mathematics, History of Mathematics

This chapter explores the relationship between mathematics and narrative from an Aristotelian perspective. Aristotle's philosophy of mathematics is radically different from that of Plato. For ... More

## Algebraic Thought in Ancient and Medieval China

*Victor J. Katz and Karen Hunger Parshall*

### in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691149059
- eISBN:
- 9781400850525
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149059.003.0005
- Subject:
- Mathematics, History of Mathematics

This chapter takes a look at the scope of mathematics in Ancient and Medieval China. Although the Chinese engaged in numerical calculation as early as the middle of the second millennium BCE, the ... More

## Algebraic Thought in Medieval India

*Victor J. Katz and Karen Hunger Parshall*

### in Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691149059
- eISBN:
- 9781400850525
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149059.003.0006
- Subject:
- Mathematics, History of Mathematics

This chapter explores medieval Indian algebraic thought in the works of Āryabhạta, author of the astronomical treatise Āryabhạtīya (ca. 500 CE), and Brahmagupta, who wrote the ... More

## Mathematical Mysteries in Byzantium: The Transmission of Fermat’S Last Theorem

*Judith Herrin*

### in Margins and Metropolis: Authority across the Byzantine Empire

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691153018
- eISBN:
- 9781400845224
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153018.003.0015
- Subject:
- History, World Medieval History

This chapter examines how the mathematical mysteries of Diophantus were preserved, embellished, developed, and enjoyed in Byzantium by many generations of amateur mathematicians like Pierre de ... More

## Mathematical Foundations of Quantum Mechanics: New Edition

*John von Neumann (ed.)*

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780691178561
- eISBN:
- 9781400889921
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691178561.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical ... More

## The Early Tradition on Pythagoras and Its Development

*Leonid Zhmud*

### in Pythagoras and the Early Pythagoreans

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199289318
- eISBN:
- 9780191741371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199289318.003.0002
- Subject:
- Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This chapter reviews references to Pythagoras by the authors of the pre-Platonic period. It shows that in the course of the fourth century, studies in mathematics, particularly geometry and ... More

## The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

*Jürgen Renn and Hanoch Gutfreund*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174631
- eISBN:
- 9781400888689
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174631.001.0001
- Subject:
- Physics, History of Physics

First published in 1922 and based on lectures delivered in May 1921, Albert Einstein's The Meaning of Relativity offered an overview and explanation of the then new and controversial theory of ... More

## Mathematics without Apologies: Portrait of a Problematic Vocation

*Michael Harris*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175836
- eISBN:
- 9781400885527
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175836.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers, this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in ... More

## Advances in Analysis: The Legacy of Elias M. Stein

*Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159416
- eISBN:
- 9781400848935
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159416.001.0001
- Subject:
- Mathematics, Numerical Analysis

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His ... More

## Graph Theory: A Look Back—The Road Ahead

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0013
- Subject:
- Mathematics, Applied Mathematics

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution ... More

## The Tarskian Turn: Deflationism and Axiomatic Truth

*Leon Horsten*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015868
- eISBN:
- 9780262298643
- Item type:
- book

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015868.001.0001
- Subject:
- Philosophy, General

This book investigates the relationship between formal theories of truth and contemporary philosophical approaches to truth. The work of mathematician and logician Alfred Tarski (1901–1983) marks the ... More

## How to Explain Number Theory at a Dinner Party

*Michael Harris*

### in Mathematics without Apologies: Portrait of a Problematic Vocation

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175836
- eISBN:
- 9781400885527
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175836.003.0012
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter continues the discussion began in Chapter α. It presents the third part of author's response to the question, “What is it you do in number theory, anyway?” Working his way up to the ... More

## Mathematicians on the geometrization of the Hamilton–Jacobi formalism

*JESPER LÜTZEN*

### in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0024
- Subject:
- Physics, History of Physics

It has long since been remarked by mathematicians that William Rowan Hamilton's method contains purely geometrical truths, and that a peculiar mode of expression, suitable to it, is required in order ... More

## Greek Mathematicians: A Group Picture

*R. Netz*

### in Science and Mathematics in Ancient Greek Culture

- Published in print:
- 2002
- Published Online:
- February 2010
- ISBN:
- 9780198152484
- eISBN:
- 9780191710049
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198152484.003.0011
- Subject:
- Classical Studies, European History: BCE to 500CE

This chapter examines who the Greek mathematicians were by taking an imaginary group picture taken at a conference of ancient Greek mathematicians — a conference held in heaven, so that everyone is ... More

## No Apologies

*Michael Harris*

### in Mathematics without Apologies: Portrait of a Problematic Vocation

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175836
- eISBN:
- 9781400885527
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175836.003.0014
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents the author's reflections about G. H. Hardy's A Mathematician's Apology. Upon rereading Hardy's Apology to prepare for writing this chapter, he was appalled to see what a hearty ... More