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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 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


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


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


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


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


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


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