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Elwes R: Huge Numbers

Huge Numbers

Elements in the Philosophy of Mathematics

This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to Bertrand Russell and the orientation referred to as 'scientific philosophy' that was active between 1850 and 1930. To give a better sense of the field, the Element further contains two examples of topics studied, that of mathematical structuralism and visual thinking in mathematics. These are in part presented from a methodological point of view, focussing on mathematics as an activity and questions related to how mathematics develops. In addition, the Element contains several examples from mathematics, both historical and contemporary , to illustrate and support the philosophical points.

The Element introduces the philosophy of mathematical practice, which takes mathematical practice and contrasts it with mathematical philosophy, a term traced back to Bertrand Russell's scientific philosophy. It discusses mathematical structuralism and visual thinking, focusing on methodological aspects and historical and contemporary examples.

Introducing the Philosophy of Mathematical Practice

How playwrights from Alfred Jarry and Samuel Beckett to Tom Stoppard and Simon McBurney brought the power of mathematics to life on the stage The discovery of alternate geometries, paradoxes of the infinite, incompleteness, and chaos theory revealed that, despite its reputation for certainty, mathematical truth is not immutable, perfect, or even perfectible. Beginning in the last century, a handful of adventurous playwrights took inspiration from the fractures of modern mathematics to expand their own artistic boundaries. Originating in the early avant-garde, mathematics-infused theater reached a popular apex in Tom Stoppard’s 1993 play Arcadia. In The Proof Stage, mathematician Stephen Abbott explores this unlikely collaboration of theater and mathematics. He probes the impact of mathematics on such influential writers as Alfred Jarry, Samuel Beckett, Bertolt Brecht, and Stoppard, and delves into the life and mathematics of Alan Turing as they are rendered onstage. The result is an unexpected story about the mutually illuminating relationship between proofs and plays—from Euclid and Euripides to Gödel and Godot. Theater is uniquely poised to discover the soulful, human truths embedded in the austere theorems of mathematics, but this is a difficult feat. It took Stoppard twenty-five years of experimenting with the creative possibilities of mathematics before he succeeded in making fractal geometry and chaos theory integral to Arcadia’s emotional arc. In addition to charting Stoppard’s journey, Abbott examines the post-Arcadia wave of ambitious works by Michael Frayn, David Auburn, Simon McBurney, Snoo Wilson, John Mighton, and others. Collectively, these gifted playwrights transform the great philosophical upheavals of mathematics into profound and sometimes poignant revelations about the human journey.

How Theater Reveals the Human Truth of Mathematics

The Proof Stage

Plato und die Mathematik – Die Mathematik und Plato

Mathematics Study Resources

What kind of objects does mathematics investigate, and in what sense do these objects exist? Why are we justified in considering mathematical statements as part of our knowledge, and how can they be validated? A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses – such arguments form the second focus of this book. The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it.
This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.
The Author
Jörg Neunhäuserer earned his doctorate in mathematics at&nbsp;Freie Universität Berlin. He has published numerous articles in academic journals and has taught mathematics lectures in various bachelor's and master's programs at the universities of Berlin, Clausthal, Dresden, Hanover, and Lüneburg. His German-language books on Mathematical Concepts and Beautiful Theorems of Mathematics are also available from Springer Spektrum.

Introduction to the Philosophy of Mathematics

A Memoir

Building Things

Literary Methods in the Social Sciences

Why have there been so few women mathematicians? This book does not seek an answer in absence but in the forces, ruptures, and intensities that shape the becoming of a femme philosophe-a mathematician, scientist, and philosopher-within the shifting assemblages of eighteenth- and nineteenth-century Europe.

A Feminist Genealogy of Automathographies

Numbers and Narratives

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author's motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features<ul> <li>Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates</li> <li>Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof</li> <li>Draws attention to connections with other areas of mathematics</li> <li>Plenty of exercises for students, both straightforward problems and more in-depth investigations</li> <li>Introduces many concepts that are required in more advanced topics in mathematics</li> </ul>New to the second edition<ul> <li>Complete solutions to all exercises, and hints for the in-depth investigations</li> <li>Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory</li> <li>A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties</li> <li>A thorough correction of typos and errors across all chapters</li> <li>Updates to the bibliography</li> </ul>

A Path into Rigorous Mathematics

Number Systems

Logic, Epistemology, and the Unity of Science

Part I: Cultural & Fundamental Frameworks

An Intellectual History of Science in the Renaissance

Plato, Whitehead, Aristotle

On Mathematics, Unity, and the Good

Liber Historica

A lavishly illustrated compendium of the most significant publications that have informed mathematical knowledge throughout history.

The books that unlocked the power of numbers

The Mathematicians' Library

Huge Numbers

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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