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Simplicity Ideals Of Practice In Mathematics And The Arts


Author : Roman Kossak
language : en
Publisher: Springer
Release Date : 2017-06-28


Download Simplicity Ideals Of Practice In Mathematics And The Arts written by Roman Kossak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-28 with Mathematics categories.


To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice.

Humanizing Mathematics And Its Philosophy


Author : Bharath Sriraman
language : en
Publisher: Birkhäuser
Release Date : 2017-11-07


Download Humanizing Mathematics And Its Philosophy written by Bharath Sriraman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.


This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.

What Is A Mathematical Concept


Author : Elizabeth de Freitas
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-22


Download What Is A Mathematical Concept written by Elizabeth de Freitas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Education categories.


Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Aspects


Author : Edward A. Vazquez
language : en
Publisher: University of Chicago Press
Release Date : 2018-01-02


Download Aspects written by Edward A. Vazquez and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Art categories.


Stretching lengths of yarn across interior spaces, American artist Fred Sandback (1943–2003) created expansive works that underscore the physical presence of the viewer. This book, the first major study of Sandback, explores the full range of his art, which not only disrupts traditional conceptions of material presence, but also stages an ethics of interaction between object and observer. Drawing on Sandback’s substantial archive, Edward A. Vazquez demonstrates that the artist’s work—with all its physical slightness and attentiveness to place, as well as its relationship to minimal and conceptual art of the 1960s—creates a link between viewers and space that is best understood as sculptural even as it almost surpasses physical form. At the same time, the economy of Sandback’s site-determined practice draws viewers’ focus to their connection to space and others sharing it. As Vazquez shows, Sandback’s art aims for nothing less than a total recalibration of the senses, as the spectator is caught on neither one side nor the other of an object or space, but powerfully within it.

Visualization Explanation And Reasoning Styles In Mathematics


Author : P. Mancosu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30


Download Visualization Explanation And Reasoning Styles In Mathematics written by P. Mancosu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.


In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

99 Variations On A Proof


Author : Philip Ording
language : en
Publisher:
Release Date : 2019-01-29


Download 99 Variations On A Proof written by Philip Ording and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-29 with Mathematics categories.


An exploration of the art of mathematics through 99 different proofs of the same theorem This lively and compelling book offers a unique, multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from "Medieval," "Topological," and "Doggerel" to "Chromatic," "Electrostatic," and "Psychedelic." Along the way, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo--whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp--Ording explores new ways to examine the aesthetic possibilities of mathematical activity. This mathematical take on Queneau's Exercises in Style--a collection of 99 retellings of the same story--draws unexpected connections to everything from mysticism and technology to architecture and sign language and includes diagrams, notations, and other imagery that are as amusing as they are edifying. With a rare blend of humor and scholarly aplomb, Ording illustrates the inherent creative potential and flexibility of mathematical language despite its reputation for precision and rigor. Readers of this playful and expansive compendium of mathematical exposition and style will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Every reader, no matter their level of expertise, will discover in these proofs surprising new aspects of the mathematical landscape.

A Beginner S Guide To Constructing The Universe


Author : Michael S. Schneider
language : en
Publisher: Harper Collins
Release Date : 2014-04-01


Download A Beginner S Guide To Constructing The Universe written by Michael S. Schneider and has been published by Harper Collins this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-01 with Science categories.


The Universe May Be a Mystery, But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round. Why one and two weren't considered numbers by the ancient Greeks. Why squares show up so often in goddess art and board games. What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster and a cathedral. And much more.