Mathematics and the Aesthetic

a general mathematical theory of the fine arts, which would do for aesthetics what had been achieved in another philosophical subject, logic, by the symbolisms of Boole, Peano, and Russell. (p. 127) Birkhoff admitted that the aesthetic ...

Author: Nathalie Sinclair

Publisher: Springer Science & Business Media

ISBN: 9780387381459

Category: Mathematics

Page: 288

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Explaining Beauty in Mathematics An Aesthetic Theory of Mathematics

mathematical value repository makes perfect sense. My conception of aesthetic judgement trivially yields a unified depiction of mathematical aesthetic judgements and the rest of aesthetic judgements, since the process of articulation ...

Author: Ulianov Montano

Publisher: Springer Science & Business Media

ISBN: 9783319034522

Category: Philosophy

Page: 220

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This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.

Mathematics and Beauty

In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics.

Author: Nathalie Sinclair

Publisher:

ISBN: STANFORD:36105114444016

Category: Education

Page: 196

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In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professional mathematician, there is a particular focus on middle school, where negative feelings toward mathematics frequently begin. Offering specific recommendations to help teachers evoke and nurture their students’ aesthetic abilities, this book: Features powerful episodes from the classroom that show students in the act of developing a sense of mathematical aesthetics. Analyzes how aesthetic sensibilities to qualities such as connectedness, fruitfulness, apparent simplicity, visual appeal, and surprise are fundamental to mathematical inquiry. Includes examples of mathematical inquiry in computer-based learning environments, revealing some of the roles they play in supporting students’ aesthetic inclinations.

The Art of Mathematics

Thus, I mean a mathematical theory. So, statement (*) now concerns itself with whether or not a mathematical aesthetic theory can exist which includes mathematics. The answer seems clearly negative. At least it is clear that no ...

Author: Jerry P. King

Publisher: Springer

ISBN: 9781489963390

Category: Mathematics

Page: 313

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The beauty of mathematics eludes all but a small, select handful of people. This monumental classic will illuminate the aesthetic delights of mathematics for all to behold. Why should only a tiny aristocracy hold the key to appreciating the elegance of mathematics? Why should intelligent, cultured people, who can easily articulate the brilliance of Shakespeare's imagery, quake at the prospect of deciphering a simple algebraic formula? Jerry King, a mathematics professor and a poet, razes the barriers between a world of two cultures and hands us the tools for appreciating the art and treasures of this elegant discipline. In his fluid, poetic voice, he initiates us into the splendid wonders of the Mathworld. He provides us with an original framework for contemplating mathematics as art. He deepens our ultimate comprehension of art by comparing the beauty of a Rembrandt as well as a Jackson Pollock with the riches to be mined in an elegant proof. Like the great philosophers of the past, Dr. King searches for pure Truth--a quest possible today only in the realm of mathematics. With his infectious enthusiasm, he explains with utmost clarity the intellectually stimulating underpinnings of both pure and applied mathematics. He goes on to decry how our educational system has failed by perfunctorily teaching us mathematics, depriving us of the pillars of beauty upon which mathematics rests. Never before has a book spoken so eloquently to our soul in instilling an appreciation for the grandeur of mathematics. Through Dr. King, the muses of mathematics will no longer sing for others and not for us. The elegant world of mathematics awaits us all to savor.

Mathematical Aesthetic Principles nonintegrable Systems

A Restatement of the Mathematical Aesthetic Principles When we first considered a set of mathematical aesthetic principles in Chapter 1 , we did not have an appreciation of the importance of nonintegrability , nor of the value of ...

Author: Murray Muraskin

Publisher: World Scientific

ISBN: 9810222009

Category: Mathematics

Page: 215

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Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as ?aesthetic? and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.

On Aesthetics in Science

THE MATHEMATICAL UNCONSCIOUS SEYMOUR A. PAPERT It is deeply embedded in our culture that the appreciation of mathematical beauty and the ... For Poincaré the distinguishing feature of the mathematical mind is not logical but aesthetic .

Author: WECHSLER

Publisher: Springer Science & Business Media

ISBN: 0817633790

Category: Science

Page: 180

View: 739

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Catalog of NIE Education Products

... Aesthetic Education Program ) RD 010 001 Basic Skills Mathematics and Science The Actor ( Part of the Aesthetic ... RD 010 003 Curriculum Development in Elementary Mathematics : Nine Programs RD 020 032 Aesthetics in the Everyday ...

Author:

Publisher:

ISBN: MINN:30000010697088

Category: Education

Page:

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The Mathematics of Harmony

A Combinatorial Approach to the Harmony of Mathematics 4.1.1. Mathematical, Aesthetic and Artistic Understanding of Harmony In the Introduction we mentioned that the Harmony Problem is one of the “key” problems of mathematics entering ...

Author: Alekse? Petrovich Stakhov

Publisher: World Scientific

ISBN: 9789812775825

Category: Mathematics

Page: 694

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Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ?Mathematics of Harmony,? a new interdisciplinary direction of modern science. This direction has its origins in ?The Elements? of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the ?golden? algebraic equations, the generalized Binet formulas, Fibonacci and ?golden? matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and ?golden? matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

The Mathematical Experience

Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust , as exciting as a telephone book , as remote as the laws of infangthief of fifteenth century Scotland .

Author: Philip J. Davis

Publisher: Houghton Mifflin Harcourt

ISBN: 0395929687

Category: Mathematics

Page: 440

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Traces the history of mathematics, offers profiles of major mathematicians and their discoveries, and looks at the philosophy of mathematics

Aesthetics of Interdisciplinarity Art and Mathematics

Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.

Author: Kristóf Fenyvesi

Publisher: Birkhäuser

ISBN: 9783319572598

Category: Mathematics

Page: 290

View: 444

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This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.