Download or read book Explaining Beauty in Mathematics An Aesthetic Theory of Mathematics written by Ulianov Montano and published by Springer Science & Business Media. This book was released on 2013-12-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematics and Beauty written by Nathalie Sinclair and published by . This book was released on 2006-09-08 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Beauty in Mathematics Symmetry and Fractality written by Vladimir A. Testov and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most important concepts underlying beauty are the concepts of symmetry and fractality, but the relationship of these concepts has not yet remained clear. For centuries, beauty was understood only as a stable order and symmetry. Synergetic worldview allows us to give a new assessment: beauty can be seen as an attractor, the result of self-organization of nature, or the flight of human thought. On the one hand, fractality can be considered one of the manifestations of symmetry in an expansive sense.

Download or read book Aesthetics of Interdisciplinarity Art and Mathematics written by Kristóf Fenyvesi and published by Birkhäuser. This book was released on 2017-11-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Weil Conjectures written by Karen Olsson and published by Macmillan + ORM. This book was released on 2019-07-16 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A New York Times Editors' Pick and Paris Review Staff Pick "A wonderful book." --Patti Smith "I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge." --Parul Sehgal, The New York Times An eloquent blend of memoir and biography exploring the Weil siblings, math, and creative inspiration Karen Olsson’s stirring and unusual third book, The Weil Conjectures, tells the story of the brilliant Weil siblings—Simone, a philosopher, mystic, and social activist, and André, an influential mathematician—while also recalling the years Olsson spent studying math. As she delves into the lives of these two singular French thinkers, she grapples with their intellectual obsessions and rekindles one of her own. For Olsson, as a math major in college and a writer now, it’s the odd detours that lead to discovery, to moments of insight. Thus The Weil Conjectures—an elegant blend of biography and memoir and a meditation on the creative life. Personal, revealing, and approachable, The Weil Conjectures eloquently explores math as it relates to intellectual history, and shows how sometimes the most inexplicable pursuits turn out to be the most rewarding.

Download or read book Beautiful Mathematics written by Martin Erickson and published by MAA. This book was released on 2011-12-22 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical ideas with aesthetic appeal for any mathematically minded person.

Download or read book The Philosophy of Mathematics Education Today written by Paul Ernest and published by Springer. This book was released on 2018-06-09 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

Download or read book Advances in Experimental Philosophy of Logic and Mathematics written by Andrew Aberdein and published by Bloomsbury Publishing. This book was released on 2019-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.

Download or read book Beauty A Very Short Introduction written by Roger Scruton and published by Oxford University Press, USA. This book was released on 2011-03-24 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a book that is itself beautifully written, renowned philosopher Roger Scruton explores this timeless concept, asking what makes an object--either in art, in nature, or the human form--beautiful.--From publisher description.

Download or read book Mathematics Through the Eyes of Faith written by Russell Howell and published by Harper Collins. This book was released on with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book description to come.

Download or read book New Aesthetic Thought Methodology and Structure of Systemic Philosophy written by Wu, Jie and published by IGI Global. This book was released on 2019-10-25 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methodologies of aesthetic thought have always had a deep, historic foundation and serve as a staple of philosophy. Researchers have begun re-examining the structure and levels of aesthetics by tracing the history of this practice and studying European and Asian traditions. This systematic perspective is an emerging topic of exploration yet requires an appropriate level of research that further investigates the recent discoveries of systemic aesthetics in today’s modern world. New Aesthetic Thought, Methodology, and Structure of Systemic Philosophy is an essential reference source that discusses the organic connection between philosophy, mathematics, and aesthetics, as well as its application to other fields of human sciences. This book analyzes the history of aesthetics and studies the contemporary laws and function of beauty and nature. Featuring research on topics such as fundamental principles, mathematical methods, and humanistic logic, this book is ideally designed for philosophers, physicians, scientific researchers, mathematicians, systems engineers, complexity professionals, anthropologists, art designers, academicians, and students seeking coverage on the structure of artistic beauty through a systematic approach.

Download or read book Indiscrete Thoughts written by Gian-Carlo Rota and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.

Download or read book Scientific Theories and Philosophical Stances written by Claus Beisbart and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-05-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of his seminal monograph "The scientific image", Bas van Fraassen is a key figure in philosophy of science. In this book, other philosophers with various outlooks critically discuss his work on theories, empiricism and philosophical stances. The book starts with a new article by van Fraassen on his preferred account of theories, the so-called semantic view. This account is now 50 years old, and van Fraassen takes this anniversary as an opportunity to review the account, its history and the philosophical discussion about it. In the main part of the book, Nancy Cartwright, Finnur Dellsén, Matthias Egg, Steven French, Michael Friedman, Milena Ivanova and Michela Massimi discuss van Fraassen's contributions to philosophy. Three chapters focus on his engagement with realism (French, Friedman, Ivanova). Others study his voluntarism (Cartwright) and his view on representation (Massimi). Finally, there are contributions about his elaboration of empiricism (Dellsén) and his proposal to consider philosophical positions as stances (Egg). The volume includes a laudatio written by Steven French and finishes with a reply by van Fraassen to his critics.

Download or read book The Aesthetics of Science written by Milena Ivanova and published by Routledge. This book was released on 2020-01-16 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume builds on two recent developments in philosophy on the relationship between art and science: the notion of representation and the role of values in theory choice and the development of scientific theories. Its aim is to address questions regarding scientific creativity and imagination, the status of scientific performances—such as thought experiments and visual aids—and the role of aesthetic considerations in the context of discovery and justification of scientific theories. Several contributions focus on the concept of beauty as employed by practising scientists, the aesthetic factors at play in science and their role in decision making. Other essays address the question of scientific creativity and how aesthetic judgment resolves the problem of theory choice by employing aesthetic criteria and incorporating insights from both objectivism and subjectivism. The volume also features original perspectives on the role of the sublime in science and sheds light on the empirical work studying the experience of the sublime in science and its relation to the experience of understanding. The Aesthetics of Science tackles these topics from a variety of novel and thought-provoking angles. It will be of interest to researchers and advanced students in philosophy of science and aesthetics, as well as other subdisciplines such as epistemology and philosophy of mathematics.

Download or read book Mathematical Cultures written by Brendan Larvor and published by Birkhäuser. This book was released on 2016-05-25 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection presents significant contributions from an international network project on mathematical cultures, including essays from leading scholars in the history and philosophy of mathematics and mathematics education.​ Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematical research and teaching, and great variation in the place of mathematics in the larger cultures that mathematical practitioners belong to. The reflections on mathematical cultures collected in this book are of interest to mathematicians, philosophers, historians, sociologists, cognitive scientists and mathematics educators.

Download or read book A Conversation on Professional Norms in Mathematics written by Pamela E. Harris and published by American Mathematical Soc.. This book was released on 2021-10-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas. This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.

Download or read book Masters of Mathematics written by Robert A. Nowlan and published by Springer. This book was released on 2017-05-13 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”