Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. Drawing on literature, art, and photography, it explores how the Victorian mathematical conception of form still resonates today.

Claude P. Bruter (editor), Mathematics in Art: Mathematical Visualization in Art and Education, Springer-Verlag, New York, 2002, pp. X + 337, ISBN 3-540-43422-4.

This study aims to alleviate the current tense employment situation and study the entrepreneurial situation of teachers and students in colleges and universities. Firstly, based on the educational concept of Science Technology Engineering Arts Mathematics, Ideological and Political Education is added to psychological capital to explore the effect of the combination of the two on entrepreneurial performance. An entrepreneurial performance impact model is constructed, and the questionnaire is set. Secondly, the influence of psychological capital combined with IPE on sports morality (...) is explored, and a sports morality questionnaire is designed. Finally, the questionnaire results are analyzed. The results showed that most of the participants in the survey are under the age of 25. The 25- to 29-year-olds are the smallest among those surveyed. The respondents who participated in the survey had the most undergraduate degrees, accounting for 43.4%. The 40 items on entrepreneurial performance this time obey a normal distribution, and the scale has good reliability and validity. The main factor analysis results obtained by principal component analysis include 6 factors. Their total explanatory power exceeds 67%, and the six factors screened out this time are well represented. The model tolerance is between 0.45 and 0.5, and the Variance Inflation Factor value is less than 10. The scale does not suffer from multi-collinearity issues. IPE significantly strengthens the effect of psychological capital on entrepreneurial performance. The influences of various sports on sportsmanship, bravery, self-confidence, and self-transcendence are significantly different, and the P value is less than 0.001. The difference in aggressiveness is less than 0.01, indicating that it is very significant. Different sports have significant differences in the cultivation of sports morality, and the P value is less than 0.05. The differences in self-discipline are also significant, and there are extremely significant differences in compliance with rules, and the P value here is less than 0.001. There are no significant differences in sporting qualities. IPE combined with psychological capital has a significant impact on entrepreneurial performance. These contents provide references for the entrepreneurship education of teachers and students in colleges and universities. The contribution lies in expanding the research on psychological capital in entrepreneurial performance and laying a foundation for the combination of psychological capital and IPE. (shrink)

The purpose of this paper is the influence of Science- Technology- Engineering- Art- Mathematics education on the Olympic education of primary and middle school students. The research object is the Beijing Olympic model school. The frame structure and educational concept of STEAM education are studied, and a questionnaire survey on the current situation of Olympic education is conducted. Finally, improvement measures based on the survey results are provided combined with STEAM education, and the teaching effect is analyzed. The results show (...) that after the improvement of the educational model, the student’s mastery of the Olympic knowledge has been greatly improved. The proportion of students who can master all knowledge increases from 5.78 to 8.45%, by 2.67%. The proportion of students with knowledge of most Olympic sports increases from 48.6 to 55.67%, by 7.07%. The proportion of students with little or no knowledge drops to 1.54%. Meanwhile, students are increasingly interested in Olympic events, especially after being inspired by the STEAM education model. The proportion of students who are very concerned about Olympic events has increased by 6.45%. The proportion of students who are more concerned about Olympic events has increased by 5.11%. Thus, the Olympic education work has achieved some results. Students gradually become interested in the Olympic events. They begin to actively pay attention to the Olympic events and learn the Olympic spirit. Then, their physical literacy is improved. (shrink)

Comparisons made between art and mathematics so often centre on the beauty of mathematics and how its forms might be seen as aesthetically pleasing. Yet the prominence of beauty as an attribute is less prevalent in contemporary art. Rather, art has a much broader scope of concern, perhaps with a greater emphasis on providing apparatus through which we might better understand who we are. This paper considers some performative aspects of contemporary art and draws parallels with some examples of mathematical (...) activity within educative contexts. It argues that the performative dimension of mathematics is underemphasised in school activity and that the social and linguistic conditioning of mathematics within performance is a crucial aspect of the discipline being addressed in school and vocational courses. In particular, proficiency with concretisations of mathematics and the social dynamics that attend these is integral to the broader proficiency of moving between concrete and abstract domains. (shrink)

The Liberal Arts deal with the human being as a whole and hence with what lies at the essence of being human. As a result, the Liberal Arts have a far greater capacity to do good than other fields of study, for their foundation in philosophy enables them to bring students into contact with the ultimate questions which they are free to accept. Even if these questions have little or no ‘market value’, it should be obvious that the way they (...) are taught and learned is going to have a powerful impact upon the future of the students and society. It is suggested here that mathematics has an integral role in the study of the liberal arts in a first degree at a university where the ‘meal ticket’ is subsequently studied in the graduate or professional school. (shrink)

This work, in continuity with the article published by Ferdinando Casolaro and Giovanna Della Vecchia in Vol 5, 2017 of this series, in which we noted that in the centuries since the eight century B.C. at the 13th century A.D. the evolution of Astronomy and historical events have influenced the development of Mathematics, intends to demonstrate how the Architecture and Literature of the following centuries have further conditioned the development of the sciences in Italy and, in particular, of Mathematics, identifying (...) the affinities and, in some cases, the coincidences between the different forms of thought that invite us to make a serious reflection on the uniqueness of culture. (shrink)

In the present paper the roots of the Art of the Catalan philosopher Ramon Llull are examined. Moreover the impact of the Art on seventeenth mathematics is briefly discussed.

Science and esthetics.--Theory of regularity and coordination.--Technology of art production.

Mathematicians frequently use aesthetic vocabulary and sometimes even describe themselves as engaged in producing art. Yet aestheticians, in so far as they have discussed this at all, have often downplayed the ascriptions of aesthetic properties as metaphorical. In this paper I argue firstly that the aesthetic talk should be taken literally, and secondly that it is at least reasonable to classify some mathematics as art.

Mathematicians often say that their theorems, proofs, and theories can be beautiful. They say mathematics can be like art. They know how to move creatively and freely in their domains. But ordinary people usually cannot do this and do not share this view. They often have unpleasant memories from school and do not have this experience of freedom and creativity in doing mathematics. I myself have been a mathematician, and I wish to highlight some of the creative aspects in doing (...) mathematics. I always had the feeling that there is much freedom in mathematics and that one can do as one pleases as long as one avoids contradictions (and one can even live with contradictions for a while). In mathematics one only needs to define something and there it is! Just imagine it, and it immediately exists. Where else, besides fiction, does one have such power? --- This essay has three parts. In the first, I lay out some historical facts and views that I will need later. Second, I insert an interlude with Kant, pointing out some of his claims and insights in aesthetics, and some aspects in mathematics that I think he overlooked or underestimated. Third, I will bring out some aspects of higher mathematics that I will show are similar to art. These aspects are in the doing and creating of mathematics, not in the finished theories. They are usually not found in textbooks. I want to show that a researcher in mathematics is like a painter or composer, exploring and creating. To see this, one has to adopt a first-person perspective. In this way I will show that aesthetics plays a role and leaves its traces also in mathematics. (shrink)

A textbook for students who are learning how to write a mathematical proof, a validation of the truth of a mathematical statement.

The history of the continuous inclusion of mathematics in liberal education in the West, from ancient times through the modern period, is sketched in the first two sections of this chapter. Next, the heart of this essay (Sects. 3, 4, 5, 6, and 7) delineates the central role mathematics has played throughout the history of Western civilization: not just a tool for science and technology, mathematics continually illuminates, interacts with, and sometimes challenges fields like art, music, literature, and philosophy – (...) subjects now universally considered to be liberal arts. Section 8 adds an international perspective to the contemporary liberal arts story by describing some instructive mathematical achievements from many cultures and societies. Finally, Sect. 9 addresses how contemporary mathematics teaching can use the history of mathematics viewed as a liberal art to enhance the appreciation and understanding of mathematics for all students. (shrink)

Mathematics stand in a privileged relationship with aesthetics: a relationship that follows two main directions. The first concerns the introduction of mathematical considerations into aesthetic discourse. For instance, it is common to mention the mathematical architecture of certain artistic productions. The second leads from aesthetics to mathematics. In this case, the question is that of the role and meaning that aesthetic considerations may assume in mathematics. It is indeed a widely held view among mathematicians, of whatever socio-historical context, not only (...) to see their discipline as presenting a strong aesthetic dimension, but also to consider that this dimension plays a fundamental role in the process of developing and understanding mathematics. The main ambition of this paper is to show how Nelson Goodman’s aesthetics can be used to justify this point of view and to propose a thesis concerning the aesthetic functioning of mathematics. This first result allows to resituate Goodman’s aesthetics within a very classical tradition that will be described. Finally, the underlying ambition is to show the keys provided by Goodman’s theory for the philosophy of mathematics. (shrink)

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to (...) write proofs with elegance and precision. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.1 (2004) 12-22 [Access article in PDF] Art of a Child with Autism:Drawing Systems and Proto Mathematics Julia Kellman Sung, a five year old girl with autism, was enrolled by her mother in the university Saturday art program with the hope that Sung's favorite church school teacher, a graduate student in art education, would be able to tutor her daughter during the weekly classes. (...) Though hesitant because of her inexperience with autistic children and because of Sung's frequently angry tantrums on Sundays and the little girl's inability to speak, the young teacher, nonetheless, agreed to the plan. Her concerns proved unfounded, for Sung was able to work in the midst of the churning mass of noisy pre-K classmates without any signs of the fury that drove her to screaming, biting fits in church school. Additionally, and to everyone's delight, Sung's ability to develop as an image-maker was itself confirmed within the first few weeks of art class, dispelling any remaining doubts of her art aptitude or the value of art classes for the little girl.Additional questions and considerations arose about Sung and her art during the classes. How might one understand Sung's changing imagery? What might such explanations and images suggest about Sung herself and her activities? What might her art indicate about her similarity to other children and their art making? The possible answers to these and related queriespresented themselves during the semester, suggesting new avenues for inquiry surrounding both the wordless little girl and her Saturday morning creations.What follows is the story of Sung and her graphic development as it unfolded during the art class. Further, it is an attempt to uncover what Sung's drawings suggest about methods that are useful in the examination of the art of an autistic child. Documentation was carried out with a 35 mm. camera and color copier throughout the semester. Ethnographic methods including participant observation and interviews were employed to gather contextual data. Alfred Schutz's phenomenological sociology allowed for [End Page 12] consideration of nonverbal and verbal social interactions and behaviors. 1 A search of the literature of early mathematical development and drawing systems provided the underpinnings for early insights and later hypotheses. Here is Sung's story. Sung Sung, thick black hair swung forward to hide her face, lies prone in the middle of the busy classroom oblivious to the surging, chattering children around her, so intent is she on the sketchbook in which she draws. Next to her left elbow teeters a stack of a half dozen boxes of thick craypas from which she snatches colors, never looking at the hue she grabs. Her drawing behavior has a pattern; it looks like this. Shuffle through the identical boxes. Choose a box. Open it. Snatch out a bright waxy craypa. Hold it close to the eyes. Sniff it. Lick it. If the craypa passes muster, scribble with it in rich heavy lines — banana-like arcs, large solid dots the size of cherries, rectangular patches, and a variety of forms that come and go from one drawing to the next, like heat lightening on a summer evening. Her less frequent forms include: an enclosed yellow irregular shape with a dark dot in the middle suggesting a fried egg; a two-sided zig-zag; X forms; and solid and empty trapezoids made sail-like with superimposed crosses serving as mast and boom.Unlike the chosen craypas, however, those that do not pass Sung's inspection suffer a terrible fate; they are broken in two and their pieces tossed without ceremony to opposite sides of the room to be trodden into flat, bright smears by the other children in the class, pathetic traces of Sung's art. The craypas boxes themselves also play a role. For when they are closed they are used as blocks or toys, objects to be neatly stacked and restacked or placed side by side on the floor. When they are open, however, they are mere receptacles, passively holding... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 1-12 [Access article in PDF] Art and Mathematics in Education Richard Hickman and Peter Huckstep We begin by asking a simple question: To what extent can art education be related to mathematics education? One reason for asking this is that there is, on the one hand, a significant body of claims that assert that mathematics is an art, and, on the other, (...) work in art that has a mathematical basis. Observations of these kinds are not trivial. They have significant implications for the teaching of these areas of the curriculum in at least two ways. First, there is the methodological issue of the extent to which we should teach mathematics and art separately, and second, the teleological question of why they appear in the curriculum at all. So the relationship between the nature of mathematics and art, perceived or real, bears down on questions of the individuation and the justification of these disciplines, or, in other words, upon pedagogy and purpose. Although in principle both the pedagogy and the purpose of any discipline are distinct, there are important connections between them, as we shall draw out.As far as mathematics goes, it has been stressed that the purposes of even rudimentary aspects of mathematics such as counting do need to be made explicit to pupils. 1 What have been seen as errors in understanding are internally linked with pupils' ideas of the purposes of counting. Anna Sierpinska discusses a similar situation within the broader aspect of what she calls "theory" in higher mathematics. 2 More generally, John Passmore, in his analysis of pupils' understanding includes the case where a pupil sees no need to understand since he or she cannot understand the point of learning the subject. 3 If the purposes of art and mathematics are strikingly similar then there is reason to suppose that certain pedagogical approaches that [End Page 1] follow from this will improve understanding of both mathematics and art, and therefore understanding of reasons for engaging in math-based and art-based activities.In schools we see what appears to be some evidence of connections between art and mathematics in cross-curricular work, such as that described in Jacqueline Cossentino and David Schaffer. 4 Apart from providing much-needed motivation, an important value of this approach toward mathematics is that it can illuminate pupils' understanding of some of its purpose by, at the very least, allowing them to recognize instances of mathematics at work, often in unsuspecting contexts. In particular, by facilitating some transference of knowledge pupils can appreciate the so-called "power" of mathematics in its widespread application to the world of artefacts produced by themselves and others.Can we go further than displaying connections between these disciplines? Can we treat mathematics itself as art? In particular, can we suppose that pupils can make mathematics just as they can make artefacts? Some writers seem to imply this by invoking the notion of creativity as a common property between the two disciplines. 5 Leaving aside the ironic sense of creativity in, for example, the case of "creative accountancy" pupils must indeed "make" sense of mathematics and they must originate mathematical assertions of their own that have not been directly taught. In both respects mathematics is similar to the learning of a language. Further than this, we value pupils' inventiveness in their approaches to areas of mathematics, calculations for example.The linking of mathematics and art via creativity has its most persuasive force in the change of attitude toward axiomatic foundations. 6 The story is familiar: for centuries Euclidean geometry was (wrongly) supposed to offer truths of the actual space in which we lived, since its axioms were thought to be confirmed by our intuitions of space. However, when it was found that consistent and useful axiomatic systems could be constructed by making certain alterations to these axioms, it became clear that mathematics was not simply discovered. It involved a significant measure of creativity. Yet one thing is clear: the sense that children make of mathematics, the original utterances they make... (shrink)

In this paper, we introduce a suppositional view of linguistic practice that ranges over fiction, science, and mathematics. While having similar con- sequences to some other views, in particular Linsky and Zalta’s plenitudinous platonism, the view advocated here both differs fundamentally in approach and accounts for a wider range of phenomena and scientific discourse.

This text is organized around the distinction between finite and infinite. It includes a brief overview of what different philosophers have said about infinity, and looks at some of the arguments to the effect that one should adopt a pro-infinity attitude. Other chapters contain an exposition of the ontological schools; interactions among these schools and various theories of truth; the relationship between mathematics and values; a history of mathematics; an analysis of mathematical knowledge; the role of mathematics in eduction; the (...) implications of religion for the philosophy of mathematics; and referenc eto mathematical objects. (shrink)

Andrew Marr has built this masterful study of Mutio Oddi on a set of ironies. He begins with a bitter blow of fortune: Oddi, in the middle of an apparently promising life as mathematician and architect in his native Urbino, had fallen afoul of his lord the Duke, accused of participating in a plot to depose him. After years of apparently unjust imprisonment, he was released in 1610, but into exile. Yet Oddi managed to recast his career in Milan and (...) then in Lucca, building upon a varied set of skills, and even returned eventually to Urbino. That varied set of skills had resulted from yet another, earlier, set of reversals and recoveries: he had turned to mathematics only after first training as an artist in the studio of Federico Barocci, a field he had been forced to abandon due to problems with his eyesight. Oddi was widely respected in his day, not only for his achievements themselves but also for his persistence and ingenuity in overcoming such obstacles. Yet to modern historians of .. (shrink)

In philosophical discourse, vagueness is commonly regarded as an undesirable and problematic aspect of human experience. Such standpoints are not unfounded. However, in this article, I argue that vagueness may in certain instances also possess an instrumental role that supports specific modes of human aspiration, including the artistic and the mathematical. In particular, I investigate the ways in which vagueness not only hinders but also fosters the emergence of an aesthetic quality of experience during the imaginative endeavours of fine art (...) and mathematics. The manner in which the benefit from felt vagueness ties into the formation of artistic and mathematical scenarios helps to illuminate deep and often unnoticed relations between these two domains of human ingenuity. In this article, the overall concept of experience and the particular features of human experience, such as the aesthetic and the vague, are examined in the context of John Dewey’s philosophical pragmatism. In Dewey’s philosophical framework, the human mind and culture are understood as natural phenomena. As such, the Deweyan approach fits the paradigm of a twenty-first century scientific understanding of the inherent ontological unity of all modes of human existence and activity. (shrink)

Art and Abstract Objects presents a lively philosophical exchange between the philosophy of art and the core areas of philosophy. The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete (i.e., material, causally efficacious, located in space and time). Da Vinci's Mona Lisa is currently located in Paris. Richard Serra's Tilted Arc is 73 tonnes of solid steel. Johannes Vermeer's The Concert was stolen in 1990 and remains missing. Michaelangelo's (...) David was attacked with a hammer in 1991. By contrast, the standard way of thinking about repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, symphonies is that they must be abstract (i.e., immaterial, causally inert, outside space-time): consider the current location of Melville's Moby Dick, the weight of Yeats' "Sailing to Byzantium", or how one might go about stealing Puccini's La Boheme or vandalizing Mozart's Piano Concerto No. 9. Although novels, poems, and symphonies may appear radically unlike stock abstract objects such as numbers, sets, and propositions, most philosophers of art think that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. -/- This volume examines how philosophical enquiry into art might itself productively inform or be productively informed by enquiry into abstracta taking place within not just metaphysics but also the philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. While the contributors chiefly focus on the relationship between philosophy of art and contemporary metaphysics with respect to the overlap issue of abstracta, they provide a methodological blueprint from which scholars working both within and beyond philosophy of art can begin building responsible, mutually informative, and productive relationships between their respective fields. (shrink)

Creativity is an essential factor in ensuring the sustainable development of a society. Improving students’ creativity has gained much attention in education, especially in Science, Technology, Engineering, Arts, and Mathematics education. In a quasi-experimental design, this study examines the effectiveness of a project-based STEAM program on the development of creativity in Chinese elementary school science education. We selected two fourth-graders classes. One received a project-based STEAM program, and the other received a conventional science teaching over 6 weeks. Students’ creativity was (...) assessed before and after the intervention using a multi-method approach, including a test of divergent thinking, a story completion through the Consensus Assessment Technique, a creative self-efficacy measure, and a group-based creative project. Moreover, all students received a test of their science knowledge after the intervention. The results showed that compared with the control group, the creativity of the experimental group students improved significantly for 6 weeks at both individual and group level, even though their knowledge in science were comparable. This result confirmed the effectiveness of a project-based STEAM educational program improving elementary school students’ creativity. Implications are discussed. (shrink)

Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for (...) recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. (shrink)

Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer (...) consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations. (shrink)

Mathematical Logic: An Introduction is a textbook that uses mathematical tools to investigate mathematics itself. In particular, the concepts of proof and truth are examined. The book presents the fundamental topics in mathematical logic and presents clear and complete proofs throughout the text. Such proofs are used to develop the language of propositional logic and the language of first-order logic, including the notion of a formal deduction. The text also covers Tarski’s definition of truth and the computability concept. It also (...) provides coherent proofs of Godel’s completeness and incompleteness theorems. Moreover, the text was written with the student in mind and thus, it provides an accessible introduction to mathematical logic. In particular, the text explicitly shows the reader how to prove the basic theorems and presents detailed proofs throughout the book. Most undergraduate books on mathematical logic are written for a reader who is well-versed in logical notation and mathematical proof. This textbook is written to attract a wider audience, including students who are not yet experts in the art of mathematical proof. (shrink)

Despite progress, gender gaps persist in mathematical and language-related fields, and gender stereotypes likely play a role. The current study examines the relations between parents’ gender-related beliefs and their adolescent child’s motivation and career aspirations through a survey of 172 parent-child dyads. Parents reported their gendered beliefs about ability in mathematics and language arts, as well as their prescriptive gender role beliefs. Students reported their expectancies and values in these two domains, as well as their career aspirations The results of (...) path models suggested that parents’ ability stereotypes about language boosted girls’ motivation for language arts, thereby nudging them away from STEM pathways. Girls’ career aspirations stemmed not only from their valuation of the corresponding domain, but also from their valuation of competing domains. Such findings highlight the need to consider multiple domains simultaneously in order to better capture the complexity of girls’ career decisions. For boys, parents’ language ability stereotypes were directly related to mathematical career aspirations. These results suggest that stereotypes that language arts is not for boys push them instead toward mathematics. Our study also highlighted the unique role of parental beliefs in traditional gender roles for boys’ motivation and career aspirations. Specifically, parents’ gender role stereotypes directly related to less interest in language arts only among boys. This highlights that research into gender gaps in female-dominated fields should consider stereotypes related to appropriate behavior and social roles for boys. (shrink)

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, (...) easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences. (shrink)

Why are mathematicians drawn to art? How do they perceive it? What motivates them to pursue excellence in music or painting? Do they view their art as a conveyance for their mathematics or an escape from it? What are the similarities between mathematical talent and creativity and their artistic equivalents? What are the differences? Can a theatrical play or a visual image capture the beauty and excitement of mathematics? Some of the world's top mathematicians are also accomplished artists: musicians, photographers, (...) painters, dancers, writers, filmmakers. In this volume, they share some of their work and reflect on the roles that mathematics and art have played in their lives. They write about creativity, communication, making connections, negotiating successes and failures, and navigating the vastly different professional worlds of art and mathematics. (shrink)