What is a Mathematical Concept?

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

Elizabeth de Freitas (Edited by), Nathalie Sinclair (Edited by), Alf Coles (Edited by)

9781107134638, Cambridge University Press

Hardback, published 22 June 2017

316 pages
23.7 x 16 x 2.4 cm, 0.59 kg

'Mathematics has far too often been a discipline reserved for specialists. Even philosophers have tended to limit their focus to the foundations of mathematics, rather than the productions of contemporary mathematics. This is a wonderful book that reverses this trend. It approaches mathematical concepts from a perspective that is broadly humanistic and interdisciplinary, drawing on disciplines as diverse as history, philosophy, sociology and psychology. Each of the essays is written in a non-technical yet rigorous manner that should be accessible even to the 'mathematically challenged', and taken together they present a richly innovative approach to the ontology of mathematics. This is a timely and user-friendly collection that should help restore mathematics to its rightful place as a central discipline in the humanities.' Daniel Smith, Purdue University, Indiana

Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically.

Introduction
Part I: 1. Of polyhedra and pyjamas: platonism and induction in meaning-finitist mathematics Michael J. Barany
2. Mathematical concepts? The view from ancient history Reviel Netz
Part II: 3. On treating mathematical drawings as artworks Juliette Kennedy
4. Concepts as generative devices Elizabeth de Freitas and Nathalie Sinclair
Part III: 5. Bernhard Riemann's conceptual mathematics and pedagogy of mathematical concepts Arkady Plotnitsky
6. Deleuze and the conceptualizable character of mathematical theories Simon Duffy
Part IV: 7. The vertical unity of the concept of space David Corfield
8. The perfectoid concept: test case for an absent theory Michael Harris
Part V: 9. Queering mathematical concepts Heather Mendick
10. Mathematics concepts in the news Richard Barwell and Yasmine Abtahi
11. Concepts and commodities in mathematical learning Tony Brown
Part VI: 12. A relational view of mathematical concepts Alf Coles
13. Cultural concepts concretely Wolff-Michael Roth
Part VII: 14. Ideas as species Brent Davis
15. Inhabiting mathematical concepts Ricardo Nemirovsky
Afterword. Making a thing of it: some conceptual commentary David Pimm
Index.

Subject Areas: History of mathematics [PBX], Philosophy of mathematics [PBB], Educational psychology [JNC], Philosophy [HP], General studies [GTG]