What is a mathematical concept?

Cover
 Half-title
 Title page
 Copyright information
 Table of contents
 List of images
 Notes on contributors
 Introduction
 The Context for This Book: Philosophy and Cognition
 Themes and Chapters
 On Reading the Book
 References
 Part I
 1 Of Polyhedra and Pyjamas: Platonism and Induction in Meaning-Finitist Mathematics
 Introduction
 Strong Program Meaning Finitism
 Induction
 Platonism
 Conclusion
 Acknowledgments
 References
 2 Mathematical Concepts? The View from Ancient History
 Introduction
 Infinity, Actually
 Indeed, It's Not That They Couldn't
 What We Share
 References
 Part II. 3 Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical DrawingIntroduction
 Two Subgenres
 First Moment: The Euclidean Diagram
 Second Moment: What Is the Hand?
 Third Moment: The Incidental Drawing
 Conclusion
 Acknowledgements
 References
 4 Concepts as Generative Devices
 Proposition 1: Concepts Are Not Merely Metaphors or Representations
 Proposition 2: Concepts Are Not Mental Constructs Abstracted from the Material World
 Proposition 3: Concepts Are Vibrant and Indeterminate, Having One Foot in the Virtual and One in the Actual. Proposition 4: Concepts Operate as Both Logical and Ontological DevicesProposition 5: There Is No a priori Logical Ordering between Mathematical Concepts
 Proposition 6: Concepts Emerge from Aesthetico-Political Acts
 Concluding Comments
 References
 Part III
 5 Bernhard Riemann's Conceptual Mathematics and the Pedagogy of Mathematical Concepts
 Introduction: From Conceptual Philosophy to Conceptual Mathematics
 Planes of Immanence and the Architecture of Concepts
 The Concept of Manifold: Space and Geometry in Riemann
 Conclusion: A Pedagogy of the Concept
 References. 6 Deleuze and the Conceptualisable Character of Mathematical TheoriesThe Theory of Mathematical Problems and the History of Mathematics
 Lautman, Cavaillès and the Mathematical Real
 Galois (Formal) or Poincaré (Informal) on the Mathematical Expression of Problems?
 References
 Part IV
 7 Homotopy Type Theory and the Vertical Unity of Concepts in Mathematics
 Introduction
 Varieties of Concept
 Addition, Multiplication and Exponentiation
 Groupoids, Identity and Symmetry
 Spaces and Duality
 Conclusion
 References
 8 The Perfectoid Concept: Test Case for an Absent Theory
 Perfectoid Prologue. Starting PointsScholze's Perfectoid Concept
 The Concept's Reception
 Discussion
 References
 Part V
 9 Queering Mathematical Concepts
 What Are Mathematical Concepts?
 Looking Awry at Mathematical Concepts, or What Do Mathematical Concepts Do?
 Queering Mathematical Concepts, or What Could Mathematical Concepts Do?
 Where Do We Go from Here?
 Acknowledgements
 References
 10 Mathematics Concepts in the News
 Reporting Mathematics Education
 Theoretical Background
 Framing
 Constructing Concepts
 Conclusions
 References
 11 Concepts and Commodities in Mathematical Learning.