These are some works relevant to the topic of the seminar. I have been lazy about bibliographical details, but Google will supply these. To avoid copyright violations, some of the links are to copies kept in a password-protected directory.

- Paolo Mancosu, editor,
*The philosophy of mathematical practice*

- Henri Poincaré,
*Science and method*. - Ludwig Wittgenstein,
*Philosophical investigations*. - Jacques Hadamard,
*Psychology of invention in the mathematical field*. - Jeremy Avigad, "Understanding proofs," pdf.
- Jeremy Avigad, "Understanding, formal verification, and the philosophy of mathematics," pdf.
- Arthur Jaffe and Frank Quinn, "'Theoretical mathematics': toward a cultural synthesis of mathematics and theoretical physics," html.
- William Thurston, "On proof and progress in mathematics," html.
- Other responses to Jaffe and Quinn: html.

- Immanuel Kant,
*Critique of pure reason*. B introduction: pdf. Transcendental doctrine of method, discipline of pure reason in dogmatic use: pdf. On the schematism of the pure concepts of understanding: pdf. - Michael Friedman,
*Kant and the exact sciences*; in particular, chapter 2, "Concepts and intuitions in mathematics," pdf. - Lisa Shabel, "Kant's philosophy of mathematics," pdf.
- Lisa Shabel, "Kant on the 'Symbolic Construction' of Mathematical Concepts," pdf.
- Charles Parsons, "Kant's philosophy of arithmetic," pdf.
- Edmund Husserl,
*The philosophy of arithmetic*, excerpt: pdf. - Gottlob Frege,
*The foundations of arithmetic*(the*Grundlagen*) - Gottlob Frege, "Sense and reference," pdf, and "Comments on sense and reference," pdf.
- Gottlob Frege, "Letter to Husserl," pdf.
- Gottlob Frege, "Function and concept"
- Gottlob Frege, "Concept and object"
- Gottlob Frege,
*The basic laws of arithmetic*(the*Grundgesetze*) - Gottlob Frege, "Thought," pdf.
- Patricia Blanchette, "Frege on shared belief and total functions," pdf.
- Mark Wilson, "The royal road to geometry"
- Mark Wilson, "Frege's mathematical setting," pdf.
- Mark Wilson, "Ghost world: a context for Frege's context principle"
- Richard Dedekind, "On the introduction of new functions in mathematics"
- Richard Heck and Robert May, "The composition of thoughts"

- Kenneth Manders, "Domain extension and the philosophy of mathematics"
- Mark Wilson, "Can we trust logical form?" pdf.
- Mark Wilson, "Enlarging one's stall, or how did all these
*sets*get in here?" pdf. - Sheldon Smith, "Incomplete understanding of concepts: the case of the derivative," pdf.
- Jamie Tappenden, "Mathematical concepts and definitions," pdf.
- Jamie Tappenden, "Mathematical concepts: fruitfulness and naturalness"
- Jeremy Avigad, "Number theory and elementary arithmetic" (section 4, in particular)

- Frank Keil, "Spiders in the web of belief: the tangled relations between concepts and theories," pdf.
- Ray Jackendoff, "What is a concept, that a person might grasp it?" pdf.
- Ray Jackendoff, "Conceptual semantics," pdf.
- Ray Jackendoff,
*Semantics and cognition* - James Pustejovsky, "The generative lexicon," pdf.
- Bob Carpenter,
*The logic of typed feature structures* - Bob Carpenter,
*Type-logical semantics* - Jerry Fodor,
*Concepts: where cognitive science went wrong*, Chapters 1 and 2, pdf. - Ruth Millikan, "Biosemantics," pdf.
- Mark Wilson,
*Wandering significance*

- Israel Kleiner, "Evolution of the function concept: a brief survey," jstor.
- Hans Wussing,
*The genesis of the abstract group concept*. - The Mactutor "Overview of the history of mathematics," html.

- Ludwig Wittgenstein,
*Remarks on the foundations of mathematics*, Part VI: pdf. Part VII: pdf. - Imre Lakatos,
*Proofs and refutations* - Solomon Feferman, "The logic of mathematical discovery vs. the logical structure of mathematics," pdf.
- Mark Steiner, "Mathematical explanation," pdf.
- David Sandborg,
*Explanation in mathematical practice*Chapter 4: (and title page) pdf, Chapter 5: pdf, Chapter 6: pdf, references: pdf. - John Harrison, "A formal proof of Pick's theorem," pdf.
- Jamie Tappenden, "Proof style and understanding in mathematics I: visualization, unification and axiom choice"
- Jeremy Avigad, "Mathematical method and proof" doi, pdf.
- Johannes Hafner and Paolo Mancosu, "The varieties of mathematical explanation"
- Paolo Mancosu, "Mathematical explanation: why it matters," pdf.
- Paolo Mancosu, "Mathematical style," SEP.
- Paolo Mancosu, "Explanation in mathematics," SEP.
- Andrew Arana, "Logical and semantic purity," pdf.
- Michael Detlefsen, "Purity as an ideal of proof," pdf.
- Andrew Arana and Michael Detlefsen, "Purity of methods"

- George Polya,
*How to solve it*, Part I: pdf. - George Polya,
*Mathematics and plausible reasoning, volume I: induction and analogy in mathematics*, excerpts: pdf. - George Polya,
*Mathematics and plausible reasoning, volume II: patterns of plausible inference*, excerpts: pdf. - George Polya,
*Mathematical discovery: on understanding, learning, and teaching problem solving*. - Allen Newell, "The heuristic of George Polya and its relation to artificial intelligence," pdf.
- Allen Newell and Herbert Simon,
*Human problem solving* - Herbert Simon,
*Models of thought*, volumes 1 and 2. - Herbert Simon, "Explaining the ineffable: AI on the topics of intuition, insight, and inspiration," pdf
- Alan Schoenfeld,
*Mathematical problem solving,*pdf. - Wayne Wickelgren,
*How to solve problems*, excerpts: pdf, pdf, pdf - John Hayes,
*The complete problem solver* - Craig Kaplan and Herbert Simon, "In search of insight," pdf.

- Paolo ney de Souza and Jorge-Nuno Silva,
*Berkeley problems in mathematics*. - George Polya and Jeremy Kilpatrick,
*Stanford mathematics problem book*. - Goerge Polya and Gabor Szego,
*Problems and theorems in analysis*, volumes 1 and 2. - Arthur Engel,
*Problem-solving strategies*. - Terence Tao,
*Solving mathematical problems*. - Valentin Boju and Louis Funar,
*The math problems notebook*. - Masayoshi Hata,
*Problems and solutions in real analysis*.

- K. A. Ericsson, N. Charness, P. J. Feltovich, and R. R. Hoffman,
*The Cambridge handbook of expertise and expert performance* - K. Anders Ericsson and Neil Charness, "Expert performance: its structure and acquisition," pdf.
- William Chase and Herbert Simon, "Perception in chess," pdf.
- Michelene T . H. Chi, Paul J. Feltovich, and Robert Glaser, "Categorization and representation of physics problems by experts and novices," pdf.

- John Anderson,
*Rules of the mind* - Mark Singley and John Anderson,
*The transfer of cognitive skill,*excerpt: pdf. - John Anderson and Kenneth Koedinger, "Reifying implicit planning in geometry: guidelines for model-based intelligent tutoring system design"
- Vincent Aleven, Kenneth Koedinger, and Karen Cross, "Tutoring answer explanation fosters learning with understanding"
- Robert Siegler and Zhe Chen, "Development of rules and strategies: balancing the old and the new"
- Kenneth Koedinger, "Cognitive tutors: technology bringing learning sciences to the classroom"
- Bethany Rittle-Johnson, Robert Siegler, and Martha Alibali, "Developing conceptual understanding and procedural skill in mathematics: an iterative process," pdf.
- Bethany Rittle-Johnson and Kenneth Koedinger, "Iterating between lessons on concepts and procedures can improve mathematics knowledge"
- John Stamper and Kenneth Koedinger, "Human-machine student model discovery and improvement using data"
- Alan Schoenfeld, editor,
*Cognitive science and mathematics education*. - Keith Devlin, "What is conceptual understanding?" html.
- Martina Rau et al., "Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions," pdf.
- Martina Rau et al., "Sense making alone doesn't do it: fluency matters too! ITS support for robust learning with multiple representations," pdf.
- Jo Boaler, "The role of contexts in the mathematics classroom: do they make mathematics more 'real'?", pdf.
- Jennifer Kaminski et al, "The advantage of abstract examples in learning math," pdf.
- Guershon Harel and James Kaput, "The role of conceptual entities and their symbols in building advanced mathematical concepts"
- Guershon Harel, Evan Fuller, and Jeffrey M. Rabin, "Attention to meaning by algebra teachers"

- D. Gentner, K. J. Holyoak, and B. N. Kokinov,
*The analogical mind: Perspectives from cognitive science*. - D. Gentner and C. Toupin, "Systematicity and surface similarity in the development of analogy."
- K. J. Holyoak, and P. Thagard, "Analogical mapping by constraint satisfaction."

- David Marr,
*Vision*(excerpts), pdf. - Tomaso Poggio, "The levels of understanding framework, revisited," pdf.
- David Danks, "Computational realism, levels, and constraints" (a draft of a book chapter), pdf.

- David Marr,
*Vision*. - Gerard Allwein and Jon Barwise,
*Logical reasoning with diagrams* - Janice Glasgow, N. Hari Narayanan, and B. Chandrasekaran,
*Diagrammatic reasoning: cognitive and computational perspectives* - Jill Larkin and Herbert Simon, "Why a diagram is (sometimes) worth ten thousand words," pdf.
- Marcus Giaquinto,
*Visual thinking in mathematics: an epistemological study*, Chapter 4, Chapter 5, Chapter 6, Chapter 8, Chapter 12. - Jeremy Avigad, review of Giaquinto's book
- Marcus Giaquinto, "Visualizing in mathematics"
- Marcus Giaquinto, "Cognition of struture"
- Paolo Mancosu, "Visualization in logic and mathematics," pdf
- Ken Manders, "The Euclidean diagram"
- John Mumma, "Proofs, pictures and Euclid," pdf.
- John Mumma, "The role of geometric content in Euclid's diagrammatic reasoning", pdf.
- Jeremy Avigad, Edward Dean, and John Mumma, "A formal system for Euclid's
*Elements*," pdf. - John Anderson and Ken Koedinger, "Abstract planning and perceptual chunks: Elements of expertise in geometry." pdf.

- Philip Kitcher,
*The nature of mathematical knowledge* - Ken Manders, "Euclid or Descartes: representation and responsiveness"
- Jeremy Avigad, "Methodology and metaphysics in the development of Dedekind's theory of ideals," pdf.
- Andrew Arana and Paolo Mancosu, "On the relationship between plane and solid geometry," pdf.
- Jeremy Avigad and Rebecca Morris, "Character and object," pdf.

- Mohan Ganesalingam, "The language of mathematics," html.
- Andrei Paskevich, "The syntax and semantics of the ForTheL language," pdf.
- The Naproche project, html.
- Jeremy Avigad, "Mathematical type inference"

- Mark Wilson, "The unreasonable uncooperativeness of mathematics in the natural sciences"
- Chris Pincock, "Towards a philosophy of applied mathematics"
- Robert Batterman,
*The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence*.

- John Harrison,
*Handbook of practical logic and automated reasoning.* - J. Alan Robinson and Andrei Voronkov, editors,
*Handbook of automated reasoning*, volumes 1 and 2.