**December 7**

- Giaquinto,
*Visual thinking in mathematics: an epistemological study*, Chapter 8, Chapter 12. - Larkin and Simon, "Why a diagram is (sometimes) worth ten thousand words," pdf.
- Mancosu, "Visualization in logic and mathematics," pdf

**November 30**

This week, we'll have a brief discussion of Wickelgren, and then move on to talk about Euclidean diagrammatic reasoning. Read any of the following:

- Mumma, "Proofs, pictures and Euclid," pdf.
- Mumma, "The role of geometric content in Euclid's diagrammatic reasoning", pdf.
- Avigad, Dean, and Mumma, "A formal system for Euclid's
*Elements*," pdf.

**November 16**

This week, we'll finish the discussion of Schoenfeld, and start discussing Wickelgren's take on problem solving: pdf, pdf, pdf

**November 9**

This week we will finish up the discussion of Polya; specifically, we'll talk about the excerpt from *Patterns of plausible inference* (volume II of *Mathematics and plausible reasoning*).

After that, we will start discussing Schoenfeld, *Mathematical problem solving,* pdf.

**November 2**

This week will be devoted to the Polya, and the readings below.

**October 26**

This week will discuss Arana's paper, and then move on to Polya.

- Polya,
*How to solve it*, Part I: pdf. - Polya,
*Mathematics and plausible reasoning*, excerpts from volume I: pdf. - Polya,
*Mathematics and plausible reasoning*, excerpts from volume II: pdf.

**October 19**

This week is something of an interlude: we will discuss the draft of

- Avigad and Morris, "Character and object," arxiv.

The week after, we will finish up the discussion of explanation (including Arana's paper), and move on to problem solving. The latter will eventually include Polya, Schoenfeld, and Wickelgren, in particular.

**October 12**

We will continue with mathematical explanation and proof:

- Sandborg,
*Explanation in mathematical practice*Chapter 4: (and title page) pdf, Chapter 5: pdf. - Avigad, "Mathematical method and proof," pdf.
- Arana, "Logical and semantic purity," pdf.

If you are interested in Pick's theorem, see also John Harrison's "A formal proof of Pick's theorem," on the bibliography.

Solomon Feferman's "The logic of mathematical discovery vs. the logical structure of mathematics," a critique of Lakatos' *Proofs and Refutations*, is also worth reading.

**October 5**

This week, we will discuss and the paper by Tappenden, and then move on to explanation:

- Tappenden, "Mathematical concepts and definitions," pdf.
- Mancosu, "Mathematical explanation: why it matters," pdf.
- Steiner, "Mathematical explanation," pdf.

**September 28**

This week, we will finish the discussion of Wilson, and discuss Husserl.

- Husserl,
*The philosophy of arithmetic*, excerpt: pdf. - In case it may be helpful, here is my review of a book by Marcus Giaquinto, which tries to tease apart normative and psychological issues: pdf.

**September 21**

Read at least one of these papers by Mark Wilson:

- "Frege's mathematical setting," pdf.
- "Enlarging one's stall, or how did all these
*sets*get in here?" pdf.

Finally, look at the following study in mathematics education:

- Bethany Rittle-Johnson, Robert Siegler, and Martha Alibali, "Developing conceptual understanding and procedural skill in mathematics: an iterative process," pdf.

**September 14**

- Read Jackendoff's "What is a concept, that a person might grasp it?" pdf.

Frege on sense and reference (choose readings from among these as you wish):

- "Sense and reference," pdf, and "Comments on sense and reference," pdf.
- "Letter to Husserl," pdf.
- "Thought," pdf.

**September 7**

- Read the introdution to the second edition of the
*Critique of pure reason*for an overview of Kant's project. pdf. - Read the characterization of mathematical cognition in "The discipline of pure reason in dogmatic use," focusing on pages 630-636. pdf.
- Take a look at his account of the schemata, focusing on pages 273-274. pdf.
- Read chapter 2 of Friedman's
*Kant and the exact sciences*(chapter 1 is optional). pdf.

**August 31**

- Take a look at Avigad, "Understanding, formal verification, and the philosophy of mathematics," pdf, for a framing of the issues.
- Let me know if you would like to be on the seminar e-mail list.