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1. Introduction : the mathematical image
2. Platonism
3. Picture-proofs and Platonism
4. What is applied mathematics?
5. Hilbert and Gödel
6. Knots and notation
7. What is a definition?
8. Constructive approaches
9. Proofs, pictures and procedures in Wittgenstein
10. Computation, proof and conjecture
11. How to refute the continuum hypothesis
12. Calling the bluff.

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