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In this course, we will learn about a number of key topics in the philosophy of mathematics. In the first half we will look at classic topics in the philosophy of mathematics. We will ensure students are familiar with the main views such as platonism, nominalism, logicism, formalism, intuitionism, and structuralism, as well as the main criticisms of each. Students will learn about the philosophical significance of Russell’s paradox and Gödel’s incompleteness theorems. In the second half of the course, we will consider topics in the philosophy of mathematical practice, such as the nature of mathematical proofs, the use of diagrams in mathematical reasoning, explanation and understanding in mathematics, mathematical knowledge, computers and AI in mathematics, and the ethics of mathematics.