Topics will include Kurt Gödel's celebrated incompleteness theorems, the technical ideas and methods involved in proving them, their relation to the abstract theory of computation, and their philosophical implications. Are there mathematical truths that cannot be known? Are mathematical concepts such as number and set indeterminate to some extent? Are there limits to what can be modeled formally?
Topics will include Kurt Gödel's celebrated incompleteness theorems, the technical ideas and methods involved in proving them, their relation to the abstract theory of computation, and their philosophical implications. Are there mathematical truths that cannot be known? Are mathematical concepts such as number and set indeterminate to some extent? Are there limits to what can be modeled formally?
