The axiom of choice might be the most contested axiom in the list of foundational principles of mathematics, with advocates and opponents engaging in fierce philosophical debates.
Some regard it as obviously true while others cannot be convinced by any argument whatsoever because they know counterexamples.
How can there be so much discussion about—in mathematics, which is supposed to be neutral and objective, where every question should be settled by a computation or proof?
In the talk we will:
- Learn what the axiom of choice asserts.
- Understand why it is useful.
- Embrace the danger of adopting the axiom of choice.
- Enjoy how the axiom of choice can be safely simulated in a universe called "Gödel's sandbox".
- Touch on axioms which are less-contested but actually more severe.
Here is a list of more sessions by our group. There also the slides will be published.
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