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Joke aside, is there a field (or sub-fields) of mathematics that just... studies what breaking some axioms would do and where would it lead? This seems both com
by Ragnarork 1y ago
Joke aside, is there a field (or sub-fields) of mathematics that just... studies what breaking some axioms would do and where would it lead? This seems both completely stupid but also potentially fascinating at the same time.
- debo_ 1y agoThe mathematics equivalent of the any% speedrun community?
- mafuy 1y agoYes. Prominent example is the axiom of choice. There was a LOT of discussion about it by mathematicians. https://plato.stanford.edu/entries/axiom-choice/ https://plato.stanford.edu/entries/axiom-choice/ For instance, with it, you can double the volume of a body by looking at it from a weird angle.
- SetTheorist 1y agoThat's a very misleading description of Banach-Tarski. You need to break up the body into a few (very weird) pieces and maneuver them (via only rigid motions - rotations and translations).
- SetTheorist 1y agoParaconsistent logic looks into logical systems that allow contradictions. A lot of set-theory research is looking into the consequences of various axiomatic assumptions.
- monkeyelite 1y agoIt’s not sub-field. It’s a technique. You relax or change axioms defining your thing and see what happens.