3 ms·
Not a mathematician. Afaik category theory is more like an alternative to set theory. Langlands is more like a bridge between higher level mathematics, allowi
by moi2388 2y ago
Not a mathematician.
Afaik category theory is more like an alternative to set theory.
Langlands is more like a bridge between higher level mathematics, allowing you to transform hard problems in geometry to harmonic analysis and vice versa, and so far specifically these fields only.
- auntienomen 2y agoYeah, category theory is a framework for describing mathematical structure. It's not vacuous -- there are mathematical structures which don't fit into the framework and there are some theorems about what properties a category has. But category theory doesn't do that much on its own. The geometric Langlands conjectures are a _lot_ more specific, and a lot more focused. They're a big deal, because they're a toy model for the arithmetic Langlands conjectures, which are a generalization of the machinery that proved Fermat's Last Theorem and would give an effective method for dealing with a lot of number theory problems.