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However, there is also the pitfall - the power can only be wielded on problems which can be described in the language of that mathematical field. Here is where it's useful to have and understand multiple fields of mathematics - if you can't easily describe your problem in the language of one field, perhaps there is another field which has a language in which it is easier to describe your problem.

@chexxor The other hotness is Type Theory and HOTT in particular.

chexxor@chexxor@functional.cafeSo it becomes useful to study the truths which hold across all fields of mathematics. This requires defining a language in which you can re-define any and all other mathematical fields. I think this is what is called a "univalent foundations of mathematics". For a long time people thought set theory was that thing, but it's always felt like "a hack" to use the language of set theory as such a foundation, because it feels too concrete, too much based on counting.