I agree that ZFC was an important and useful step in mathematics — but it fell short of its aims in both ways: - you can’t provide a solid basis for all math (

I agree that ZFC was an important and useful step in mathematics — but it fell short of its aims in both ways: - you can’t provide a solid basis for all math (though, ZFC is useful to prove that) - you can’t use it to produce papers of increased assurance, eg to remove the issues that had arisen with contrary calculus proofs Category theory was intended to solve a shortcoming of ZFC: the lack of tools to reason about “large” similarity and classes — such as algebra and geometry being the same topic. Category theory formalized those notions.