👉 Fallen math refers to the set of axioms and logical principles that underpin much of modern mathematics, particularly set theory and Zermelo-Fraenkel (ZF) axioms, which are foundational to the structure of mathematics. These axioms, introduced by Ernst Zermelo and Abraham Fraenkel, aim to provide a rigorous framework for mathematical reasoning. However, they have limitations: they cannot prove the existence of certain mathematical objects (like non-measurable sets) and rely on assumptions that some mathematicians find philosophically problematic, such as the Axiom of Choice. This leads to alternative foundations like Intuitionistic mathematics, which rejects the law of excluded middle, or constructive mathematics, where proofs must be explicitly constructive. These limitations highlight the ongoing debate about the nature of mathematical truth and the foundations of mathematics, questioning whether our current axiomatic systems fully capture the essence of mathematical reality.
