Why Math’s Final Axiom Proved So Controversial | Quanta Magazine
Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.
How do mathematicians decide that something is true? They write a proof. Often they start with proofs that already exist, building on or drawing connections between proven claims. Each of these proofs, in turn, has relied on other proofs to make its point, and so on. Proofs upon proofs. Truths upon truths. But eventually this process must come to an end. At some point, things are true simply because they are. These truths are the axioms, the ground rules. And it is tempting to stop there — to declare, as Penelope Maddy, a philosopher of mathematics at the University of California, Irvine,…
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