At the beginning of Chapter 4 of his book Complex Analysis, Ahlfors writes "it is only quite recently that it became possible to prove, without resorting to complex integration or equivalent tools, that the derivative of an analytic function is continuous, or that the higher derivatives exist". I would be grateful for references to the quite recent (in 1966) "integration-free" proofs that Ahlfors is alluding to.
2026-04-01 07:15:27.1775027727
Developing the theory of analytic functions without integration
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I don't know why google failed me before I posted this question, but it's found a relevant reference now. See https://mathoverflow.net/questions/63205/is-there-an-integration-free-proof-or-heuristic-that-once-differentiable-impli