Davis and Kline both wrote as mathematical insiders—as members of the club, albeit iconoclastic ones. In contrast, John Horgan positioned himself as a defiant outsider when he wrote a Scientific Americanessay titled "The Death of Proof" in 1993. "The doubts riddling modern human thought have finally infected mathematics," he said. "Mathematicians may at last be forced to accept what many scientists and philosophers already have admitted: their assertions are, at best, only provisionally true, true until proved false."
…In the 17th century, when algebraic methods began intruding into geometry, the heirs of the Euclidean tradition cried foul. (Hobbes was one of them.) At the end of the 19th century, when David Hilbert introduced nonconstructive proofs—saying, in effect, "I know x exists, but I can't tell you where to look for it"—there was another
rebellion. Said one critic: "This is not mathematics. This is theology."
Richard Feynman reportedly commented regarding proof, "A great deal more is known than has been proved."
To return to a discussion from a few days ago, I wonder what modern day fans of evidentialism will make of these statements. Recall Annie Besant’s argument in Why I Do Not Believe in G-d - "It is not for me to prove that no such beings exist before my non-belief is justified, but for him to prove that they do exist before my belief can be fairly claimed." (emphasis mine) It is wonderful to speak in such rhetorical platitudes of rationalism about adherence to proof as the sole basis for knowledge, but the practical reality is that not just theology, but even "pure" sciences like math and physics cannot meet such a standard.