We don’t hear much about logical positivism now but it was very fashionable in the early twentieth century:
Born in Austria–Hungary, Gödel (1906–1978) could not adjust to the presumption of atheism fashionable there in his day: “Despite his brilliance, Gödel never felt that he fit in with the Vienna Circle, since his theistic beliefs clashed with the popular ideas of logical positivism, which argued that the only real knowledge is that which can be demonstrated empirically. In 1931, he published what is known as Gödel’s incompleteness theorems.” – Aimee Lamoureux, “Despite Being A Renowned Mathematician, Kurt Gödel Starved Himself Out Of Paranoia” All That’s Interesting, July 11, 2018
Gödel’s incompleteness theorems (“among the most important results in modern logic” according to the Stanford Encyclopedia of Philosophy) showed that “we cannot devise a closed set of axioms from which all the events of the external world can be deduced.” Logical positivism never really recovered from the blow Gödel dealt it. Atheism had to be established on some other ground.
News, “How Kurt Gödel destroyed a popular form of atheism” at Mind Matters News
Gödel also wrote a proof of the existence of God, based on Anselm’s work’ It was not published until after his death.
More scandalous still, Gödel was not a Darwinist: “I believe that mechanism in biology is a prejudice of our time which will be disproved.”
Gregory Chaitin and Robert J. Marks discuss Gödel in more detail:
Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”
and
Gregory Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. Chaitin discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.