Apparently so. See: “This is Math’s Fatal Flaw” (Veritasium, 33:59 min), May 22, 2021
Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.
Indeed. That was the remarkable insight of Kurt Gödel (1906–1978), which destroyed formerly triumphant positivist philosophy.
When you get to the bottom of the universe (if you do), it’s mostly questions, not answers.
Hat tip: Philip Cunningham