Tao seems to be ignoring the common possibility that post-rgorous mathematical analysis makes mistakes, including proofs of (later realized to be) false statements.
The tick-tock analogy of a poster here makes more sense: rigor informs intuition, decreasing likelihood of error, and intuition generates hypotheses to be verified with rigor. But mathematicians I know don't think in intuition that can be perfectly converted into rigor.
The tick-tock analogy of a poster here makes more sense: rigor informs intuition, decreasing likelihood of error, and intuition generates hypotheses to be verified with rigor. But mathematicians I know don't think in intuition that can be perfectly converted into rigor.