Reason and Incomplete Paradigms

Mathematicians may exercise reason to produce incorrect answers, or to add non-rational elements onto rational, though incomplete works. Reason does not necessarily arrive at a decisive conclusion in mathematics at least. In some cases the complexity may be a challenge that is not immediately resolvable. Consider the mathematics prizes that were left unsolved before AI calculated a correct answer recently. Mathematicians of the 19th century at some point were said to dislike infinities; and Gregory Cantor developed the paradigm of trans-finite numbers and sets and was repressed from academia and driven to become a monastic. Reason does not invariably cohere with a majority, and reason may be partial rather than complete to anyone at times with the exception of God.