The last century saw the breakdown of the dream of the mechanical universe where it was imagined that given sufficient intellect and effort all truths could be discovered and known. Gödel’s Incompleteness Theorems, which form the basis for the concept of Undecidability, revealed that there exist true statements that cannot be proven to be true. This undeniably shook the Mathematical Worldview, but was this Worldview shaken enough? When deduction is not possible, inductive inference can serve in its stead and form a different kind of base. What progress could be made in Mathematics if uncertainty was embraced and inductive inference employed to its maximum potential? Perhaps Mathematics should have been sufficiently stirred to follow the lead of the Physical Sciences and learn to embrace uncertainty when necessary.
Kevin H Knuth