like Paul i think once you introduce the question what into the mathematical process you are doing applied math.
if i were to offer an answer to the what question for ***"1 + 1 = 2" is a certain solution to a mathematical problem, I can ask you: one and one what?*** the answer i'd give in order to keep the discussion out of the applied math realm would be 'what ever'.
i think if you want to delve into uncertainty and the human condition with respect to it you would need to get into probability and statistical math. but then it seems we are forced to ask the question when and how is it that a solution to a mathematical problem requires the application of statistics or probability. again we are talking applied math here. i believe if we stay out of the applied use of math and remain in purely mathematical process's we would see that probability and statistics can converge into 'certain' solutions.
or would it be the other way around? i don't really know, probably Paul would know.
regards, tim