Is it really the case? Was there a proof of sort that shows mathematical facts are more certain than empirical facts? What are the arguments for and against that claim?
Yes, there is a reason why mathematical facts are more certain for us than empirical facts:
One can prove mathematical theorems.
But nobody could prove general empirical statements, e.g., the laws of nature. In the domain of science, which builds on empirism, we can at best confirm our general hypotheses, but all confirmation does not prevent from finding a counter example at a later time.