Its a pretty poor philosophical premise. Math by its nature is reliable mainly from its abstract nature. For it to become unreliable would require upheavals in reality. If you pick up one of something and put it in an empty box and pick up one more and put it in and the box contains anything but two then we have lost object permanence. As for instruments they have had issues with reliability and improvements or new instruments are made. Im not even talking about technical things but the metric system originally relied on some model artifacts kept in France but it was recognized that even the stable platinum–iridium it was made of does degrade over long periods and the SI standard that evolved from it measures everything utilizing the fundamental constants of nature and if this proved unreliable (and to be clear they moved to SI when seeing the difference in the model artifact took our most sensitive instruments) then it would again change. Science is not a religion and it will change based on any more accurate methods or information that it gets.