>>11661685In a sense.
The people saying theorems can't be falsifiable are correct, but consider this: all theorems depend on certain assumptions, and the physical world need not conform to those assumptions.
For example, one can prove that the symmetries of non-relativistic spacetime do not change lengths or durations, but we know that length contraction and time dilation are real so that theorem's assumptions have been falsified, but of course the theorem itself isn't wrong.
If you're interested in mathematics in and of itself, not in relation to the physical world, then a theorem can't really be falsified as it has been proven to be true. Conjectures can be falsified, and it is the conjecture that is the appropriate analogue of the scientific theory. A theorem is like a scientific theory that has been supported by direct and powerful evidence; the only way to "falsify" a theorem is to move to a larger class of objects where the theorem no longer holds, or to show that the entire logical system is inconsistent.
