Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), but it's not the issue here (see for example there for this point).

Unfortunately, it is well known that string theory is not appreciated by some of the physics community, because of its alleged non-falsifiability. Nevertheless, here and there, I hear some say that there are some possible indirect experiments...

So, to do justice to string theory, I ask those who can to explain here (for mathematicians) one reason why this theory is non-falsifiable or one experiment that would test it.