Well, math is certainly a language.
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If 1*1=1 is not mathematically provable to us, then that would be a problem with the system of math we've designed it seems
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Not *necessarily*, from the simple fact that just because a formal system cannot formally prove something does not mean that it is untrue. This is just a limitation of any formally defined system.
I'm not sure of the details of a 1x1 = 1 proof, but under the assumption that it cannot be proved (likely not the case), it's an example of something that is self evidently true that cannot be proved within the formal system of mathematics.
As many of you have shown through simple logic, it is not hard to see that 1x1 = 1 is true. Because of the axiomatic structure of mathematics however, that doesn't necessarily mean it's easy to prove.
This isn't surprising. It's a problem of regression; the system will always be incomplete because you're never going to have all of the axioms, thus leaving some portion of the formal system unprovable. However, thankfully axioms are, generally, obviously true, so I don't think we have a real problem here.