I recently learned that the physical world is also undecidable. For example, the spectral gap problem in quantum mechanics is one such problem. Scientists have proven that no matter how perfectly and completely we can mathematically describe a material on the microscopic level, we're never going to be able to predict its macroscopic behavior.

This has profound implications, such as for the possibility of a theory of everything. This does not necessarily mean that a theory of everything is impossible, but it does indicate that such a theory might not be able to provide a complete description or prediction of all physical phenomena, which is contrary to the belief of some physicists.