Uncertainty of truth of mathematical proofs

According to the article Mathematical proofs getting harder to verify, it is now very difficult and sometimes impossible to be certain about the correctness of mathematical proofs.

I can envision the rise of the special profession of mathematical patching. It would work as follows.

  1. A fundamental theorem is proved, but its proof is difficult to verify.
  2. A lot of mathematics is being based upon that theorem.
  3. Another fundamental theorem is proven and receives similar honorable status in mathematics.
  4. A contradiction is found, which means that both theorems cannot be both true.
  5. In order to save the rest of mathematics, the theorems are patched.

Patching, in this context, means adding qualifications to the theorems, so that fully-qualified versions of the theorems do not contradict each other. The qualifications will be based upon the actual way the theorems are used in subsequent mathematical development, which is normally less than the full generality of the theorem.

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