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.

Author: Omer Zak

I am deaf since birth. I played with big computers which eat punched cards and spew out printouts since age 12. Ever since they became available, I work and play with desktop size computers which eat keyboard keypresses and spew out display pixels. Among other things, I developed software which helped the deaf in Israel use the telephone network, by means of home computers equipped with modems. Several years later, I developed Hebrew localizations for some cellular phones, which helped the deaf in Israel utilize the cellular phone networks. I am interested in entrepreneurship, Science Fiction and making the world more accessible to people with disabilities.