I don't know that they are orthogonal, one follows from the other. Here's the logic as I see it:

  1. A proof is a program.
  2. A mentally validated proof is a mentally validated program.
  3. Mental validation is insufficient to verify programs are correct.
  4. Therefore mental validation is insufficient to verify proofs are correct.

There's all kinds of work in formal methods for creating provably correct programs. It seems like you are calling for the converse: computer verifiable proofs.

I'n not sure how you'd do this, but I think you'd need to have some notational system that encompasses all of mathematics to start. Where are Russell and Whitehead when you need them? :)

Automated verification of proofs is such a good idea that it looks like people are working on this now.

Your argument for automated verification of proofs is persuasive. Thanks for bringing the idea up, it has provided me with some interesting things to think about while procrastinating.


TGI says moo

In reply to Re^4: OT: Mathematics for programming (again) by TGI
in thread OT: Mathematics for programming (again) by vrk

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