proofs

P=NP means you can get computers to write their own math proofs.

Who here got into programming out of a passion for translating formal functional specifications into formal proofs?

Then building proofs of concepts and outlines; then, applying a bunch of troubleshooting principles; repeat until problem is solved.

It contains proofs of very many results from elementary number theory, like Fermat's Little Theorem here.

Your point could even be extended by saying that there are proofs for a paraconsistent ZF with a universal set.

Takes a lot more than proofs, code reviews, or tests in isolation to begin to make a strong security argument.

The reason this book is different from any other is because the proofs are all combinatorial, like counting beaded necklaces or otherwise.

Many of the programming problems required knowledge of major math theorems and proofs.

We include the necessary code to run J-Bob in ACL2 and Scheme, as well as a transcript of the proofs in the book.

> P=NP means you can get computers to write their own math proofs.

At least this much was shown in original post; All proofs Goedel's theorem rely on the ability of a very particular language to be self-describing.

As if we have proofs that humans won't do such a thing?

And this is where Anatoly's false distinction between "syntactic" and "semanitc" proofs breaks down.

I get that you can discuss proofs with no notion of "true" or "false", but how do you discuss completeness without them?