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Comment by krunck | Hacker News Reader

The section header "Theorem mining — better than crypto?" makes me wonder: instead of POW based cryptocurrencies, could we use POT(Proof of Theorem)? Machines could grind away looking for theorems. It's still a POW method, but it provides some potentially useful output.

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This wouldn't work because all theorems are trivially extensible. Either by adding extra theorems via conjunction, e.g. my new theorem C = previously-mined theorems {A} ∪ {B}; or by adding garbage to the end, e.g my new theorem C = {A} ∪ {...arbitrary nonsense that cancels out}, e.g. (+ 0 + 0 + 0), or (- 1 + 1 - 1 + 1), or vastly more complex formulations.

Logic isn't the study of merely finding out what's true, but what's true and interesting.

It's only useful if the theorems proven are interesting. Maybe there could be a cryptocurrency for mathematicians where you post theorem statements and put money in them. First one to find a proof gets whatever money was in the theorem.

The way blockchain works is that you generate a problem based on the contents of the block. If the proof you find is in no way related to a block it cannot be a cryptocurrency.

You could make a system to reward people for finding proofs, but it would be more of a Bounty system or a Leaderboard than a cryptocurrency. Indeed people do put up prizes for those kind of things today.

Most useful proof-of-work yet...

However, it is somewhat hard to mathematically define all criteria used to recognize *useful* theorem.

There may be many propositions that are true, but cause no excitement among mathematicians.

You have to know in advance about how long it will take to mine the next block. Is it possible to do it here? Probably not.

Proof of... proof?

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