Cryptocurrency smart contracts provide a framework by which people can bet on the solution to mathematics or computational problems. A cryptocurrency smart contract is a piece of software used on a cryptocurrency which can be used to transfer funds if the conditions of the contract are satisfied. For example, one can make a contract that says “Gil Kalai will give Andrew Booker 20 coins if Andrew can find integers $x,y,z$ where $x^{3}+y^{3}+z^{3}=33$” (no Gil and Andrew never made this contract). Cryptocurrency smart contracts are also able to issue their own tokens and these tokens could have a value on the free market in the same way that national currencies, Bitcoin, or baseball cards have value. For example, a smart contract can be used to issue tradable tokens to the entities that find solutions to the equation $x^{3}+y^{3}+z^{3}=n$.

Since cryptocurrency smart contracts are able to issue their own tokens, these tokens can be used as a reward for proving theorems or solving computational problems in mathematics and these tokens can provide an alternate source of funding for mathematical research especially for set theory.

Smart contracts can also be used to bet on things that happen on the blockchain, but the winner of the bet can only be determined based on information on the blockchain. However, if there is a reward for solving a problem or doing a mathematical computation on the blockchain, then the solver of that mathematics problem is more likely to post the solution on the blockchain and therefore the bet can successfully be carried out on the blockchain.

Of course, cryptocurrency smart contracts have their limitations since they are slow, inefficient, and since it is a pain to completely formalize a proof of a result and post that proof on a blockchain. In the near future, I therefore see cryptocurrency smart contracts being used to bet on computational problems in mathematics rather than on theorems that require proofs since it will be a pain to completely formalize a proof and post it on the blockchain.

Cryptocurrency smart contracts are very new since the main cryptocurrency for smart contracts, Ethereum, has only been out since 2015. See this post for relevant discussion along with some issues that may arise when using smart contracts to reward computational mathematics. I have not heard of anyone else discuss using cryptocurrency smart contracts for funding and rewarding the solutions to mathematics problems.

One possible issue with using cryptocurrency smart contracts for betting on results is that it typically takes several years for a new mathematical result to be obtained and posted on the blockchain and nobody wants their coins or tokens stuck in a smart contract for all that time. A remedy for this problem would be for the people placing their bets to bet not on a single problem but instead to be on multiple problems so that the smart contract can be closed as soon as one of those problems has been solved.

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