While I believe that this is a sensible proposal, I do not believe there will be too much of a market (in the near future) for it for societal reasons. Our current society unfortunately does not have a sufficient appreciation for mathematics and mathematical theorems for this to have much of a market cap. To see why this is the case, we can compare this proposal to the proposal for cryptocurrency mining algorithms that are designed to advance science. I propose that a scientific cryptocurrency mining algorithm should attract a much larger market capitalization than a theorem-proof market, but since scientific cryptocurrencies do not have much of a market, one should not expect for shares of theorems to attract much of a market either.
A market for mathematical conjectures requires participants to not only actively understand the mathematics behind the conjectures, but to also understand these theorems in their complete formalism. Perhaps AI systems may be developed to translate the formalism into English, but such a system may be flawed and may be subject to hacking in the sense that the statement in English may not be exactly the same as the formal statement, and it may be really easy to prove the formal statement. Since such a market requires a substantial amount of effort from the users, it is unlikely that there will be many users who are willing to put in the effort into understanding the mathematics along with the formalism.
It is also likely for the market to favor simple propositions that are easy to understand such as the bounded gaps between primes conjecture. For example, Beal’s conjecture states that there are no positive integers a,b,c,x,y,z with ax+by=cz and x,y,z≥3 and where a,b,c have no common factor. This conjecture was formulated by the billionaire Michael Beal. Beal attached a million dollar prize to this conjecture. This conjecture is a generalization of Fermat’s last theorem. Beal’s conjecture is a reasonably interesting conjecture, but it seems like Beal’s conjecture is the very best mathematics problem that amateur mathematicians can come up with and fund with one’s own money. This means that the market for mathematical theorems will be small and will mainly for theorems that anyone can understand such as the Twin Prime conjecture. It would be more satisfying if the market for mathematical theorems better represents the type of problems and questions that your typical mathematician were interested in.
Cryptocurrency mining algorithms can be used to solve scientific problems, but the users of the cryptocurrency do not even have to care very much about the underlying scientific problem. This is because a cryptocurrency is much more than its mining algorithm, and the details about the mining algorithm are relatively unimportant to the functionality of the cryptocurrency. If chosen correctly, the underlying scientific/mathematical problem does not harm or interfere very much with the cryptocurrency, so there is really no excuse for the cryptocurrency community to waste all those resources on cryptocurrencies on non-scientific problems because the cryptocurrency community does not have to. The cryptocurrency community needs to have a desire to not waste energy along with the philosophy that solving the most important scientific problem is profitable (this would be a self-fulfilling prophecy). The cryptocurrency community should also have a basic awareness of mining algorithms that are designed to solve a scientific problem (they do not need to know the specific details). This basic awareness should be part of the due diligence that every cryptocurrency enthusiast should partake in order to try to maximize profit, so this understanding should be natural for the cryptocurrency sector. Since there is still only one dominant minable cryptocurrency (namely Bitcoin), one only needs one scientific mining algorithm, so the cryptocurrency community does not even need to understand multiple scientific mining algorithms. They just need to know one. It is easier to know about one cryptocurrency mining algorithm than it is to know the market value of many theorems.
Right now Bitcoin has a market capitalization of about 500 billion dollars, and if Bitcoin was set up correctly, it could have had a mining algorithm that was designed to solve a very important scientific problem without the cryptocurrency community even thinking about this. Unfortunately, Bitcoin’s mining algorithm was never designed to advance science, and at this point, the cryptocurrency community is not very interested (due to anti-intellectualism) in using cryptocurrency technologies to solve any scientific problem. The cryptocurrency community to a great extent has no concept or understanding of Bitcoin or what it means for a cryptocurrency mining algorithm to solve a scientific problem. And those who think they understand what it means for a cryptocurrency mining algorithm to be designed to solve a scientific problem are quite antagonistic to cryptocurrency mining being used for any scientific purpose. Since the cryptocurrency community hates using cryptocurrency mining for a scientific purpose so much, one should expect for any market for proofs of theorems to be very small and undeveloped.
Nobody should expect for there to be a sizable theorem/proof market when that requires ~100 times as much effort from users than a market for cryptocurrencies with scientific mining algorithms and when there is no sizable scientific mining algorithm market.
With everything being said, we make a tradeoff with cryptocurrencies with scientific mining algorithms. Cryptocurrency mining algorithms such as SHA-256 must satisfy stringent conditions, so there are limited options in designing a cryptocurrency with a mining algorithm to advance science, and it is hard to fork a cryptocurrency to replace its scientific problem.
I would rather see people work on making scientific cryptocurrency mining more of a reality than imagining a market that is unlikely to exist any time soon because scientific cryptocurrencies are more feasible with the current state of the world.
While I believe that this is a sensible proposal, I do not believe there will be too much of a market (in the near future) for it for societal reasons. Our current society unfortunately does not have a sufficient appreciation for mathematics and mathematical theorems for this to have much of a market cap. To see why this is the case, we can compare this proposal to the proposal for cryptocurrency mining algorithms that are designed to advance science. I propose that a scientific cryptocurrency mining algorithm should attract a much larger market capitalization than a theorem-proof market, but since scientific cryptocurrencies do not have much of a market, one should not expect for shares of theorems to attract much of a market either.
A market for mathematical conjectures requires participants to not only actively understand the mathematics behind the conjectures, but to also understand these theorems in their complete formalism. Perhaps AI systems may be developed to translate the formalism into English, but such a system may be flawed and may be subject to hacking in the sense that the statement in English may not be exactly the same as the formal statement, and it may be really easy to prove the formal statement. Since such a market requires a substantial amount of effort from the users, it is unlikely that there will be many users who are willing to put in the effort into understanding the mathematics along with the formalism.
It is also likely for the market to favor simple propositions that are easy to understand such as the bounded gaps between primes conjecture. For example, Beal’s conjecture states that there are no positive integers a,b,c,x,y,z with ax+by=cz and x,y,z≥3 and where a,b,c have no common factor. This conjecture was formulated by the billionaire Michael Beal. Beal attached a million dollar prize to this conjecture. This conjecture is a generalization of Fermat’s last theorem. Beal’s conjecture is a reasonably interesting conjecture, but it seems like Beal’s conjecture is the very best mathematics problem that amateur mathematicians can come up with and fund with one’s own money. This means that the market for mathematical theorems will be small and will mainly for theorems that anyone can understand such as the Twin Prime conjecture. It would be more satisfying if the market for mathematical theorems better represents the type of problems and questions that your typical mathematician were interested in.
Cryptocurrency mining algorithms can be used to solve scientific problems, but the users of the cryptocurrency do not even have to care very much about the underlying scientific problem. This is because a cryptocurrency is much more than its mining algorithm, and the details about the mining algorithm are relatively unimportant to the functionality of the cryptocurrency. If chosen correctly, the underlying scientific/mathematical problem does not harm or interfere very much with the cryptocurrency, so there is really no excuse for the cryptocurrency community to waste all those resources on cryptocurrencies on non-scientific problems because the cryptocurrency community does not have to. The cryptocurrency community needs to have a desire to not waste energy along with the philosophy that solving the most important scientific problem is profitable (this would be a self-fulfilling prophecy). The cryptocurrency community should also have a basic awareness of mining algorithms that are designed to solve a scientific problem (they do not need to know the specific details). This basic awareness should be part of the due diligence that every cryptocurrency enthusiast should partake in order to try to maximize profit, so this understanding should be natural for the cryptocurrency sector. Since there is still only one dominant minable cryptocurrency (namely Bitcoin), one only needs one scientific mining algorithm, so the cryptocurrency community does not even need to understand multiple scientific mining algorithms. They just need to know one. It is easier to know about one cryptocurrency mining algorithm than it is to know the market value of many theorems.
Right now Bitcoin has a market capitalization of about 500 billion dollars, and if Bitcoin was set up correctly, it could have had a mining algorithm that was designed to solve a very important scientific problem without the cryptocurrency community even thinking about this. Unfortunately, Bitcoin’s mining algorithm was never designed to advance science, and at this point, the cryptocurrency community is not very interested (due to anti-intellectualism) in using cryptocurrency technologies to solve any scientific problem. The cryptocurrency community to a great extent has no concept or understanding of Bitcoin or what it means for a cryptocurrency mining algorithm to solve a scientific problem. And those who think they understand what it means for a cryptocurrency mining algorithm to be designed to solve a scientific problem are quite antagonistic to cryptocurrency mining being used for any scientific purpose. Since the cryptocurrency community hates using cryptocurrency mining for a scientific purpose so much, one should expect for any market for proofs of theorems to be very small and undeveloped.
Nobody should expect for there to be a sizable theorem/proof market when that requires ~100 times as much effort from users than a market for cryptocurrencies with scientific mining algorithms and when there is no sizable scientific mining algorithm market.
With everything being said, we make a tradeoff with cryptocurrencies with scientific mining algorithms. Cryptocurrency mining algorithms such as SHA-256 must satisfy stringent conditions, so there are limited options in designing a cryptocurrency with a mining algorithm to advance science, and it is hard to fork a cryptocurrency to replace its scientific problem.
I would rather see people work on making scientific cryptocurrency mining more of a reality than imagining a market that is unlikely to exist any time soon because scientific cryptocurrencies are more feasible with the current state of the world.