> In our world, you cannot patent theorems but people publish them anyway. Why?
You'll never have enough information to know what theorems went unpublished. You can only speak to the probability based on incentives. Public institutions and Universities may be incentivized to publish theorems, but that same incentive doesn't exist in corporations. A valuable money making theorem that could give competitors and advantage would never be published unless a patent could be formed using the technique that circumvents the limitations by including other processes.
Even with the existing patent system, trade secrets still exist: WD-40, Coca-Cola, Twinkies...etc. When it comes to money, the default is to preserve.
You'll never have enough information to know what theorems went unpublished. You can only speak to the probability based on incentives. Public institutions and Universities may be incentivized to publish theorems, but that same incentive doesn't exist in corporations. A valuable money making theorem that could give competitors and advantage would never be published unless a patent could be formed using the technique that circumvents the limitations by including other processes.
Even with the existing patent system, trade secrets still exist: WD-40, Coca-Cola, Twinkies...etc. When it comes to money, the default is to preserve.