anonymous question
How did fundamental scientific research work before the emergence of state academies of sciences? There were two main mechanisms.
First. A scientist conducted their research independently and at their own expense, satisfying their own private interest.
Second. A scientist found a patron, usually some aristocrat, and conducted research at the patron’s expense, while simultaneously fulfilling their minor whims and contributing to the increase of the patron’s prestige.
What are the contraindications to using these mechanisms even after the state withers away? Effectively, only one. It is claimed that quite many fundamental scientific projects are too expensive to implement for a single patron to be able to afford. Well, since the time of pre-state science, financial institutions have made good progress, so funds with billion-dollar budgets are by no means an exotic rarity now.
The question of motivation remains. What would prompt a potential sponsor of fundamental science to invest in a particular fund? Exactly the same considerations apply here as in patronage or philanthropy: the sponsor satisfies their sense of self-importance and gets good PR. Accordingly, for money to flow into fundamental science, it needs good marketing: stroking the egos of sponsors, vividly highlighting the results obtained and the breathtaking prospects. This is, of course, very soulless, but far fairer than the current model, where money is forcibly collected into a black box, and the report on results is given in the most tedious form possible, understandable only to narrow specialists, but not to those who pay.
Yes, it may happen that a stateless society will not fund certain fundamental mega-projects, and the Large Hadron Collider will never be built. Well, so be it; on the other hand, thousands of small projects will receive funding that would not have been allocated under a state because of it.

Of course, fundamental science will always compete for donations with art, sports, Mashinka’s nonsense, and Ancap-chan (donate here: 1A7Wu2enQNRETLXDNpQEufcbJybtM1VHZ8) – but this is a normal market process. I, too, would like to work on making donating to the channel prestigious.