BLS signature aggregation was finalized as an IETF standard in 2019. It's the reason Ethereum can support over a million staking nodes.

BLS was invented back in 2001, but was expensive to verify. A paper published in 2018 showed how to verify n aggregated signatures on the same message m with just 2 pairings instead of n+1.

https://ethresear.ch/t/pragmatic-signature-aggregation-with-...

PoS is an application of what?

to be really pedantic, I'd say PoS is an economic breakthrough rather than heavy-duty computer science, strictly speaking. the actual math of the consensus algorithms seems relatively simple, the challenge is aligning all the incentives so that adversaries in a group of anonymous people have nothing to gain by subverting the rules.

I will gladly give a Turing award to whoever formally proves the safety and liveness of Gasper like Lamport did for Paxos.