> I think that when the singularity occurs all of the problems in physics will solve, like in a vacuum, and physics will advance centuries if not millennia in a few pico-seconds

It doesn't matter how smart you are, you still need to run experiments to do physics. Experiments take nontrivial amounts of time to both run and set up (you can't tunnel a new CERN in picoseconds, again no matter how smart you are). Similarly, the speed of light (= the speed limit of information) and thermodynamics place fundamental limits on computation; I don't think there's any reason at all to believe that intelligence is unbounded.

Kind of, I mean you have to verify things experimentally but thought can go a very long way, no? And we're not talking about humans thinking about things, we're talking about an agent with internet access existing in a digital space, so what experiments it would do within that space are hard for us to imagine. Of course my post isn't meant to be taken seriously, it's more of a fun sci-fi idea. Also I'm implying not necessarily reaching the limits of the things you mentioned, but rather, just taking a massive step in a very short time window. Like, the time window from the discovery of fire to the discoveries of Quantum Mechanics but in a flash.