To me the most baffling thing about differential equations is the fact that somehow the Universe is able to solve them in real time. I mean, of course there are

To me the most baffling thing about differential equations is the fact that somehow the Universe is able to solve them in real time. I mean, of course there are PDEs like the Navier-Stokes equation that describe phenomena emerging from the simple interactions of an immense number of particles, so you could say that the Universe doesn’t “solve” them per se, rather, it runs the discretized simulation on an extremely fine scale, and the whole continuous PDE is our “simplification” of the problem. However, there are equations like the Einstein field equations that operate on a seemingly continuous domain, and whose solutions are impossibly complex in nontrivial cases… So how does the Universe do it? One can say that this question is beyond what science should be concerned with; the Universe evolves according to these equations, because this is what the Universe is. Yet, from a computational point of view it irks me…