It's pretty strange: it seems that the person writing should be quite advanced in physics and mathematics (though I am not able to comment on her actual scienti

It's pretty strange: it seems that the person writing should be quite advanced in physics and mathematics (though I am not able to comment on her actual scientific merit), but it clearly misses very important and well-known facts. For example, the fact that it is not true that any differential equation has uniqueness of solutions given its boundary conditions (there are very simple example, which are usually covered in any introductory class not more than half an hour after the concept of differential equation has been introduced, see for example https://math.stackexchange.com/a/1319537/59728 https://math.stackexchange.com/a/1319537/59728). In reality, the proof of uniqueness of solutions is usually a very difficult for every new class of equations being introduced, if it is true at all. There is no general result. Also, it seems to me a completely non trivial point that the physics is actually governed by (a system of) differential equations. The physical laws we currently know are commonly if not always expressed as differential equations, but every physicist is aware that there are a lot of inconsistencies and holes in our current understanding of the universe. Where do we get the assurance that the "ultimate law" is again a differential equation? Maybe we are not finding it just because we expect it to be a differential equation, but it is not, and we first have to revolutionize the way we think physical laws (maybe more or less as we had to do when we realized quantum physics). In short, it seems a rather naive position.