Especially for someone knowledgeable about things like the Riemann hypothesis.To be fair to Cuch there is no substitute for an undergrad maths degree. Not physics, or electrical engineering or economics or, lord help us, finance.
(But the friend of a friend osmosis thing was rather weak!)
I think it is more nuanced.I'm struggling to imagine physicists thinking about mathematics, because most of those I've met didn't know it.
IMHO, HHC is just a crude approximation, while negative probabilities are simply an erroneously used name for signed measures or Wigner function (which is a quasi-probability). Another depressing (with its prevalence) curiosity is - assuming that we've lost the battle for the "quasi" prefix - claiming that the negative probability (negative values of the Wigner function) indicates quantum behaviour of a system. In fact, there are multum of examples of quantum systems which have non-negative everywhere Wigner functions and classical systems with negative Wigner functions in student textbooks). Who cares, though - nowadays scientists need to produce a lot of buzz and Nature publications, and not something actually useful.Here's a question on how to overcome the contradiction and incompatibility between Fourier's equation (Fick's Law) and the theory of relativity (in the latter case speed of heat propagation is infinite while in the latter case nothing is faster than light).
A fix for this conundrum is to stick a 2nd order time derivative to Fourier PDE and hey presto resulting in the Hyperbolic Heat Conduction (HHC) equation, a bit like the telegrapher's equation. But we need to introduce the second sound into the PDE.
IMO it is the same tale as with negative probabilities.
1. This is not the mathematical approach ... too many assumptions (in fact, it violates the 2nd law of thermodynamics).
2. Second sound is fiction (it has no physical reality)
3. HHC is a weak description of relativity but it is still Newtonian.
4. You can't just stick bits and pieces to a PDE and hope it will work. (disclaimer: I did QM/SR/GR at undergrad but I don't remember 1/2 of it)
At which step in inventing HHC did it go wrong? What is the major (implicit) assumption here?