Gabriel,
While I completely applaud this effort, I'll point out that my review of Terry Sejnowski's book applies here.
I think there are self-evident facts (measurements or observations) that constraint different types of experimental and computational approaches. But humans provide such observations that are unique to humans and these provide special glimpses into neuronal computations. Most notably human natural language which rather uniquely allows one neocortex to communicate it own computations to another neocortex. (Did I just give you a headache?) The measurements here which include experimental probing responses and proofs of computational capability of self-evident truths are not wet neuroscience but neuroscience nevertheless. Generally a probe has a scalar value result, perhaps (subject reported) confidence, and response time.
Here are some tests in the self-evident truth realm that any math or computational solutions need to be able to predict. I believe these provide deep insight into some amazingly quick, precise, and complicated neural computations every normal human has in his brain and probably every animal (except the neocortical non-human animals cannot prove it). This isn't just question answering. This is imagination too (with probe, confidence, and response time).
I always believed that computing machines (that I think you call 'simulations') are math just like equations are math. I think the dichotomy between math and computation is a false dichotomy.
All that said, I completely agree that if we can find some fundamentally enlightening ways to employ classical mathematics that physicists use for deduction of unexpected simplifications in measurement prediction, that would be good and amazing. The "geometric" concept is very old but it is nice to see it competing against gradient descent on layered completely connected perceptrons (partial differentials).
