satt:

For example, I can think of a situation where psychologists & psychometricians have missed a similar phenomenon: negatively correlated cognitive tests. I know of a couple of examples which I found only because the mathematician Warren D. Smith describes them in his paper "Mathematical definition of 'intelligence' (and consequences)".

That's an extremely interesting reference, thanks for the link! This is exactly the kind of approach that this area desperately needs: no-nonsense scrutiny by someone with a strong math background and without an ideological agenda.

David Hilbert allegedly once quipped that physics is too important to be left to physicists; the way things are, it seems to me that psychometrics should definitely not be left to psychologists. That they haven't immediately rushed to explore further these findings by Smith is an extremely damning fact about the intellectual standards in the field.

Duckworth & Seligman discovered that in a sample of 164 schoolchildren, a composite measure of self-discipline predicted GPA significantly better than IQ, and self-discipline didn't correlate significantly with IQ. Does self-discipline now count as an independent intellectual ability?

Wouldn't this closely correspond to the Big Five "conscientiousness" trait? (Which the paper apparently doesn't mention at all?!) From what I've seen, even among the biggest fans of IQ, it is generally recognized that conscientiousness is at least similarly important as general intelligence in predicting success and performance.