Practical intelligence is clearly multidimensional, and there's no reason why someone who scores well on one dimension should also score well on the others.
Any suggestion that talent-for-math = general-intelligence is actually rather dumb. Ditto for assumptions about poor math skills, which can easily be a product of poor teaching rather than unusually low native ability.
If IQ tests measure anything, it's raw mental speed and memory - useful traits, but not nearly enough to draw a bounding box around general intelligence, which also includes abilities such as intuitive modelling, creative originality, and informal inference.
As the cliche goes, smart people can do stupid things in at least some situations.
Raw high IQ is just as likely to get you to wrong conclusions quickly as it is to give you useful predictions. If your modelling skills don't give you a good working model of the situation you're in, you're going to have a bad time.
Outside of core STEM, modelling depends on social and cultural experience and contextual training. If you don't have those, you're going to be handicapped even if you have a stratospheric IQ.
To be fair, this doesn't actually contradict most of the rest of what you say. But this correlation does suggest that there are some shared factors (whether innate, or developed, or both) that affect many or all kinds of "practical intelligence"; one might reasonably call these factors "general intelligence".
>Practical intelligence is clearly multidimensional
I wouldn't call that clear at all! Of course no matter how intelligent a person is, there will be environments in which they do poorly. Feynman would do poorly in the environment called, "Everyone find Feynman and beat him up". But that environment is very contrived, or, more formally, has a high Kolmogorov complexity.
Legg and Hutter argue quite strongly for single-dimensional practical intelligence in this paper (I don't agree with their reasoning, but the point is that it's definitely not blatantly "clear" that practical intelligence is multidimensional): https://arxiv.org/pdf/0712.3329.pdf
Any suggestion that talent-for-math = general-intelligence is actually rather dumb. Ditto for assumptions about poor math skills, which can easily be a product of poor teaching rather than unusually low native ability.
If IQ tests measure anything, it's raw mental speed and memory - useful traits, but not nearly enough to draw a bounding box around general intelligence, which also includes abilities such as intuitive modelling, creative originality, and informal inference.
As the cliche goes, smart people can do stupid things in at least some situations.
Raw high IQ is just as likely to get you to wrong conclusions quickly as it is to give you useful predictions. If your modelling skills don't give you a good working model of the situation you're in, you're going to have a bad time.
Outside of core STEM, modelling depends on social and cultural experience and contextual training. If you don't have those, you're going to be handicapped even if you have a stratospheric IQ.