I keep hearing people dismiss IQ as just a number with no real biological basis. The argument seems to be that you cannot point to anything in the brain that corresponds to g and therefore it is just a mathematical artifact of how we analyze test data. But I also know there is neuroscience research connecting brain structure and function to cognitive ability. What does the actual evidence say about the relationship between IQ and what is physically happening in the brain?
The biological correlates of intelligence are actually pretty well documented at this point and the dismissal of IQ as a pure statistical abstraction does not hold up against the neuroscience literature. Brain volume correlates with IQ at around r equals 0.3 to 0.4 across multiple large studies. White matter integrity, particularly the efficiency of connections between brain regions, correlates with cognitive ability measures. Processing speed as measured by reaction time tasks correlates with IQ and also with neural conduction velocity. The P300 brainwave component, which reflects how quickly the brain processes and categorizes information, correlates with g. Glucose metabolism studies show that higher IQ individuals actually use their brains more efficiently, showing less activation on cognitively demanding tasks rather than more. The neural efficiency hypothesis has held up reasonably well across decades of research. None of this means IQ maps onto a single brain structure or region, g appears to reflect the efficiency of a distributed network rather than any localized area 
The neural efficiency finding is the one that surprises people most 
Most assume smarter brains must be working harder. The opposite appears to be true. Higher IQ is associated with doing more with less, which is actually a pretty elegant biological signature for general cognitive ability 