Does motivation and interest correlate highly with IQ and can someone be smart but perform poorly in a particular field? Suppose a person is considered intelligent based on his IQ score. For example, suppose Bob has a high IQ score and is very interested in pure mathematics. He would most probably excel in this field. Now suppose Bob hated biology. He can't bring himself to learn anything about this field. Does this mean that Bob is "not intelligent" in the field of biology and only intelligent in the field of pure mathematics?

In other words, does motivation and interest correlate highly with IQ? Somebody can be "smart" but still perform poorly in various fields?
I have to disagree with Arnon a bit and want to expand on some of his points. The following is not meant as an answer to the question but just an extended comment to Arnon's answer.

General intelligence vs multiple intelligences

There are theories of intelligence that posit a general intelligence which determins performance in all areas. According to these theories performance in different areas must be correlated. And there are theories which assume different "intelligences" (verbal, spatial etc.) and a possibly different performance in different areas.



Intelligence vs talent

There are psychologists that use the term "intelligence" for an equally high performance in all areas, and the term "talent" for high performance in only one area and relatively lower performance in all other areas. Example:

IQ profile of a highly intelligent individual
---------------------------------------------

 IQ   verbal   mathematical   spatial      etc.

130     x           x            x          x      &lt;- high intelligence

120

110

100

 90


versus:

IQ profile of a talented individual
-----------------------------------

 IQ   verbal   mathematical   spatial      etc.

130                 x                              &lt;- mathematical talent

120

110

100     x                        x          x      &lt;- average intelligence

 90


Fluid vs crystallized intelligence

Many theories assume two different aspects of intelligence: fluid intelligence, that is the potential or capacity for cognitive performance, and crystallized intelligence, that is the knowledge and learning an individual has acquired.



Depending on which theory you follow – general versus multiple intelligences, intelligence versus talent, fluid and/or crystallized intelligence –, your concept of what intelligence is will differ. Since the scholars creating IQ tests also have different opinions on this matter, their tests are (often extremely) differently constructed and test results from different tests often correlate only to a certain degree. That is, an individual scoring a high IQ in one test can have an average IQ according to another. Which is why, when reporting an IQ, you must also report the test with which it was measured, because otherwise the result is meaningless.

Measurement error and confidence interval

IQ tests don't measure very exactly. There is always a certain measurement error involved. Beacause of this, psychologists always calculate a range of values (a confidence interval) in which the true value of the individual probably lies. The exact true intelligence is always unknown and can in fact differ widely from a given test result. Therefore serious psychologists do not put much faith in the IQ score (that is considered unprofessional and ignorant) but rather report wether the individual's intelligence is average, above average or below average. No current IQ test allows for a more accurate assessment. Repeating measurements (with different tests to avoid learning and on different days) can increase exactness.