How are the logical and mathematical skills of people with ADHD? How does rationality and the logical thought processes of those with and without ADHD compare? Please explain the source of the differences. Are the differences thought to be caused by dopamine, serotonin, or norepinephrine? Or is there some other neurological explanation?
How do the math skills of those with ADHD compare to others? As above, please explain in detail from a biochemical perspective.
How do the rationality and logical thought processes those with and without ADHD compare? Please explain the source of this difference. Is the difference thought to be caused by dopamine, serotonin or norepinephrine or some other neurological explanation.


ADHD is typically associated with a reduction in dopamine and/or norepinephrine. Though the two neurotransmitters are similar on a structural level, norepinephrine is associated with vigilant attentiveness, whereas dopamine is associated with cognitive alertness. ADHD is commonly associated with a reduction in dopamine activity, and since norepinephrine is synthesized by dopamine, there are typically deficiencies in both.

In the brain, cortical norepinephrine (NE) is released during attentional patterns so that learning can commence and be enhanced. When we receive information that goes against sensory information (or what we had previously thought true), NE levels 'spike' and then subside once the information is sufficiently integrated. With lower levels of NE, it is harder to pick up on information, and thus the information may not be consolidated and 'learned'. NE also affects memory for facts and specific details in those with ADHD, and thus it can be harder to recall factual information when necessary. You can guess what happens next, as factual information is crucial for building a 'bank' of information in the brain.

Rationality (by definition) factors in how much information is available, and uses it to maximize expected utility. Those who suffer from ADHD have less information available to them, as they do not pick up on information in the way that the average person might. It is not that they are less capable of rational thought -- they simply have less information to make informed, rational decisions.

ADHD is occasionally associated with lateral thinking, which is a method of problem-solving that relies on creative thinking moreso than step-by-step logic. However, I have found no evidence in scientific literature that suggests a link between the two.


  How do the math skills of those with ADHD compare to others? As above please explain in detail from a biochemical perspective.


It depends on how salient math is to the individual. Albert Einstein and Paul Erdős were both considered to have ADHD, and nobody would doubt their math skills. :)

Learning disabilities do tend to work in conjunction. Of those with arithmetic learning disabilities, a quarter of them have ADHD, and up to 31% of those with ADHD are reported to have math learning disabilities. Inattention is typically associated with mathematical learning, as failure to learn to automize computational skills leads to calculation error and slower internalization rate. Children with ADHD typically have problems with fluency of calculation. In other words, it takes longer for them to make calculations internally, and this does not appear to normalize with age. This is because holding information in your head is an essential component of making mental calculations, and this is something that those with ADHD struggle with.

Interestingly enough, math performance in ADHD sufferers has shown to improve with a) more computational practice (so that mental math becomes more 'intuitive'), and b) music playing in the background while attempting to solve math problems. You can read more about this in the article I linked to above.