What are the cognitive effects of increasing testosterone levels in men? I've recently became interested in the effects if testosterone on the cognitive function in men, but cannot find much hard scientific evidence on the subject. 

What are the cognitive effects of increasing testosterone levels in men?. There's a tremendous amount of anecdotal evidence from body builders, etc, but I'm looking for hard science, where the levels were measured before and after, and the trials were less than a month long.

Some of the claims made about increased testosterone levels seem very interesting, and I would like to know if any of that is true. 


does increasing testosterone levels increase subjective feeling of well being in men?
does increased testosterone benefit concentration ?
does increased testosterone benefit non-sexual motivation or ambition?
does increased testosterone benefit logical/math/engineering endeavors?


Here's what I see on Wikipedia snippet on testosterone and brain:


  The literature suggests that attention, memory, and spatial ability
  are key cognitive functions affected by testosterone in humans.
  Preliminary evidence suggests that low testosterone levels may be a
  risk factor for cognitive decline and possibly for dementia of the
  Alzheimer's type,[70][71][72][73] a key argument in life extension
  medicine for the use of testosterone in anti-aging therapies. Much of
  the literature, however, suggests a curvilinear or even quadratic
  relationship between spatial performance and circulating
  testosterone,[74] where both hypo- and hypersecretion (deficient- and
  excessive-secretion) of circulating androgens have negative effects on
  cognition.
I've discussed a lot of this recently on my answer to this question: Are there recent theories on physiognomy? In summary, yes.


Can't remember which of the tons I referenced mentioned well-being, but if you run a search function (Ctrl F, or ⌘F if you don't like good computers) on the text of the freely available articles I provided hyperlinks for, I guarantee you'll find it, and it was a positive relationship with testosterone.
Testosterone ($T$) might affect concentration, but I'd bet it's not a beneficial effect if so, or at least that it's moderated strongly by context. $T$ relates to spatial intelligence, but also to aggression, which may reflect some effect on impulsivity.
$T$ affects motivation, but again, I wouldn't call it a benefit, as the specific motives it affects probably aren't optimally healthy to say the least, and every action has its opportunity cost. Specifically, $T$ increases dominance and competitiveness in men, which is probably to say that it increases the need for power. It also increases sensation seeking and risk tolerance / decreases risk aversion, which is probably to say that it affects the behavioral activation and inhibition systems. Some evidence suggests testosterone interacts with competitive experiences differently for women.
For logical/math/engineering problems, $T$ is probably more unequivocally beneficial, because it relates to spatial intelligence.


$T$ is probably most studied in men; I'm not sure effects are similar for women in general. Estradiol in women may act more like testosterone in men in some ways.  I can copy content from my other answer here if desired, or expand on particular points if there is further interest. Please comment if so; I would also welcome collaborative edits.