Sherlock Holmes is hailed as a genius. It's true, for the most part, but he can be so oblivious sometimes…
He arrives at the crime scenes, makes superficial (and embarrassing), obvious deductions, and leaves to solve the crimes. He never really considers the possibility of intelligence in the people who surround him.
He certainly never expects to see the intelligence of a certain member of the forensics team. Not that this man puts himself on display the way Sherlock does. Instead, he carefully guards his genius behind an intricate facade of normal, boring, obnoxious.
Why? Partly, because it amuses him. He dislikes the consulting detective's arrogance, and it pleases him to know that he can stand right in front of the man and deceive him.
Arrogance aside, he does like Sherlock. He enjoys listening to the stream of observations that eventually provide a crucial clue. There's no need to make the detective self-conscious, or cause him to (heaven forbid) look for affirmation of his ideas from another analytical mind.
Anderson can poke holes in Sherlock's logic easier than anything. So many of those carefully explained deductions include hunches, not that Sherlock would ever admit to something like using his gut. He can see a myriad of possibilities, of course, and so can Anderson, but Anderson would like to see Sherlock continue developing his instincts, so he merely observes, and makes idiotic remarks.
Crime scenes are fun. Especially with the addition of John, who has the miraculous ability to nurture Sherlock's genius, but also encourages him to explain his thought processes, which pleases Anderson.
Before John, Anderson had to rely on close observation-the movement of Sherlock's eyes around the crime scene, knowing the things he pokes and prods or sniffs at. To amuse himself, Anderson makes lists of clues and the possibilities they imply, then tracks Sherlock's progress around the crime scene and reconstructs the detective's thought process.
Often, they arrive at nearly the same conclusion. Not quite so often, Sherlock is more keenly observant, and shows Anderson a different perspective. Now days, with John asking questions, Anderson is better able to keep up. He does approve of John. He considered jealousy, the first few times Sherlock brought John along to the crime scenes, but quickly discarded the notion. For one, John was practically a saint, dealing with Sherlock's uncontrollable behavior. And it has helped Sherlock immensely. Anderson estimates a 19% increase in the speed of Sherlock's deductions, undoubtedly caused by John's presence, which seems to motivate him to show off.
He worries for John's safety, of course, but easily consoles himself with the knowledge that John would seek out trouble wherever he could find it, and at least caring for the doctor is on Sherlock's agenda. Also, Anderson may be a bit of a sociopath. He's not as bad as Sherlock, of course, but he does have to do an awful lot of soul-searching to find some sort of empathy. Usually he fakes that kind of thing; it's easier. Especially when his facade is amusingly tedious and grumpy. Sally, his stalwart coworker who finds herself secretly attracted to the "freak," as she calls him, seems to find a little bit of Sherlock in Anderson. He can usually get away with showing only slightly more empathy than Sherlock himself.
Sometimes, he wishes Sherlock would catch on. He's slightly disappointed that the genius detective never does. Does he really think forensics would hire a complete moron? Anderson goes out of his way to act idiotic around Sherlock, just a little more idiotic than should seem likely, but does Sherlock notice? Not consciously, at least. He takes the time to denounce Anderson, and Anderson takes this as a good sign that Sherlock's subconscious, at least, may sense something. That's all that occurs… but it's not as if they're kindred souls, so Anderson doesn't mind terribly much.
Unlike Sherlock, Anderson doesn't think that people are boring. To him, people are fascinating. Always changing, always so emotional, so complex. Never straightforward. It's a puzzle worth considering. And that's the fundamental difference between him and Sherlock, Anderson thinks. Normal people being interesting, if you just looked close enough.
Anderson dances around revealing his brilliant mind to another brilliant mind, but he is very good at judging what Sherlock will or won't notice, and he always stops a step short of revealing himself. Because at heart, Anderson is an observer. He doesn't want to use his genius, the way Sherlock, or Mycroft, or Moriarty do. He might as well be a god, interfering in the little affairs of men (getting a little too narcissistic, he always reminds himself when he gets to the god part).
It's not his job.
He remains as neutral as possible, and watches. He watches Sherlock and John, he watches London, he watches everything. His thrill is in not getting caught. He likes it. Really, he does. But yes, someday, maybe, he will tell people that he is one of the greatest minds of this day and age… and laugh at the look on Sherlock's face.
