I don't want his awkwardness to be silent. I want him to be silent, and his awkwardness to be salient. Also, his parents are ridiculous. His father is a paranoiac conspiracy theorist who does not live with the family while the story takes place, but made the decision to hold Lawrence back and his mother a former research chemist who is now a quadriplegic and won't leave her bed.
Maybe he does poorly with tests and homework. It could be that school bores him so much he doesn't bother doing his work. The school would hold him back because they don't realize he's actually a genius.
Actually, in some places he would be referred to Special Education as emotionally handicapped. Simple refusal to participate wouldn't be enough, though. It would have to be something that would make it impossible for him to stay in a regular classroom. Given what you've told us so far, you might want to Google Oppositional Defiant Disorder to see if that gets you where you need to go. In New York City, at least, self-contained classes for severe EH kids are extremely dysfunctional, so someone with a very high IQ would be even more frustrated.
Would you consider writing the story from the point of view of somebody who might be trying to help this boy? Just trying to think of a way in to telling this story. Some teacher, or classmate or relative or neighbour?
How, exactly, does this serve the purposes your story? It sounds more like additional stuff to get in the way.
Yes, actually, I would. Thank you for your thought, I hadn't considered it. If I post my first thousand or so words on here and you still think yours would work better, I will rewrite it if other criticisms lead me in that direction. Critiques like those are the exact reason I am on this site. I understand why some of this might seem irrelevant, because I'm not giving all of the details, but if I post my first small portion, and my details don't make sense, I will rewrite. Nothing I am doing, of which I am aware, is unintentional, but I am far from an expert in writing. I do not want to overwhelm myself with critiques, because it is difficult to verbalize what I am thinking about doing with this story, so people are seeming to think it is something that it isn't. There are many details, and I just want to get an idea of how the details might be expressed, from people who have written before. (This is my first book, aside from a misbegotten, gargantuan mess I once started). I tend to derive my ideas from very specific types of books and authors, so I just wanted some different thoughts on this (and will be wanting more later on). I thank you profusely for weighing in, and I promise that I will be more receptive to criticism when you have seen my work.
To me personally, your premise doesn't sound like it works. I'm not entirely sure I get what you're wanting to achieve here either. Perhaps a synopsis or a brief outline of the story could help? More often than not, it's the story that dictates how it should be told, not the character per se.
I think that this would be a great story written in first person. It would be pretty difficult to write it in third person if he doesn't talk.
Coming from someone who has high functioning autism in my close family, I'd suggest A LOT of research if you plan to go down that route with this character. Also, I'd suggest doing research on existing savants and learning what constitutes a genius in advanced mathematics, science, philosophy, etc. It would be ridiculous to write a 16 year old boy as anywhere near the level of a competent mathematician or scientist who is gifted with brilliance or has been prolific in the field for many years. This is a mistake made by many modern crime shows and the like as they want to cast the young, pretty, naive types yet have them play roles that necessitate many more years of learning/ practise. It's easy to get carried away with a character if you really want to underline how clever they are, but be aware, we know quite a lot about intelligence now and how the brain works. There are limits if you want your character to be believable. I also don't agree with the being held back. I don't see that as particularly believable, but if you have a good reason and explain it well, fair enough. Misunderstanding of social inadequacies in impoverished schooling systems (provided he doesn't score well in tests despite his intelligence) is not too incredible.
Try make him not smart in everything, just hyper-obsessed with math and economics. Having him unwilling to do English assignments would account for him being held back.
As well, I am unsure about how he will have a relationship with the drug dealer, the other pariah, if he doesn't communicate. Trying to evoke empathy/sympathy in a drug dealer character for a boy who doesn't speak will be difficult to make believable. Is the social issue/intelligence necessary to the story? Because it seems you might be painting yourself into a corner or making it overly complex. And I think one of the difficulties is in making your character two dimensional because we cannot understand the world these other people live in. My daughter is high functioning autistic, but that does not define her. She is lovely and brilliant in other ways. I think your character may need some of that - some redeeming feature that compensates for the handicap. Parents of handicapped children often make this point, that there children have other special features that compensate. This may make you character one that the reader can relate to? We all have our "handicaps" and our strengths. I think you are exaggerating your protagonists handicaps for the story (which makes good story) but maybe exaggerate his redeeming qualities as well? Else he may come off as someone we neither like not relate to...