Mike TwoMcmillion, I just recently read this and loved it. Thank you so much for summarizing why being human has its own dignity and can be its own superpower.
Not only does the Rithmatist have Magic Turtle Graphics (and who cannot love like that), it really is the Anti-Hogwarts.
However those Rithmatists are chosen, most have little skill or interest in fundamental geometry, the basis of their magic system. Classes are long, tedious, and boring taught by teachers whose primary qualification is not love of the subject or ability to teach but desire for the status and position that tenure provides. There's 10 years of indentured servitude once students graduate. Their society knows about them and their magic but doesn't trust them and resents them. There's no "boy who survived" hero and magic fart candy.
The Rithmatist offers an unusually gritty magic world despite details that sparkle in the background: the applied magic of chalking-driven steampunk engines and a wonderful North American continent made up of islands and Sweet and Sour Lo Mein as Italian cuisine.
The hero is a muggle with a gift of mathematical ability and (this is the really best bit), he has to work really hard to master his subject. I loved when he looked self-critically at his early attempts at the 9-point defense and was able to critically analyze it, to see how he's improved since then. He's constantly reading and studying and improving his knowledge and understanding, even as the class system keeps him walled off from that enticing library just a few steps away from his normal life.
I loved the uncomplaining efforts of his mom, who with her husband, had a dream, took a gamble, lost, and accepted the consequences of making adult choices with adult risks. That is so unbelievably rare in fiction. Yes, his father's work and efforts paid off but only after eight years of both sadness and her self sacrifice.
I love how Joel is bad at being a hero. He's reckless, he can be a bully, and he often picks the worst approach counter to his best interests. And I love how the professor and the head of school both call him out on this, using the maturity and wisdom they've earned with age to teach him to be a better person. How many SF/Fantasy books can you think of where people actually talk through their problems, apologize, try to make amends, and work towards becoming better people? Joel's relationship with Melody is perfect because she too has a lot of growing up to do and plenty of sharp edges and frustration inherent to her character.
Rithmatist is my favorite Sanderson novel to date. And it's the heart and growth that makes it that way for me.