School Is Cool
This theme is taken quite literally. The schools this story are almost as cool as Hogwarts, but gets extra points for being theoretically plausible. Everyone in this story is smart and intelligence is actually presented as a positive thing rather than a conspiratorial threat invented to keep idiots down. Of course, the intellectual stimulant behind the decision to pit students against students rather than, say, the Navy Seals or specially marine-trained CIA agents does seem to be a big plot hole, but an argument can be made that school is so cool that these students are already bring the smarts to their advantage of being younger and more idealistic.
Teamwork Is Cool
The students are not just some collection of weird geniuses who excel at everything they do. There is a realism to their intellectual pursuits in the sense that each of the are especially gifted in one area. This means when their school is attacked and they are place in the position of fighting for their lives, they must depend upon others whose skills exceed their own while also being prepared to put their own exceptional skills to work when required. Stories based on students in schools generally tend to put competition above cooperation and collaboration and it is a very positive portrayal of the theme that very often in life things turn out better when people are working together rather than constantly in competition.
Science Is Cool
The basis for this novel is the classic Jules Verne tale 20,000 Leagues Under the Sea. Verne is, of course, one of the progenitors of the entire science fiction genre, but he was fairly unique among those who created the genre in trying to remain as scientifically plausible as possible even while describing the most unlikely of fictions. This unofficial sequel remains true to that vision from choosing high school science geeks as its protagonists (and villains) to bringing back the scientifically advanced Nautilus submarine of Captain Nemo in Verne’s story to its updating of what scientific capabilities that submarine have made possible.