Is lumosity.com based on science?
Zickefoose et al. did a study, and showed that while you might improve while playing the game, it called into question if you actually improved outside of just getting better at the game.

Redick et al. also reported that when they did a double blind study in brain games like Luminosity that you improved in the games, but they didn't see any transfer from game to every-day life. 

Also see my previous answer on the topic: Cognitive Science Forum