Khan Academy

This is taking a much more traditional route to brain fitness but, unless you're a true genius, Khan Academy's app will likely give your mind plenty new and difficult concepts with which to grow. Khan Academy's mission is to provide a free, world-class education to everyone. This app helps their cause by letting users access the Academy's complete library of over 4,200 educational videos and articles. Want to re-learn calculus? Here's your chance. [free; iOSWindows]