Don’t be fooled by “easy.”
It is certainly true that Synthesis Tutor attends to topics that might seem readily familiar and previously “learned.” But there is significantly more to learning mathematics than just mastering the facts, algorithms, and mechanics of doing calculations. To be a powerful, thinking citizen of the world, one not only needs these mechanics, but also the context, connections, and big-picture understanding behind them. Textbooks teach students to answer textbook exercises, all of whose answers are at the back of the book. The Tutor teaches students to think about problems not yet solved, or maybe not even yet asked!
To do that, students must engage in an awareness of their own learning, meta-cognition. And here, discussing “familiar” topics from a new and advanced perspective provides the opportunity for exactly that. We probe into subtlety, nuance, and context. (And further, by doing so, we also pre-empt a slew of mathematical misconceptions that often haunt students for years. Let's get those misconceptions out of the way, right away!)
When we lean into the familiar, we do so to teach the unfamiliar, namely, how to think like a mathematician.