I was sad to see that not once did the author mention the works of Polya. Discovering new ideas in mathematics ultimately boils down to solving an existing prob

I was sad to see that not once did the author mention the works of Polya. Discovering new ideas in mathematics ultimately boils down to solving an existing problem in a new way or solving a completely new problem. I believe students should be posed the fundamental questions that forced many of the most beautiful ideas in math to be discovered. The advantage we have now is that if the students get stuck, they don't have to wait 2000 years for someone to discover how to find the area under a curve. We can give them hints. The teacher can compress time with a well thought out question pointing the students in the right direction.