Truly new ideas are so hard because they require an entirely new mindset to contain them. First you need the mindset or else the ideas look like nonsense.
Like your example, leaps in math may be easy to see in retrospect but were hard to come by without anticipating a world that supports their existence: The concept of zero. The concept of limits. The concept of imaginary numbers. None of these are hard concepts, but on face value they seem arbitrary and "not entirely real". It is only deeply through exploring their implications that they have value. This is difficult not only because there are so many possible random ideas that lead to nowhere but also because fruitful ones seem like they must have been considered already.
How many people thought that "zero" might be a useful abstraction but didn't go further because it seemed like it must already have been considered? If you want to have a new idea, take a germ of a simple idea and follow it curiously without self-doubt. Think of the famous story of how Feynman came up with quantum electrodynamics: trying to understand the physics of a wobbling plate.
Like your example, leaps in math may be easy to see in retrospect but were hard to come by without anticipating a world that supports their existence: The concept of zero. The concept of limits. The concept of imaginary numbers. None of these are hard concepts, but on face value they seem arbitrary and "not entirely real". It is only deeply through exploring their implications that they have value. This is difficult not only because there are so many possible random ideas that lead to nowhere but also because fruitful ones seem like they must have been considered already.
How many people thought that "zero" might be a useful abstraction but didn't go further because it seemed like it must already have been considered? If you want to have a new idea, take a germ of a simple idea and follow it curiously without self-doubt. Think of the famous story of how Feynman came up with quantum electrodynamics: trying to understand the physics of a wobbling plate.