Math is one of those fields where there seems to be a clear correlation betwixt youth and creativity. It's just the consequence of having fresh eyes looking at an ancient problem ;)
But experience is clearly necessary due to the shear vastness of the topic. I find history and philosophy of math to be just as engaging and often crucial. Understanding the origins of probability in 17th century gambling houses, for example, sheds enormous light on the subject.
To that end, I think something like "Mathematical Evolutions" might be the best place to start:
"To tell the tale of The Isometric Problem, one must begin by quoting Virgil..."
I'm not sure the peak is driven by fresh eyes. I think fluid intelligence is a big requirement and the brain peaks in that regard in your 20's. It doesn't mean you can't still make great progress later in life, but it sure does get harder in my personal experience.
But experience is clearly necessary due to the shear vastness of the topic. I find history and philosophy of math to be just as engaging and often crucial. Understanding the origins of probability in 17th century gambling houses, for example, sheds enormous light on the subject.
To that end, I think something like "Mathematical Evolutions" might be the best place to start:
"To tell the tale of The Isometric Problem, one must begin by quoting Virgil..."
https://www.maa.org/sites/default/files/pdf/upload_library/2...