See also Bill Thurston’s classic Math Overflow answer to a student wondering where they fit compared to a Gauss or Euler:
https://mathoverflow.net/questions/43690/whats-a-mathematici...
“The product of mathematics is clarity and understanding. Not theorems, by themselves. [Their importance is not just in their specific statements], but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.
The world does not suffer from an oversupply of clarity and understanding (to put it mildly)… In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining --- they depend very heavily on the community of mathematicians.”
https://mathoverflow.net/questions/43690/whats-a-mathematici...
“The product of mathematics is clarity and understanding. Not theorems, by themselves. [Their importance is not just in their specific statements], but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.
The world does not suffer from an oversupply of clarity and understanding (to put it mildly)… In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining --- they depend very heavily on the community of mathematicians.”