Suppose I come up with an idea about how to solve a math problem. I decide to (try to) write a proof, with no intention of sharing the proof with anyone. Later on, I’m better at working with stuff in that domain of math, which is useful for communicating with others about the subject—whether it’s being better at asking questions, or better at answering them.
At a more meta level, I might create a list of ‘math beliefs’ I have. Over time, thinking it over, doing research, learning more, trying to write proofs, succeeding and failing, sometimes finding a statement is true, or that a special case is true, or the whole is wrong, etc. - my beliefs change upon reflection/computation/research/feedback.
Why I might mkae a list of my beliefs:
To revise them.
Hypothetical situation:
Suppose I come up with an idea about how to solve a math problem. I decide to (try to) write a proof, with no intention of sharing the proof with anyone. Later on, I’m better at working with stuff in that domain of math, which is useful for communicating with others about the subject—whether it’s being better at asking questions, or better at answering them.
At a more meta level, I might create a list of ‘math beliefs’ I have. Over time, thinking it over, doing research, learning more, trying to write proofs, succeeding and failing, sometimes finding a statement is true, or that a special case is true, or the whole is wrong, etc. - my beliefs change upon reflection/computation/research/feedback.
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