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In fact it is the soul of mathematics to carry out such a dialogue with one's own proof.
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We're talking about a perfectly innocent and delightful activity of the human mind-a dialogue with one's own mentality.
What does the author mean by "with one's own proof" and "with one's own mentality" in the above sentences?
The word 'one' means any person, but not a particular person. [Definition under 'C1']
You can often substitute the word 'you'.
Examples:
One has an obligation to one's friends. ["You have an obligation to your friends"]
One ought to make the effort to vote. ["You should make the effort to vote"]
On one's own means 'on your own', 'by yourself', 'alone'.
one's own proof means your proof: not anyone else's proof.
one's own mentality means your thoughts, your way of thinking, your mind.
