In fact it is the soul of mathematics to carry out such a dialogue with one's own proof.


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?

  • Basically it means talking to yourself (only in a meaningful way -- not psychotic). Note that "one's own" has a different connotation in other contexts, meaning your own family or people.
    – Hot Licks
    Nov 9, 2019 at 22:14
  • Don't ask about "with one's own". Ask about "one's own proof" or "one's own mentality".
    – GEdgar
    Nov 9, 2019 at 22:17

1 Answer 1


The word 'one' means any person, but not a particular person. [Definition under 'C1']

You can often substitute the word 'you'.


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.

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