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Your opinion of yourself becomes your reality. If you have all these doubts, then no one will believe in you and everything will go wrong. If you think the opposite, the opposite will happen. It’s that simple.
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Ian Stewart
Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.
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