Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.
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- Mathematical discoveries, small or great are never born of spontaneous generation.
- It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of natur β¦ βΆ
- Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.
- When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that con β¦ βΆ
- There are no solved problems; there are only problems that are more or less solved.
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