For a long time the objects that mathematicians dealt with were mostly…

Henri Poincare
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For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or … ▶
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A small error in the former will produce an enormous error in the latter.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

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