Science and method / by Henri Poincaré ; translated by Francis Maitland ; with a preface by Bertrand Russell.

  • Henri Poincaré
Date:
[1914?]
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Licence: In copyright

Credit: Science and method / by Henri Poincaré ; translated by Francis Maitland ; with a preface by Bertrand Russell. Source: Wellcome Collection.

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    unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. But that is also precisely what causes it to give a large return , and in fact the more we see this whole clearly and at a single glance, the better we shall perceive the analogies with other neighbouring objects, and con- sequently the better chance we shall have of guessing the possible generalizations. Elegance may result from the feeling of surprise caused by the un- looked-for occurrence together of objects not habitu- ally associated. In this, again, it is fruitful, since it thus discloses relations till then unrecognized. It is also fruitful even when it only results from the con- trast between the simplicity of the means and the complexity of the problem presented, for it then causes us to reflect on the reason for this contrast, and gener- ally shows us that this reason is not chance, but is to be found in some unsuspected law. Briefly stated, the sentiment of mathematical elegance is nothing but the satisfaction due to some conformity between the solu- tion we wish to discover and the necessities of our mind, and it is on account of this very conformity that the solution can be an instrument for us. This aesthetic satisfaction is consequently connected with the economy of thought. Again the comparison with the Erechtheum occurs to me, but I do not wish to serve it up too often. It is for the same reason that, when a somewhat lengthy calculation has conducted us to some simple and striking result, we are not satisfied until we have shown that we might have foreseen, if not the whole result, at least its most characteristic features. Why is this ? What is it that prevents our being contented
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