# Quote — Henri Poincaré, The Value of Science

> Mathematics have a triple aim. They must furnish an instrument for the study of nature. But that is not all: they have a philosophic aim and, I dare maintain, an esthetic aim. They must aid the philosopher to fathom the notions of number, of space, of time. And above all, their adepts find therein delights analogous to those given by painting and music. They admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective; and has not the joy they thus feel the esthetic character, even though the senses take no part therein? Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts?
>
> This is why I do not hesitate to say that mathematics deserve to be cultivated for their own sake, and the theories inapplicable to physics as well as the others. Even if the physical aim and the esthetic aim were not united, we ought not to sacrifice either.

- Author: [Henri Poincaré](https://www.leafyquotes.com/henri-poincare.md)
- Book: [The Value of Science](https://www.leafyquotes.com/henri-poincare/the-value-of-science.md)
- Source: [Wikiquote](https://en.wikiquote.org/wiki/Henri_Poincar%C3%A9#Ch._5:_Analysis_and_Physics) ([CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/))
- Topics: [science](https://www.leafyquotes.com/topics/science.md), [beauty](https://www.leafyquotes.com/topics/beauty.md)
- Quote page: https://www.leafyquotes.com/henri-poincare/the-value-of-science/mathematics-have-a-triple

## More from this book

> Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility. A world as exterior as that, even if it existed, would for us be forever inaccessible.

[Quote page](https://www.leafyquotes.com/henri-poincare/the-value-of-science/does-the-harmony.md)

> Time and Space … It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.

[Quote page](https://www.leafyquotes.com/henri-poincare/the-value-of-science/time-and-space.md)

> The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile or vain.

[Quote page](https://www.leafyquotes.com/henri-poincare/the-value-of-science/the-advance-of-science.md)