Astronomy is useful because it raises us above ourselves; it is useful because it is grand. It shows us how small is man’s body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.
Brunnian Link Tiling by Ross Hilbert Via Flickr: A hyperbolic tiling created using the Fractal Science Kit fractal generator. See www.fractalsciencekit.com/ for details.
A Hyperbolic Tiling replicates a polygon over the hyperbolic plane represented by the Poincare disk in such a way as to form a hyperbolic tiling pattern. The Poincare disk is a model for hyperbolic geometry that maps the hyperbolic plane onto the unit disk.
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.
Les mathématiciens n’étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d’autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse.
Henri Poincaré, La science et l'hypothèse (1902)