The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
Pure mathematics is, in its way, the poetry of logical ideas.
The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
May not music be described as the mathematics of sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music -music the dream, mathematics the working life.
Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
John W.N. Sullivan
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.