Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it.

--- The Assayer (Il saggiatore), 1623

Act one, scene four

Valentine: When your Thomasina was doing maths it had been the same maths for a couple of thousand years. Classical. And for a century after Thomasina. Then maths left the real world behind, just like modern art, really. Nature was classical, maths was suddenly Picassos. But now nature is having the last laugh. The freaky stuff is turning out to be the mathematics of the natural world.

Tom Stoppard's "Arcadia"
Faber and Faber paperback edition, 1993, p. 44-5.


Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

R. Courant, 1941
in What is Mathematics?


Laser beams reflected from the moon, allowing measurement of the moon's distance, is only one illustration of the spectacular quality of laser light. There are many others, as well as myriad everyday uses for the laser. But for several years after the laser's invention, colleagues used to tease me about it, saying, "That's a great idea, but it's a solution looking for a problem." The truth is, none of us who worked on the first lasers imagined how many uses there might eventually be. This illustrates a vital point that cannot be overstressed. Many of today's practical technologies result from basic science done years to decades before. The people involved, motivated mainly by curiosity, often have little idea as to where their research will lead. Our ability to forecast the practical payoffs from fundamental exploration of the nature of things (and, similarly, to know which of today's research avenues are technological dead ends) is poor. This springs from a simple truth: new ideas discovered in the process of research are really new.

Charles H. Townes
How the Laser Happened, p. 4.

Charles Townes, with Nikolai Basov and Alexander Prokhorov, is winner of the 1964 Nobel prize in physics.

Zen Proverb

True beauty is a deliberate, partial breaking of symmetry.

The Dynamics of Ambiguity, Giuseppe Caglioti, p. 55.