Thich Nhat Hanh (Coming Home: Jesus and the Buddha as Brothers, Riverhead Books, New York (1999)):

Scientists like to speak in the language of mathematics. There are many good mathematicians among us. Those of us who look at reality and speak about reality in the language of mathematics find that there is no other language that can speak as well as mathematics does about reality. When a mathematician admires reality in terms of mathematics, he has the tendency to believe God is the best mathematician. Otherwise how could things be arranged in such a way? If God is not a mathematician, how could he create things perfectly in this way?

To know and to understand are two different things. When you climb a ladder, unless you abandon the lower step, you will not be able to climb to a higher one. Knowledge is like that. If you are not ready to let go of your knowledge, you cannot get a deeper knowledge of the same thing. The history of science proves this. You discover a new thing that helps you to understand better. Yet you are aware that some day you'll have to let go of that thing in order to discover something deeper and higher.

Understanding is a process. It is a living thing.

Concentration is the food of understanding. You have to be concentrated for understanding to be possible. When you want to solve a mathematical problem, you have to concentrate. You cannot turn on the radio and let your mind be dispersed. When you are standing in front of a tree, you have to concentrate on the tree. This brings you understanding of the tree. In your daily life, we have to live in a concentrated way. When eating, you have to eat in concentration. When drinking, you have to drink in concentration.

From a review by Peter Hilton of The Pleasures of Counting, in MAA's Monthly, May '98:

"One is claiming, in short, that there is a quality of beauty in mathematics, just as there is in a work of art or a piece of music. I was, in fact, suggesting in my own essay ["The joy of mathematics" Coll. Math. J. 23 (1992)] that, just as any sensitive human being can be brought to appreciate beauty in art, music or literature, so that person can be educated to recognize the beauty in a piece of mathematics. The rarity of that recognition is not due to the "fact" that most people are not mathematically gifted but to the crassly utilitarian manner of teaching mathematics and of deciding syllabi and curricula, in which tedious, routine calculations, learned as a skill, are emphasized at the expense of genuinely mathematical ideas, and in which students spend almost all their time answering someone else's questions rather that asking their own."

The following all are from Reuben Hersh's What is Mathematics, Really?, Oxford University Press, 1997:

Edward Everett (1794-1865), the first American to receive a PhD in math at Gottingen and co-speaker with Abraham Lincoln at Gettysburg battlefield: "In pure mathematics we comtemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven."

Mary Somerville (1780-1872), scholar and mathematician: "Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mathematical conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, ..., all oh which must have existed in that sublimely omniscient Mind from eternity."

Reuben Hersh himself: "Mathematics is part of human culture and history, which are rooted in our biological nature and our physical and biological surroundings. Our mathematical ideas in general match our world for the same reason that our lungs match earth's atmosphere."


Life may look different from mathematics—but's that's because we have the wrong idea about mathematics. Most people have some sort of mental image of what biologists, or physicists, or astronomers—or even bank mangers—do. ... What concerns me is that when we think of mathematics, the only mental image that most of us have is what we did at school, and we tend to assume that this is all the mathematics that exists. Not so. Mathematics is not a long-dead subject preserved in dusty tomes, in which all the questions have been solved and all the answers are listed at the back of the book. It is a vibrant, lively, ever-growing subject: Indeed, more new mathematics is being created today then ever before. Further, this mathematics is not just ever-more-complicated answers to bigger and bigger sums. It lies on a far higher conceptual level. Mathematics is the study of patterns, regularities, rules, and their consequences—the science of significant form—and nowhere is form more significant than in biology. —Ian Stewart, Life's other secret: the new mathematics of the living world, John Wiley and Sons (1998), p. 29-30.


Gary Snyder (A Place in Space, Counterpoint, Washington D.C., (1995) p 173-4.) The more objective and rational the language, it is though, the more accurate this exercise in giving order to the world will be. Language is considered by some to be a flawed mathematics, and the idea that mathematics might even supplant language has been flirted with. This idea still colors the commonplace thining of many engineer types and possibly some mathematicians and scientists.
But the world–ordered according to its own inscrutable mode (indeed a sort of chaos)–is so complex and vast on both macro and micro scales that it remains forever unpredictable. The weather, for hoary example. And take the very mind that ponders these thoughts: in spite of years of personhood, we remain unpredictable even to our own selves. Often we wouldn't be able to guess what our next thought will be. But that clearly does not mean we are living in hopeless confusion; it only means that we live in a realm in which many patterns remain mysterious or inaccessible to us.

Ken Wilber (Quantum Questions, Mystical Writings of the World's Great Physicists, edited by Ken Wilber, Shambhala Publications, Boston (1984)):Simply because religious experience is apprehended in an "interior" fashion does not mean it is merely private knowledge, any more than the fact that mathematics and logic are seen inwardly, by the mind's eye, makes them merely private fantasies without public import. Mathematical knowledge is public knowledge to all equally trained mathematicians; just so, contemplative knowledge is public knowledge to all trained contemplatives.



Gary Snyder
(Mountains and Rivers Without End, Counterpoint Publications, Washington, DC (1996))
Taken from from "Old Woodrat's Stinky House"

Coyote and Earthmaker whirling about in the world winds found a meadowlark nest floating and drifting: stretching it to cover the waters and made us an earth--



Us critters hanging out together

something like three billion years.


Three hundred something million years

the solar system swings around

with all the Milky Way--


Ice ages come one hundred fifty million years apart

last about ten million

then warmer days return--


A venerable desert woodrat nest of twigs and shreds

plastered down with ambered urine

a family house in use eight thousand years,

& four thousand years of using writing equals

the life of a bristlecone pine--


A spoken language works

for about five centuries,

lifespan of a douglas fir;

big floods, big fires, every couple hundred years,

a human life lasts eighty,

a generation twenty.


Hot summers every eight or ten,

four seasons every year

twenty-eight days for the moon

day / night the twenty-four hours


& a song might last four minutes,

a breath is a breath.

The difference between a good mechanic and a bad one, like the difference between a good mathematician and a bad one, is precisely this ability to select the good facts from the bad ones on the basis of quality. He has to care! This is an ability about which formal traditional scientific method has nothing to say. —Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, First Morrow Quill Paperback Edition, William Morrow and Company, New York (1979)

From A Number Sense: At present, at any rate, vary little evidence exists that great mathematicians and calculating prodigies have been endowed with an exceptional neurobiological structure. Like the rest of us, experts in arithmetic have to struggle with long calculations and abstruse mathematical concepts. If they succeed, it is only because they devote a considerable time to this topic and eventually invent well-tuned algorithms and clever short-cuts that any of us could learn if we tried and that are carefully devised to take advantage of our brain's assets and get round its limits. What is special about them is their disproportionate and relentless passion for numbers and mathematics, occasionally fueled by their inability to entertain normal relations with other fellow humans, a cerebral disease called autism. I am convinced that children of equal initial abilities may become excellent or hopeless at mathematics depending on their love or hatred of the subject. Passion breeds talent – and parents and teachers therefore have a considerable responsibility in developing their children's positive and negative attitudes toward mathematics. In Gulliver's Travels, Jonathan Swift describes the bizarre teaching methods used at the mathematics school of Lagado, in Balnibarbi Island:

I was at the mathematical school, where the master taught his pupils after a method scarcely imaginable to us in Europe. The proposition and demonstration were fairly written on a thin wafer, with ink composed of a cephalic tincture. This the student was to swallow upon a fasting stomach, and for three days following eat nothing but bread and water. As the wafer digested, the tincture mounted to his brain, bearing the proposition along with it. But the success hath not hitherto been answerable, partly by some error in the quantum or composition, and partly bye the perverseness of lads, to whom this bolus is so nauseous, that they generally steal aside, and discharge it upwards before it can operate; neither have they been yet persuaded to use so long an abstinence as the prescription requires.

Although Swift's description reaches the height of absurdity, his basic metaphor of learning mathematics as a process of assimilation has an undeniable truth. In the final analysis, all mathematical knowledge is incorporated into the biological tissues of the brain.

Geometria est archetypus pulchritudinis mundi. (Geometry is the archetype of the beauty of the world.) —Johannes Kepler

Descartes' proof of the existence of God:
When I imagine a triangle, although there may nowhere in the world be such a figure outside my thought, or even have been, there is nevertheless in this figure a certain determinate nature, form or essence, which is immutable and eternal, which I have not invented, and which in no wise depends on my mind, as appears from the fact that diverse properties of that triangle can be demonstrated, viz. that its three angles are equal to two right angles, that the greatest side is subtended by the greatest angle, and the like, which now, whether I wish it or do not wish it, I recognize very clearly as pertaining to it, although I never thought of the matter at all when I imagined a triangle for the first time, and which therefore cannot be said to have been invented by me ... but now, if just because I can draw the idea of something from my thought, it follows that all which I know clearly and distinctly as pertaining to this object does really belong to it, may I not derive from this an argument demonstrating the existence of God? It is certain that I no less find the idea of God, that is to say, the idea of a supremely perfect Being, in me, than that of any figure or number whatever it is; and I do not know any less clearly and distinctly that an actual and eternal existence pertains to this nature than I know that all which I am able to demonstrate of some figure or number truly pertains to the nature of this figure or number, and therefore although all that I concluded in the preceding Meditations were found to be false, the existence of God would pass with me as at least as certain as I have ever held the truth of mathematics to be....I clearly see that existence can no more be separated from the essence of God than can its having its three angles equal to two right angles be separated from the essence of a rectilinear triangle, ... —Rene Descartes, as quoted by Rueben Hersh in What is Mathematics, Really?, Oxford University Press (1997), pp. 116-117.

Quotes from Women Mathematicians