A Quote by Philip J. Davis

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

Philip J. Davis

Quote Topics

Alluring Aspects Beautiful Blooming Endlessly Mathematics Theories Way

Quote Author

Philip J. Davis
American - Mathematician
Born: January 2, 1923

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

George Polya

On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.

Jean Dieudonne

There are two kinds of paradoxes. They are not so much the good and the bad, nor even the true and the false. Rather they are the fruitful and the barren; the paradoxes which produce life and the paradoxes that merely announce death. Nearly all modern paradoxes merely announce death.

Gilbert K. Chesterton

Perhaps the greatest paradox of all is that there are paradoxes in mathematics.

Edward Kasner

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

G. H. Hardy

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

Hans Reichenbach

If we could turn around and stand back, then we would see the whole complete pattern. And therefore what we have to do in this lifetime is to perfect this pattern, so that it will continue a most beautiful pattern next time and next time and next time and next time because we vowed until samsara is empty! Now, that's going to be a long time, so you'd better get prepared for the long haul, and the best way to do that is to really prepare yourself as much as possible in this lifetime, and not waste your opportunities so that we can genuinely benefit beings, endlessly, endlessly, endlessly.

Tenzin Palmo

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.

L. E. J. Brouwer

This is how we know we are in a loving relationship. We are blooming, and the one we love is blooming as well.

Brenda Shoshanna

"Did God have a mother?" Children, when told that God made the heavens and the earth, innocently ask whether God had a mother. This deceptively simple question has stumped the elders of the church and embarrassed the finest theologians, precipitating some of the thorniest theological debates over the centuries. All the great religions have elaborate mythologies surrounding the divine act of Creation, but none of them adequately confronts the logical paradoxes inherent in the question that even children ask.

Michio Kaku

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.

Eric Temple Bell

One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.

Danica McKellar

I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.

Ian Stewart

When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.

Edward Kasner

You are not supposed to get it. It's a paradox. All of mathematics is built on paradoxes. That's the biggest paradox of all-all this orderliness, and at the heart, impossibility. Contradiction. Heaven built on the foundations of hell.