A Quote by Gerolamo Cardano
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
Quote Topics
Quote Author
Related Quotes
The evolutionary explanation for origins, although impossible either to prove or to test scientifically, is nevertheless defended by its proponents on the basis that it is the only explanation which is naturalistic, not involving the 'supernatural' element of a divine Creator.
We're back around to [Buckminster] Fuller again. Back around to the recognition of patterns, which may be true or may not be. But nevertheless, have enough of a semblance that they're worth exploring. That, to me, is where my work begins.
However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.
Some lines were never meant to be crossed, however good your cause may seem.
A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.
In a free society, there comes a time when the truth - however hard it may be to hear, however impolitic it may seem to say - must be told.
Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.
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.
Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.
All my writing is about the recognition that there is no single reality. But the beauty of it is that you nevertheless go on, walking towards utopia, which may not exist, on a bridge which might end before you reach the other side.
Without accepting the fact that everything changes, we cannot find perfect composure. Unfortunately, although it is true, it is difficult for us to accept it. Because we cannot accept the truth of transience, we suffer.
Without accepting the fact that everything changes, we cannot find perfect composure. But unfortunately, although it is true, it is difficult for us to accept it. Because we cannot accept the truth of transience, we suffer.
The adoption of the required attitude of mind towards ideas that seem to emerge "of their own free will" and the abandonment of the critical function that is normally in operation against them seem to be hard of achievement for some people. The "involuntary thoughts" are liable to release a most violent resistance, which seeks to prevent their emergence. If we may trust that great poet and philosopher Friedrich Schiller, however, poetic creation must demand an exactly similar attitude.
The Republican establishment may in fact be so desirous of getting rid of the Tea Party as its base, they may be willing to lose some elections in order to get rid of their base and put up a new base.
At times the world may seem an unfriendly and sinister place, but believe that there is much more good in it than bad. All you have to do is look hard enough. and what might seem to be a series of unfortunate events may in fact be the first steps of a journey.
Related Authors
Ada Lovelace Quotes
English
Mathematician
Alfred North Whitehead Quotes
English
Mathematician
Benoit Mandelbrot Quotes
French
Mathematician
Carl Friedrich Gauss Quotes
German
Mathematician
Charles Babbage Quotes
English
Mathematician
David Hilbert Quotes
German
Mathematician
G. H. Hardy Quotes
British
Mathematician
George Polya Quotes
Hungarian
Mathematician
Hannah Fry Quotes
English
Mathematician
Henri Poincare Quotes
French
Mathematician
Isaac Barrow Quotes
English
Mathematician
Isaac Newton Quotes
English
Mathematician
Norbert Wiener Quotes
American
Mathematician
Pythagoras Quotes
Greek
Mathematician
Rene Descartes Quotes
French
Mathematician
Seymour Papert Quotes
American
Mathematician