A Quote by Martin Gardner
In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
Related Quotes
In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
In a way, composing on the melodic level is an expression of a melodic truth, almost like a geometric truth. If it has clarity, other people will recognize it. There's no way of isolating it in a gallery on a white wall and saying, "This is a work of art. This is a mathematical proof."
A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.
This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
These abnormal aspects included the shapes of UFOs and their behavior. Most of the UFOs seen in the daytime were said to have had simple geometric shapes-discs, ovals, spheres, cylinders-and surfaces that looked like metal. Such shapes are not only nonexistent among known aircraft, but contrary to all known theories of flight, in most cases offering control and performance disadvantages rather than advantages.
The truth about the world, he said, is that anything is possible. Had you not seen it all from birth and thereby bled it of its strangeness it would appear to you for what it is, a hat trick in a medicine show, a fevered dream, a trance bepopulate with chimeras having neither analogue nor precedent, an itinerant carnival, a migratory tentshow whose ultimate destination after many a pitch in a many a mudded field is unspeakable and calamitous beyond reckoning.
People that are that good at motivating and inspiring are rare. In many cases, you wish it was parents, and in many cases it is, but in a lot of cases it happens outside the family as well - or, in some cases, only.
I just tend toward more lush, full sounds in my productions. I don't have any preference when it comes to analogue versus digital; I use what's best for the application. Analogue synthesis is nice, but it's just one tool among many, and it has its place.
I have seen some astrologers who predicted wonderful things; but I have no reason to believe they predicted them only from the stars, or anything of the sort. In many cases it is simply mind-reading. Sometimes wonderful predictions are made, but in many cases it is arrant trash.
Peter was dull; he was at first Dull; - Oh, so dull - so very dull! Whether he talked, wrote, or rehearsed - Still with his dulness was he cursed - Dull -beyond all conception - dull.
I've learned that, in many cases, people say, 'I want ground truth,' and they don't really mean it. There are warts all over this organization, as there are in many organizations, but you just have to tell truth to power and let the chips fall where they may.
Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.
Muscular dystrophy ... was never seen until Duchenne described it in the 1850s. By 1860, after his original description, many hundreds of cases had been recognised and described, so much so that Charcot said: 'How is it that a disease so common, so widespread, and so recognisable at a glance - a disease which has doubtless always existed - how is it that it is recognised only now? Why did we need M. Duchenne to open our eyes?'
Proof is boring. Proof is tiresome. Proof is an irrelevance. People would far rather be handed an easy lie than search for a difficult truth, especially if it suits their own purposes.
I believe when I am in the mood that all nature is full of people whom we cannot see, and that some of these are ugly or grotesque, and some wicked or foolish, but very many beautiful beyond any one we have ever seen, and that these are not far away... and the simple of all times and the wise men of ancient times have seen them and even spoken to them.
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