It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.
David HilbertRelated topics
general hypothesis lay number possible problem requirement rigor should remains meansRelated quotes
I made a very bad mistake; I miscounted these scraps of information on the record as 92, and in continual homage to this man who had been so influential to me, I began creating or constructing my own films on this so-called "magic" number of 92 ... but when I eventually made a film about John Cage and met him, I explained this to him, and he found it very amusing because there are only 90 stories on the two sides of the record, and I'd based three years of my filmic career on this mathematical error!
Peter Greenaway
When you have arrived at your country house and have saluted your household, you should make the rounds of the farm the same day, if possible; if not, then certainly the next day. When you have observed how the field work has progressed, what things have been done, and what remains undone, you should summon your overseer the next day, and should call for a report of what work has been done in good season and why it has not been possible to complete the rest, and what wine and corn and other crops have been gathered.
Cato the Elder
Suppose that the organism is given the problem of determining the analysis of a stimulus at a certain level of representation - e.g., the problem of determining which sequence of words a given utterance encodes. Since, in the general case, transducer outputs underdetermine perceptual analyses, we can think of the solution of such problems as involving processes of nondemonstrative inference. In particular, we can think of each input system as a computational mechanism which projects and confirms a certain class of hyputheses on the basis of a certain body of data.
Jerry Fodor
I do not want to discuss evolution in such depth, however, only touch on it from my own perspective: from the moment when I stood on the Serengeti plains holding the fossilized bones of ancient creatures in my hands to the moment when, staring into the eyes of a chimpanzee, I saw a thinking, reasoning personality looking back. You may not believe in evolution, and that is all right. How we humans came to be the way we are is far less important than how we should act now to get out of the mess we have made for ourselves.
Jane Goodall
[The career a young man should choose should be] one that is most consonant with our dignity, one that is based on ideas of whose truth we are wholly convinced, one that offers us largest scope in working for humanity and approaching that general goal towards which each profession offers only one of the means: the goal of perfection ... If he works only for himself he can become a famous scholar, a great sage, an excellent imaginative writer [Dichter], but never a perfected, a truly great man.
Karl Marx