
George Pólya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1962)
Source: The Design of Everyday Things (1988, 2002), Ch. 5, p. 131.
George Pólya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1962)
Academy of Achievement interview (1991)
Context: The idea of being constructive, creative, positive, in trying to bring out the best in one's own self and the best in others follows from what I've just been saying. Again, I repeat my belief in us, in ourselves, as the product of the process of evolution, and part of the process itself. I think of evolution as an error-making and error-correcting process, and we are constantly learning from experience. It's the need to dedicate one's self in that way, to one's own self, and to choose an activity or life that is of value not only to yourself but to others as well.
"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago
Context: I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.
2000s, Thus Spake Stallman (2000)
Source: Take The Risk (2008), p. 40
“he who thinks great thoughts often makes great errors”
Re: Pause for keystroke http://groups.google.com/group/comp.lang.lisp/msg/4539e251e76e966a.
Usenet articles, Miscellaneous
" The Little Thoughts of Thinking Machines http://www-formal.stanford.edu/jmc/little.html", Psychology Today, December 1983, pp. 46–49. Reprinted in Formalizing Common Sense: Papers By John McCarthy, 1990, ISBN 0893915351
1980s
1850 - 1870
Context: My dear Frédéric Bazille, I ask myself what you can be doing in Paris during fine weather, for I suppose that it must also be very fine there. Here my dear fellow, it is is charming, and I discover every day always beautiful things. It is enough to become mad [fou], so much do I have the desire to do it all, my head is cracking. Damn it, here it is the sixteenth, put aside your cliques and your claques, and come spend a couple of weeks here, it would be the best thing that you could do, because in Paris it cannot be very easy to work.
This very day, I still have a month to stay in; furthermore my sketches are becoming finished, I have even set to work additionally [remis] on some others. In sum, I am content enough with my stay here, even though my studies are very far from what I would wish. It is decidedly frightfully difficult to make something complete in all respects, and I think that there are scarcely any but those who content themselves with the approximate. Very well, my dear fellow, I want to struggle, scrape, start over again [recommencer], because one can do what one sees and understands, and it seems to me, when I see nature, that I am going to do it all, write it all out, but them go try to do it.... when one is on the job..
All this proves that one must only think about this. It is by force of observation and reflection that one finds. So let us grind away and grind away constantly. Are you making any progress? Yes, I am sure of it, but what I am sure of is that you do not work enough and not in the right way. It is not with carefree guys like your Villa and others that you will be able to work. It would be better all alone, and yet, all alone there are plenty of things that one cannot make out. In the end all of this is terrible, and it is a rough task.
... It is frightening what I see in my head.