Fools pretend to foretell what will be the issue of things, and are laughed at for their awkward conjectures. Wise men being aware of the uncertainty of human aflairs, and having observed how small a matter often produces a great change, are modest in their conjectures.
James Burgh
Erdős knows about more problems than anybody else, and he not only knows about various problems and conjectures, but he also knows the tastes of various mathematicians. So if I get a letter from him giving me three of his conjectures and two of his problems, then it's sure that these are exactly the kind of conjectures and problems I'm interested in, and these are exactly the kind of questions I may be able to answer.
Of course, this applies not only to me, but to everybody else. So Erdős has an amazing ability to match problems with people. Which is why so many mathematicians benefit from his presence. Every letter is likely to inspire you to do some work, or every phone call will give you some problems you are interested in.Paul Erdos
One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable.
Benoit Mandelbrot
He was so crafty and cunning in petty things, as the circumventing of any great man, the change of a Favourite, &c. insomuch as a very wise man was wont to say that he believed him the wisest fool in Christendom, meaning him wise in small things, but a fool in weighty affairs.
James I of England
You know more of a road by having travelled it then by all the conjectures and descriptions in the world.
William Hazlitt
You should look at all the experimental information at hand, not only the most relevant, and be prepared to make conjectures if that helps.
Hans Bethe
Burgh, James
Burgnich, Tarcisio
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