"I turn away with fright and horror from the lamentable evil of functions which do not have derivatives." (Charles Hermite, [letter to Thomas J Stieltjes])
"Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven’t. You get the feeling that the result you have discovered is forever, because it’s concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing: you don’t get a feeling of having done an honest day’s work. Don’t get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques." (Gian-Carlo Rota, [interview])
"The chief weakness of the machine is that it will not learn by its mistakes. The only way to improve its play is by improving the program. Some thought has been given to designing a program that would develop its own improvements in strategy with increasing experience in play. Although it appears to be theoretically possible, the methods thought of so far do not seem to be very practical. One possibility is to devise a program that would change the terms and coefficients involved in the evaluation function on the basis of the results of games the machine had already played. Small variations might be introduced in these terms, and the values would be selected to give the greatest percentage of wins." (Claude E Shannon)
"The theory of functions with one independent variable is very closely connected with the theory of algebraic curves. The geometry of such a curve becomes therefore of fundamental importance." (Heegaard)
"When graphing a function, the width of the line should be inversely proportional to the precision of the data." (Marvin J Albinak)
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