“In most sciences, one generation tears down what another has built and what one has established another undoes. In mathematics alone, each generation adds a new story to the old structure” (Hermann Hankel, “Die Entwicklung der Mathematik in den letzten Jahrhunderten, 1884)
"The true method of foreseeing the future of mathematics is to study its history and its actual state." (Henri Poincaré, "Science and Method", 1908)
"One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics." (Henri Poincaré)
“Even now there is a very wavering grasp of the true position of mathematics as an element in the history of thought. I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him.” (Alfred N Whitehead, “Mathematics as an Element in the History of Thought” in “Science and the Modern World”, 1925)
“Mathematicians study their problems on account of their intrinsic interest, and develop their theories on account of their beauty. History shows that some of these mathematical theories which were developed without any chance of immediate use later on found very important applications.” (Karl Menger, “What is calculus of variations and what are its applications?”, The Scientific Monthly 45, 1937)
“The history of mathematics shows that the introduction of better and better symbolism and operations has made a commonplace of processes that would have been impossible with the unimproved techniques.” (Morris Kline, “Mathematics in Western culture”, 1953)
“Although the study of the history of mathematics has an intrinsic appeal of its own, its chief raison d'être is surely the illumination of mathematics itself.” (Charles H Edwards Jr, “The Historical Development of the Calculus”, 1979)
“Mathematical research should be as broad and as original as possible, with very long range-goals. We expect history to repeat itself: we expect that the most profound and useful future applications of mathematics cannot be predicted today, since they will arise from mathematics yet to be discovered." (Arthur Jaffe, “Ordering the universe: the role of mathematics”, SIAM Review Vol 26. No 4, 1984)
"One of the lessons that the history of mathematics clearly teaches us is that the search for solutions to unsolved problems, whether solvable or unsolvable, invariably leads to important discoveries along the way. (Carl B Boyer & Uta C Merzbach, “A History of Mathematics”, 1991)
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