Beyond the History of Mathematics I

"The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store." (Florian Cajori, "A History of Mathematics", 1893)

 "The whole history of the development of mathematics has been a history of the destruction of old definitions, old hobbies, old idols." (David E Smith, American Mathematical Monthly, Vol. 1, No 1, 1894)

"The history of mathematics is the mirror of civilization." (Lancelot Hogben, "Mathematics for the Million", 1917)

"[…] a history of mathematics is largely a history of discoveries which no longer exist as separate items, but are merged into some more modern generalization, these discoveries have not been forgotten or made valueless. They are not dead, but transmuted." (John W N Sullivan, "The History of Mathematics in Europe", 1925)

"In the history of mathematics, the ‘how’ always preceded the ‘why’, the technique of the subject preceded its philosophy." (Tobias Dantzig, "Number: The Language of Science", 1930)

"It is a curious fact in the history of mathematics that discoveries of the greatest importance were made simultaneously by different men of genius. The classical example is the […] development of the infinitesimal calculus by Newton and Leibniz. Another case is the development of vector calculus in Grassmann's Ausdehnungslehre and Hamilton's Calculus of Quaternions. In the same way we find analytic geometry simultaneously developed by Fermat and Descartes." (Julian L Coolidge, "A History of Geometrical Methods", 1940)

"The study of the history of mathematics shows clearly enough that after each period of research and extension there follows a period of review and synthesis during which more general methods are evolved and the foundation of mathematics consolidated." (Gustave Choquet, "What is Modern Mathematics", 1963)

"The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making." (Morris Kline, "Mathematics for the Nonmathematician", 1967)

"Mathematics is a vast adventure of ideas; its history reflects some of the noblest thoughts of countless generations." (Dirk J Struik, "A Concise History of Mathematics", 1967)

"Under the present dominance of formalism, one is tempted to paraphrase Kant: the history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the of mathematics, has become empty." (Imre Lakatos, "Proofs and Refutations: The Logic of Mathematical Discovery", 1976)

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