"While science is pursuing a steady onward movement, it is convenient from time to time to cast a glance back on the route already traversed, and especially to consider the new conceptions which aim at discovering the general meaning of the stock of facts accumulated from day to day in our laboratories." (Dmitry Mendeleyev, "The Periodic Law of the Chemical Elements", Journal of the Chemical Society Vol. 55, 1889)
"The aim of ‘science’ is to attain conceptions so adequate and exact that we shall never need to change them." (William James, "The Principles of Psychology", 1890)
"Science like life feeds on its own decay. New facts burst old rules; then newly developed concepts bind old and new together into a reconciling law." (William James, "The Will to Believe and Other Essays in Popular Philosophy", 1896)
"Science works by the slow method of the classification of data, arranging the detail patiently in a periodic system into groups of facts, in series like the strata of the rocks. For each series there must be a vocabulary of special words which do not always make good sense when used in another series. But the laws of periodicity seem to hold throughout, among the elements and in every sphere of thought, and we must learn to co-ordinate the whole through our new conception of the reign of relativity." (William H Pallister, "Poems of Science", 1931)
"The distinguishing feature of modern scientific thought lies in the fact that it begins by discarding all a priori conceptions about the nature of reality - or about the ultimate nature of the universe - such as had characterized practically all Greek philosophy and all medieval thinking as well, and takes instead, as its starting point, well-authenticated, carefully tested experimental facts, no matter whether these facts seen at the moment to fit into any general philosophical scheme or not - that is, no matter whether they seem at the moment to be reasonable or not." (Robert A Millikan, "Professor Einstein at the California Institute of Technology", Science Vol. 73 (1893), 1931)
"Physics too deals with mathematical concepts; however, these concepts attain physical content only by the clear determination of their relation to the objects of experience." (Albert Einstein, "Out of My Later Years", 1950)
"Science is still the versatile, unpredictable hero of the play, creating endless new situations, opening romantic vistas and challenging accepted concepts." (René J Dubos, "Louis Pasteur: Free Lance of Science", 1950)
"The important point for us to observe is that all these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them. In the limited number of mathematically existent simple field types, and the simple equations possible between them, lies the theorist’s hope of grasping the real in all its depth." (Albert Einstein, "Ideas and Opinions", 1954)
"For Science in its totality, the ultimate goal is the creation of a monistic system in which - on the symbolic level and in terms of the inferred components of invisibility and intangibly fine structure - the world’s enormous multiplicity is reduced to something like unity, and the endless successions of unique events of a great many different kinds get tidied and simplified into a single rational order. Whether this goal will ever be reached remains to be seen. Meanwhile we have the various sciences, each with its own system coordinating concepts, its own criterion of explanation." (Aldous Huxley, "Literature and Science", 1963)
“All the efforts of the researcher to find other models, conceptions, different mathematical forms, better linguistic modes of expression, to do justice to newly discovered layers of being mean self-transformation. The researcher in his place is the human being in self-transformation to more profound insight into what is given.” (John Dessauer)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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