Object oriented models vs. data analysis - is this the right alternative?
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Submission date: 26. Oct. 2015
published in: Mathematics as a tool : tracing new roles of mathematics in the sciences / J. Lenhard ... (eds.)
Berlin : Springer, 2017. - P. 253 - 286
(Boston studies in the philosophy and history of science ; 327)
DOI number (of the published article): 10.1007/978-3-319-54469-4_14
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Traditionally, there has been the distinction between pure and applied mathematics. Pure mathematics -- so the story goes -- discovers, creates and investigates abstract structures for their own sake, while applied mathematics applies existing mathematical tools and develops new ones for specific problems arising in other sciences. The interaction between pure and applied mathematics takes place in both directions. Applied mathematics utilizes concepts and methods developed in pure mathematics, and problems from diverse applications in turn stimulate the development of new mathematical theories. And traditionally, those problems arose within a clear conceptual framework of a particular science, most notably physics. In this essay, I want to argue that this distinction between pure and applied mathematics is no longer useful -- if it ever was --, and that the challenge of large and typically rather diverse data sets, typically arising from new technologies instead of theoretically understood and experimentally testable concepts, not only calls for new mathematical tools, but also necessitates a rethinking of the role of mathematics itself.