Roles of Math in Science & Academia: Sarton vs. both Science Dean LT More and Math's Quinn

Background: Historian of Science Sarton, as a ‘study of the history of mathematics’, viewed mathematics as just one of the several sciences, with science recognised as that human activity devoted to the search for the very explanation for [i.e., for the truth about] any particular naturally occurring phenomenon.  Yet, mathematician F. Quinn, in 2012 as a ‘notice’ for the American Mathematical Society, concluded that mathematics is not science, since validity in the second is via comparison external to the model, whereas in the first it is by means of internal legitimization. Methods: Since the AAAS delineates 24 areas of science, with mathematics given predominance as its Section A, we examine the history of science so as to resolve this disagreement. Results: 1. Apparently overlooked by Sarton, by our AAAS, and by Quinn was the University of Cincinnati’s Dean of Graduate School (and Professor of Physics) LT More, whose writings in 1915 on the “limitations of science” noted that, though mathematics so ideally produces statements which, [“Q.E.D.”], are true [irrefutably so, we here repeat!], mathematics deals strictly with mental abstractions (points, lines, numbers, circles…), rather than with real-world, observable phenomena. 2. Another interesting historical note: The definition [O.E.D.] of ‘science’ notes the commonplace exclusion of ‘pure mathematics’ from science.   3. We also note SCIENCE Magazine’s 3 Oct 2014 observation that mathematically-expressed philosophical speculations about an aspect of Nature may not lead to a truth (and, therefore, not become a contribution to Science): “This [particular theoretical concept in physics] is a perfect example of how you can have beautiful mathematics and lose the physical intuition.” 4. An earlier remark, by Princeton University’s gravitational physicist, Robert Dicke, had, beginning in a 1962 publication on the ‘evidence for gravitational theories’, noted that the ‘general relativity theory’ remains as an observationally-unfounded philosophical, though mathematically-expressed, speculation.  Conclusions:  A. Though mathematics can, but need not, be used by any scientist as the language in which to express his/her scientific conclusion (‘model’), we ask: What, then, is the value and purpose of mathematics in higher education? B. In academia, the role of mathematics in these curricula is to discipline the mind of the graduate to reach any conclusion as one logically correct (even if not quite irrefutable).