By Philip J. Davis
From the Preface: "This publication is addressed to all who're eager about the character of arithmetic and its function in society. it truly is neither a textual content e-book nor a experts' e-book. It includes a couple of loosely associated essays that could be learn independently and for which i've got attempted to supply a leitmotif via throwing mild at the courting among arithmetic and customary experience. In those essays i am hoping to foster a serious perspective in the direction of either the life of good judgment in arithmetic and the ambiguous function that it might play."
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Additional resources for Mathematics & Common Sense: A Case of Creative Tension
Tillers, eds. The Dynamics of Judicial Proof, Computation and Common Sense. Springer-Verlag, 2001. Jean Mawhin. ” Notices of the Amer. Math. , Oct. 2005, pp. 1041–1042. Kay L. O’Halloran. Mathematical Discourse: Language, Symbolisms and Visual Images. Continuum, 2005. indb 46 9/2/2010 2:31:12 PM 1 What Is Mathematics? As an elaboration of Q1–Q5 of “Letters to Christina,” it is time to say a few more words about what mathematics is. Strangely, this question is hardly discussed in any course of mathematics routinely taken by undergraduates or graduates.
I will inject a personal story here. Some years ago, I had a correspondence with the famous positivist British philosopher Alfred Ayer. I wrote Ayer a letter and asked him what he now considered to be the most important philosophical questions. ” I believe the question of how we know something has become increasingly important in a day when computer simulations and virtual reality increase the level of ambiguity in what is put forward as evidence. The virtual is often confused with common sense.
1. Cf. , pure and impure. indb 6 9/2/2010 2:31:15 PM What Is Mathematics? 7 One could describe the difference between pure and applied mathematics as follows: Pure mathematics is inward looking while applied mathematics is outward looking. That is to say, pure mathematics looks to the study and development of its own theories and interpretations while applied mathematics stresses the application of mathematical theories to the physical and social worlds. An example from pure mathematics is the theorem of Niels Henrik Abel that the roots of a polynomial of degree five or higher cannot, as a rule, be expressed in terms of integers subjected to the operations of elementary arithmetic and simple root extraction.