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AN ANALYSIS OF THE CERTAIN ELEMENTS OF THE PHILOSOPHICAL AND MATHEMATICAL FOUNDATION OF PHYSICS

ABSTRACT

Even non-physicists know that a great deal of mathematics is used in the physical sciences, engineering, economics, etc. Now, it is entering areas like life sciences. However,it is also vaguely known and we only try to bring it in sharper focus here that the mathematics applied in these areas is so much more permissive that a purist might go to the extent of saying that much of it has no more than formal resemblance to mathematics. For these reasons, the attitude towards their disciplines, of the mathematician on the one hand, and the theoretical physicist or even the mathematical physicist/applied mathematician on the other, are very different. For instance, the former does not regard infinity as a number; the latter treat it almost like any other number. Whereas the mathematician regards infinity as a signal of breakdown, it is not always so to the theoretical physicists for whom it is sometimes quite innocuous, sometimes useful or convenient, and sometimes it even rescues him from some rather awkward predicament, as, for instance, the singularity in second-order differential equation in quantum mechanics (as also in many cases in classical physics) allows only one of the two solutions to be acceptable, thereby givinghim a unique solution. (We may call this situation as ’infinity rescuing physics’). Of course, there are also many other situations where occurrence of infinity, or other niathematical improprieties, makes the theoretical physicist very unhappy. Very similar are the contrasting attitudes of the pure mathematician on the one hand, and applied mathematicians of all hues (including theoretical physicists) on the other, with regard to other mathematical improprieties. All these things do not have the approval of mathematical orthodoxy, as symbolized by institutions such as those of the Bourbakis.

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