|
qkg:contextText
|
Rigorous Mathematics is Narrow, Physical Mathematics Bold And Broad. ยง 224. Now, mathematics being fundamentally an experimental science, like any other, it is clear that the Science of Nature might be studied as a whole, the properties of space along with the properties of the matter found moving about therein. This would be very comprehensive, but I do not suppose that it would be generally practicable, though possibly the best course for a large-minded man. Nevertheless, it is greatly to the advantage of a student of physics that he should pick up his mathematics along with his physics, if he can. For then the one will fit the other. This is the natural way, pursued by the creators of analysis. If the student does not pick up so much logical mathematics of a formal kind (commonsense logic is inherited and experiential, as the mind and its ways have grown to harmonise with external Nature), he will, at any rate, get on in a manner suitable for progress in his physical studies. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. There is no end to the subtleties involved in rigorous demonstrations, especially, of course, when you go off the beaten track. And the most rigorous demonstration may be found later to contain some flaw, so that exceptions and reservations have to be added. Now, in working out physical problems there should be, in the first place, no pretence of rigorous formalism. The physics will guide the physicist along somehow to useful and important results, by the constant union of physical and geometrical or analytical ideas. The practice of eliminating the physics by reducing a problem to a purely mathematical exercise should be avoided as much as possible. The physics should be carried on right through, to give life and reality to the problem, and to obtain the great assistance which the physics gives to the mathematics. This cannot always be done, especially in details involving much calculation, but the general principle should be carried out as much as possible, with particular attention to dynamical ideas. No mathematical purist could ever do the work involved in Maxwell's treatise. He might have all the mathematics, and much more, but it would be to no purpose, as he could not put it together without the physical guidance. This is in no way to his discredit, but only illustrates different ways of thought. (en) |
