Science and hypothesis

Excerpt: ... APPENDIX. THE PRINCIPLES OF MATHEMATICAL PHYSICS * By Henri Poincare. Translated by George Bruce Halsted. What is the actual state of mathematical physics? What are the problems it is led to set itself? What is its future? Is its orientation on the point of modifying itself? Will the aim and the methods of this science appear in ten years to our immediate successors in the same light as to ourselves; or, on the contrary, are we about to witness a profound transformation? Such are the questions we are forced to raise in entering to-day upon our investigation. If it is easy to propound them; to answer is difficult. If we feel ourselves tempted to risk a prognostication, we have, to resist this temptation, only to think of all the stupidities the most eminent savants of a hundred years ago would have uttered, if some one had asked them what the science of the nineteenth century would be. They would have believed themselves bold in their predictions, and after the event, how very timid we should have found them. Do not, therefore, expect of me any prophecy; if I had known what will be discovered to-morrow, I should long ago have published it to secure me the priority. But if, like all prudent physicians, I shun giving a prognosis, nevertheless I can not dispense with a little diagnostic; well, yes, there are indications of a serious crisis, as if we might expect an approaching transformation. We are sure the patient will not die of it, and we may even hope that this crisis will be salutary, that it was even necessary for his development. This the history of the past seems to guarantee us. * An address delivered before the International Congress of Arts and Science, St. Louis. This crisis in fact is not the first, and to understand it, it is important to recall those which have preceded it. Mathematical physics, as we know, was born of celestial mechanics, which engendered it at the end of the eighteenth century, at the moment when it itself attained...