This paper gives wrong solutions to trivial problems. The basic error, however, is not new.
From the above account, it is clear that every conceptual element in Cauchy's theory was to be found in one or another of the special theories constructed in the previous century. Moreover, in researches of Fresnel done in 1821--1822, with which Cauchy must certainly have been familiar, many of Cauchy's results are more or less implied, although in Fresnel's work the concepts of stress and strain are always connected through a presumed linearly elastic response.Thus it might seem that Cauchy's achievement in formulating and developing the general theory of stress was an easy one. It was not. Cauchy's concept has the simplicity of genius. Its deep and thorough originality is fully outlined only against the background of the century of achievement by the brilliant geometers who preceded, treating the special kinds and cases of deformable bodies by complicated and sometimes incorrect ways without ever hitting upon this basic idea, which immediately became and has remained the foundation of the mechanics of gross bodies.
Nothing is harder to surmount than a corpus of true but too special knowledge; to reforge the tradition of his forebears is the greatest originality a man can have.
Now a mathematician has a matchless advantage over general scientists, historians, politicians, and exponents of other professions: He can be wrong. A fortiori, he can also be right. [...] A mistake made by a mathematician, even a great one, is not a ``difference of a point of view'' or ``another interpretation of the data'' or a ``dictate of a conflicting ideology'', it is a mistake. The greatest of all mathematicians, those who have discovered the greatest quantities of mathematical truths, are also those who have published the greatest numbers of lacunary proofs, insufficiently qualified assertions, anf flat mistakes. By attempting to make natural philosophy into a part of mathematics, Newton reliniquished the diplomatic immunity granted to non-mathematical philosophers, chemists, psychologists, etc., and entered into the area where an error is an error even if it is Newton's error; in fact, all the more so because it is Newton's error.The mistakes made by a great mathematician are of two kinds: first, trivial slips that anyone can correct, and, second, titanic failures reflecting the scale of the struggle which the great mathematician waged. Failures of this latter kind are often as important as successes, for they give rise to major discoveries by other mathematicians. One error of a great mathematician has often done more for science than a hundred impeccable little theorems proved by lesser men. Since Newton was as great mathematician as ever lived, but still a mathematician, we may approach his work with the level, tactless criticism which mathematics demands.
The hard facts of classical mechanics taught to undergraduates today are, in their present forms, creations of James and John Bernoulli, Euler, Lagrange, and Cauchy, men who never touched a piece of apparatus; their only researches that have been discarded and forgotten are those where they tried to fit theory to experimental data. They did not disregard experiment; the parts of their work that are immortal lie in domains where experience, experimental or more common, was at hand, already partly understood through various special theories, and they abstracted and organized it and them. To warn scientists today not to disregard experiment is like preaching against atheism in church or communism among congressmen. It is cheap rabble-rousing. The danger is all the other way. Such a mass of experimental data on everything pours out of organized research that the young theorist needs some insulation against its disrupting, disorganizing effect. Poincaré said, ``The scientist must order; science is made out of facts as a house is made out of stones, but an accumulation of facts is no more science than a heap of stones, a house.'' Today the houses are buried under an avalanche of rock splinters, and what is called theory is often no more than the trace of some moving fissure on the engulfing wave of rubble. Even in earlier times there are examples. Stokes derived from his theory of fluid friction the formula for the discharge from a circular pipe. Today this classic formula is called the ``Hagen-Poiseuille law'' because Stokes, after comparing it with measured data and finding it did not fit, withheld publication. The data he had seem to have concerned turbulent flow, and while some experiments that confirm his mathematical discovery had been performed, he did not know of them.
There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense.
How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use of knowledge gathered in a few observations, to predict by logical processes the outcomes in many other circumstances. Any logically sound theory satisfying this condition is a good theory, whether or not it be derived from ``ultimate'' or ``fundamental'' truth. It is as ridiculous to deride continuum physics because it is not obtained from nuclear physics as it would be to reproach it with lack of foundation in the Bible.
The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply.