On Differential Equations II

"Algebra, as an art, can be of no use to any one in the business of life; certainly not as taught in the schools. I appeal to every man who has been through the school routine whether this be not the case. Taught as an art it is of little use in the higher mathematics, as those are made to feel who attempt to study the differential calculus without knowing more of the principles than is contained in books of rules." (Augustus de Morgan, "Elements of Algebra", 1837)

"If one looks at the different problems of the integral calculus which arise naturally when he wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing. Whether it be electrostatics or electrodynamics, the propagation of heat, optics, elasticity, or hydrodynamics, we are led always to differential equations of the same family." (Henri Poincaré, "Sur les Equations aux Dérivées Partielles de la Physique Mathématique", American Journal of Mathematics Vol. 12, 1890)

"The works of the highest faculty of man, judgment, is always directed toward the constant limiting of the infinite, toward the breaking up of the infinite into comfortably digestible portions, differentials." (Yevgeny Zamyatin, "We", 1921)

"The difficulty involved is that the proper and adequate means of describing changes in continuous deformable bodies is the method of differential equations. […] They express mathematically the physical concept of contiguous action." (Max Born, "Einstein’s Theory of Relativity", 1922)

"It seems to be the impression among students that mathematical physics consists in deriving a large number of partial differential equations and then solving them, individually, by an assortment of special mutually unrelated devices. It has not been made clear that there is any underlying unity of method and one has often been left entirely in the dark as to what first suggested a particular device to the mind of its inventor." (Arthur G Webster, "Partial Differential Equations of Mathematical Physics", 1927)

"In order to solve a differential equation you look at it till a solution occurs to you." (George Pólya, "How to Solve It: A New Aspect of Mathematical Method", 1945)

"The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics." (John von Neumann & Oskar Morgenstern, "Theory of Games and Economic Behavior", 1947)

"What is the origin of the urge, the fascination that drives physicists, mathematicians, and presumably other scientists as well? Psychoanalysis suggests that it is sexual curiosity. You start by asking where little babies come from, one thing leads to another, and you find yourself preparing nitroglycerine or solving differential equations. This explanation is somewhat irritating, and therefore probably basically correct." (David Ruelle, "Chance and Chaos", 1991)

"If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellects that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success." (Max Born)

"Science is a differential equation. Religion is a boundary condition." (Alan Turing)

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