Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable. I am convinced that purely mathematical construction enables us to find those concepts and those lawlike connections between them that provide the key to the understanding of natural phenomena. Useful mathematical concepts may well be suggested by experience, but in no way can they be derived from it. Experience naturally remains the sole criterion of the usefulness of a mathematical construction for physics. But the actual creative principle lies in mathematics. Thus, in a certain sense, I take it to be true that pure thought can grasp the real, as the ancients had dreamed.
Albert EinsteinRelated topics
actual certain construction creative criterion experience find grasp key mathematics natural nature phenomenon physics principle pure real realization sense sole take thought thus understanding usefulness way well remains ancients lies connectionsRelated quotes
It's true that my initial training was in mathematics. However, almost by accident, I happened to take a course from Kenneth Arrow on "Information Economics,” which was so inspiring that I decided to change direction. It seemed to me that economics combined the best of both worlds: the rigor of mathematics with the immediate relevance of a social science. As for how much math I would recommend, I'd say that basic analysis, including measure theory, is certainly very useful. Also, linear algebra and stochastic processes always helps. But beyond that, I don't think a huge mathematical investment is necessary to do economic theory unless you are planning to work in an extremely technical area.
Eric Maskin
This tendency towards a Christian-European Universal Monarchy has shown itself successively in the several States which could make pretensions to such a dominion, and, since the fall of the Papacy, it has become the sole animating principle of our History. We by no means seek to determine whether this notion of Universal Monarchy has ever been distinctly entertained as a definite plan .... Thus each State either strives to attain this Universal Christian Monarchy, or at least to acquire the power of striving after it;-to maintain the Balance of Power when it is in danger of being disturbed by another; and, in secret, for power, that it may eventually disturb it itself.
Johann Gottlieb Fichte
These Peripatetics accordingly made careful investigations into the nature of all things, so as to determine which I should be avoided as evil, discounted as useless, sought after as good, or preferred as better, and finally which are called "good" or "bad" according to circumstances. There thus developed two branches of philosophy, natural and moral, which are also called ethics and physics. But, through lack of scientific skill in argumentative reasoning, many absurdities were concluded. Thus Epicurus would have the world originate from atoms and a void, and would dispense with God as its author; whereas the Stoics asserted that matter is coeternal with God, and held that all sins are equally grave. p. 76.
John of Salisbury
Starting from a drawing, a pure creation of the mind, I expand it in space by giving it three dimensions, by giving it a material body [in polystyrene] and then enlarge it to the proportions of a site where it can evolve. In this way, instead of having only the drawing before you while remaining anchored in the everyday world, you can finally leave the world and penetrate into drawing, and thus inhabit the creation of the mind instead of merely looking at it prudently in a frame on the wall. The experience consists, therefore, in abstracting yourself totally from the natural everyday world in order to feed your eyes solely on your own mental elaborations.
Jean Dubuffet
At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.
Vladimir Arnold
