Quote: in the realm of ideas, the reproducible ideas are mathematical objects; similar to science being about reproducible, physical results [»daviPJ_1981]

Quote: the mathematical abstractions of general relativity enlarge the scope of objective description and eliminate subjective elements [»bohrN_1958]

Quote: philosophy is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures

Quote: engineers depend on theorems when they 'plug in' a value and rely on a particular physical interpretation of the result [»demiRA_1977]

Quote: mathematical physics directs generalization; it allows scientists to select the important experiments

Quote: perhaps quantum phenomena and relativity theory can not be unified: different mathematical domains, even false theories can be amazingly accurate [»wignEP2_1960]

Quote: neither calculations nor machines can replace the mathematician. They can find order but not unexpected order [»poinH_1908, OK]

Quote: the results of mathematical science can agree with reality as accurately as do commercial calculations

Quote: Galileo saw mathematics as essential to physics and reading the great book of nature

Quote: mathematical analysis is a language for learning the internal harmony of the world, the only true objective reality

Quote: how can mathematics be so admirably appropriate to reality; by not being certain [»einsA_1923]

Quote: objects at all distances increase at the same ratio, whether seen through a telescope or not; e.g., consider rods at varying distances and sizes whose ends line up [»galiG_1623]

Quote: arithmetic laws are the laws of the laws of nature

Quote: a perfect, material sphere and a perfect, material plane would touch in just one point in the same way that a mathematical plane touches a mathematical sphere

Quote: atomic numbers allow an understanding of nature as pure numbers

Quote: Pythagoras discovered that chords are pleasant when in ratios of small integers; first numerical relationship in nature outside of geometry [»feynRP_1963]

Quote: universal rules--natural motion follows mechanical laws, independence of body and soul, body and souls are everywhere [»leibGW5_1705]

Quote: mechanical laws are never violated in natural motion; force and direction are always conserved

Quote: the acceleration of straight motion in heavy bodies proceeds according to the odd numbers beginning from one; i.e., the spaces passed over are to each other as the squares of the times [»galiG_1632]

Quote: an accelerating object travels half the distance as an object in uniform motion at the final velocity; probably the first mathematical integration applied to mechanics [»galiG_1632]

Quote: define a world-wide standard for the acceleration of naturally falling, heavy bodies; first world-wide standard of measure [»galiG_1638]

Quote: there is tremendous variety of behavior from the equations for viscous fluid flow with just one parameter; how much more is possible with more complex equations! [»feynRP_1964]

Quote: the complexities of things can easily and dramatically escape the simplicity of the equations which describe them

Quote: instruction modification is more important than subsequences; allows a short program to carry out a very long sequence of instructions

Quote: unlike the Euclidean method, the Babylonian idea is to remember enough to work something out or reconstruct what is needed [»feynR_1965]

Quote: physicists do Babylonian mathematics because different formulations of the same law give different clues for related laws [»feynR_1965]