Theory vs Practice III

"[...] in foundations we try to find (a theoretical framework permitting the formulation of) good reasons for the basic principles accepted in mathematical practice, while the latter is only concerned with derivations from these principles. The methods used in a deeper analysis of mathematical practice often lead to an extension of our theoretical understanding. A particularly important example is the search for new axioms, which is nothing more than a continuation of the process which led to the discovery of the currently accepted principles." (Georg Kreisel & Jean-Louis Krivine, "Elements of Mathematical Logic: Model Theory", 1967)

"The sooner we all face up to the fact that theory and practice are indissoluble, and that there is no contradiction between the qualities of usefulness and beauty, the better." (John M Ziman, "Growth and Spread of Science", Nature Vol. 221 (5180), 1969)

"For the theory-practice iteration to work, the scientist must be, as it were, mentally ambidextrous; fascinated equally on the one hand by possible meanings, theories, and tentative models to be induced from data and the practical reality of the real world, and on the other with the factual implications deducible from tentative theories, models and hypotheses." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"One important idea is that science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice." (George E P Box, Science and Statistics", Journal of the American Statistical Association 71, 1976)

"Thus statistics should generally be taught more as a practical subject with analyses of real data. Of course some theory and an appropriate range of statistical tools need to be learnt, but students should be taught that Statistics is much more than a collection of standard prescriptions." (Christopher Chatfield, "The Initial Examination of Data", Journal of the Royal Statistical Society A Vol. 148, 1985)

"The theory of our modern technic shows that nothing is as practical as the theory." (J Robert Oppenheimer, "Reflex", 1977)

"In practice, it may be impossible to purge a real system of its actual randomness and observe the consequences, but often we can guess what these would be by turning to theory. Most theoretical studies of real phenomena are studies of approximations. (Edward N Lorenz, "The Essence of Chaos", 1993)

"He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast." (Leonardo da Vinci)

"There is nothing more practical than a good theory." ([attributed to] David Hilbert)