Mathematical Reasoning Quotes & Sayings

common sense observations of human behavior support a similar dissociation in reasoning abilities which cuts in both directions. We all know persons who are exceedingly clever in their social navigation, who have an unerring sense of how to seek advantage for themselves and for their group, but who can be remarkably inept when trusted with a nonpersonal, nonsocial problem. The reverse condition is just as dramatic: We all know creative scientists and artists whose social sense is a disgrace, and who regularly harm themselves and others with their behavior. The absent-minded professor is the benign variety of the latter type. At work, in these different personality styles, are the presence or absence of what Howard Gardner has called "social intelligence," or the presence or absence of one or the other of his multiple intelligences such as the "mathematical. — Antonio R. Damasio

To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility. — Richard P. Feynman

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning. — John Locke

The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success. — Paul Dirac

Mathematical Reasoning is not only exact; it has its own criteria of reality — Paul Feyerabend

Another book gives the illusion of scientific precision by working out this reasoning in a mathematical formula using a "Mental Performance Ratio (MPR), — Kenneth L. Higbee

Logical investigations can obviously be a useful tool for philosophy. They must, however, be informed by a sensitivity to the philosophical significance of the formalism and by a generous admixture of common sense, as well as a thorough understanding both of the basic concepts and of the technical details of the formal material used. It should not be supposed that the formalism can grind out philosophical results in a manner beyond the capacity of ordinary philosophical reasoning. There is no mathematical substitute for philosophy. — Saul Kripke

For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed. — Lynn Steen

I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form. — George Boole

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications. — James R Newman

The Mathematics are Friends to Religion, inasmuch as they charm the Passions, restrain the Impetuosity of the Imagination, and purge the Mind from Error and Prejudice. Vice is Error, Confusion, and false Reasoning; and all Truth is more or less opposite to it. Besides, Mathematical Studies may serve for a pleasant Entertainment for those Hours which young Men are apt to throw away upon their Vices; the Delightfulness of them being such as to make Solitude not only easy, but desirable. — John Arbuthnot

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings. — George Washington

The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you. — John Arbuthnot

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop. — Chen-Ning Yang

[Lord Brougham's writings on the bee's cell contain] as striking examples of bad reasoning as are often to be met with in writings related to mathematical subjects. — James Whitbread Lee Glaisher

The moving power of mathematical invention is not reasoning but imagination. — Augustus De Morgan

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument. — Yuri Manin

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. — Alan Turing

We need science. We need empirical evidence. We can't just use mathematical reasoning to deduce the nature of the world. — Rebecca Goldstein

Scientific research is compounded of ... empirical procedures, general speculative ideas, and mathematical or abstract reasoning. — James Bryant Conant