A Quote by George Washington

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

Quote Topics

Beings Correctness Employment Investigation Mathematical Method Mind Rational Reasoning Truths Worthy

Quote Author

George Washington
American - President
February 22, 1732 - December 14, 1799

The knowledge of God, the belief in God, is what I call an a-rational process. It's not rational - it doesn't proceed by scientific investigation - but it's not irrational because it doesn't contradict my reasoning process. It goes beyond it.

George Coyne

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

For my part, I am convinced that the method of teaching which approaches most nearly to the method of investigation is incomparably the best; since, not content with serving up a few barren and lifeless truths, it leads to the stock on which they grew.

Edmund Burke

There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible.

Gottfried Leibniz

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

Roger Penrose

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.

David van Dantzig

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

George Dantzig

Divine Providence is connected with Divine intellectual influence, and the same beings which are benefited by the latter so as to become intellectual, and to comprehend things comprehensible to rational beings, are also under the control of Divine Providence, which examines all their deeds with a view of rewarding or punishing them. ...the method of which our mind is incapable of understanding.

Maimonides

There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible, and those of fact are contingent and their opposite is possible. When a truth is necessary its reason can be found by analysis, resolving it into more simple ideas and truths until we reach those which are primitive.

Gottfried Leibniz

The Supreme Court's 5-4 decision rejected Congress' findings and its method of reasoning, .. Is there any real justification for the court's denigrating Congress' 'method of reasoning'?.

Arlen Specter

As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy.

Isaac Newton

There are several kinds of truths, and it is customary to place in the first order mathematical truths, which are, however, only truths of definition. These definitions rest upon simple, but abstract, suppositions, and all truths in this category are only constructed, but abstract, consequences of these definitions ... Physical truths, to the contrary, are in no way arbitrary, and do not depend on us.

Georges-Louis Leclerc, Comte de Buffon

But it is strange how many rational beings believe the ultimate truths of the universe to be reducible to patterns on a blackboard.

Frederick Pollock

Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.