Quotes About Mathematics

Whether it be placing advertisements, predicting customer behavior, anticipating equipment failure or even pricing products and services, the most useful people in your strategy team in the future might not be the MBA graduates, but those with the degrees in pure mathematics.

What do I believe? I believe that two and two make four, Sganarelle, and that four and four are eight.

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, "refuge from the goading urgency of contingent happenings," and the sort of beauty changeless mountains present to sense tried by the present-day kaleidoscope of events.

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, "refuge from the goading urgency of contingent happenings," and the sort of beauty changeless mountains present to sense tried by the present-day kaleidoscope of events.

All mathematical proofs must be deductive. Each proof is a chain of deductive arguments, each of which has its premises and conclusion.

Because we are forced to learn about numbers and operations with numbers while we are still too young to appreciate them—a preparation for life which hardly excites our interest in the future—we grow up believing that numbers are drab and uninteresting. But the number system warrants attention not only as the basis of mathematics, but because it contains weighty and beautiful ideas which lend themselves to powerful applications.

Even the greatest Greek algebraist, Diophantus, who lived during the latter part of the Alexandrian Greek civilization (around A.D. 250), rejected irrationals as numbers.

predecessor of Isaac Newton at Cambridge University, maintained that irrational numbers have no meaning independent of geometric lengths.

Negative numbers, equations involving unknowns, formulas, derivatives, integrals, and other concepts we shall encounter are abstractions built upon abstractions.

Another example may also help us to appreciate the abstractness of numbers. Mathematically, is equal to . But the corresponding physical fact may not be true.

Because in our way of writing numbers the position of an integer determines the quantity it represents, the principle involved is called positional notation.

The system of positional notation we use derives from the Hindus; however, the same scheme was used two milleniums earlier by the Babylonians, but to a more limited extent because they did not have a zero.

The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

Though Leibniz may have had special reasons for considering base two, neither this base nor any other had until recently been seriously considered as a substitute for base ten. In fact, aside from incidental uses of other bases in higher mathematics to facilitate an occasional proof, the subject of bases other than ten was regarded until recently as an intellectual amusement.

Of course it must be noted that no decimal expression, no matter how many decimal places are used, will ever exactly equal an irrational number; a decimal is a fraction, and an irrational, we saw, cannot equal a fraction.

Because the knowledge of counting, adding, subtracting, and the like is regarded as a preparation for "life" we are taught it mechanically from early childhood. The practice takes precedence over the principles. No doubt this introduction to life is not especially cheering.

The mathematics and science that developed in Europe after the Renaissance became much more dependent upon quantitative results and hence upon the use of all types of numbers.

The number ?, which is the ratio of the circumference of any circle to its diameter, is irrational, though this fact was not proved until 1768. Many other examples could be given.

At about the same time that St. Augustine lived, the Roman jurists ruled, under the Code of Mathematicians and Evil-Doers, that "to learn the art of geometry and to take part in public exercises, an art as damnable as mathematics, are forbidden.

Goldbach's hypothesis

irrational number cannot equal a whole number or a fraction.

Can we combine ?2 + ?3 into the simpler ?5? Let us test this operation on whole numbers expressed as roots. Certainly ?9 + ?16 does not equal , that is, 3 + 4 does not equal 5. Hence we should not assert the analogous relation for irrational numbers.

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

The second basic function of algebra is to convert expressions into more useful ones. Gauss's