Quotes from Morris Kline

Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

A proof tells us where to concentrate our doubts.

Statistics: the mathematical theory of ignorance.

In brief, the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine.

Universities hire professors the way some men choose wives - they want the ones the others will admire.

A elegantly executed proof is a poem in all but the form in which it is written.

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.

Logic is the art of going wrong with confidence.

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.

A good expository paper will benefit far more people than most research papers. A good text is worth a thousand of the usual trifles that appear in research journals.

The feeling that one must be an authority in a subject to say anything about it is unfounded. We are all laymen outside the field of our own specialty,

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.

Aristotle says, "Now what is characteristic of any nature is that which is best for it and gives most joy. Such to man is the life according to reason, since it is that which makes him man.

The study of molecular structure attempts to get at precisely the physical constituents of molecules.

Man knew how to feed, clothe, and house himself millenniums before mathematics existed.

Geometry . . . is the science that it hath pleased God hitherto to bestow on mankind. —THOMAS HOBBES

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.

geometrical forms, such as triangles and circles, and the concepts of arithmetic, such as whole numbers and fractions, are abstractions of certain properties of physical objects.

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.