Mathematics for the Nonmathematician (Books on Mathematics)

by Morris Kline

The failure of incomes to follow a normal curve raises an interesting point because physical and mental abilities are normally distributed and these qualities should determine income.

there is a fundamental difference between the formulas obtained from data of the physical sciences and formulas derived from data of biology, psychology, the social sciences, and pedagogy. One may say that, in general, a formula developed from data of the first class continues to hold as added data are gathered.

there are romances, grand romances, and statistics,

Especially where sampling is involved, statistics do not prove anything; they tend to show.

Life is the art of drawing sufficient conclusions from insufficient premises. SAMUEL BUTLER

the theory of probability, which was first developed to solve problems of gambling, takes the gamble out of the insurance business.

The farther one proceeds with the mathematics of number, the more remote from experience are the concepts introduced and the larger is the creative role played by the mind.

mathematical deduction provides the structure of any scientific theory; it is the bond between one law and another. A scientific theory is a comprehensible and consistent collection of facts, and it is comprehensible and consistent because the facts are arranged in the form of a series of mathematical deductions.

The mathematicians are artists who use nature as their model and provide their own orderly and unifying interpretations.

To reason mathematically is to seek perfection in reasoning. The commonly used phrase “mathematical exactness” pays homage to this ideal of mathematicians.

The plight of man is pitiable. We are wanderers in a vast universe, helpless before the havocs of nature, dependent upon nature for food and other necessities, and uninformed as to why we were born and what to strive for. Man is alone in a cold and alien universe. He gazes upon the mysterious, rapidly changing, and endless world about him and is confused, baffled, and even frightened by his own insignificance.

The life of man is solitary, poor, nasty, brutish, and short. He is the prey of trivial happenings.