Your search for: franz AND kline

Our current intellectual system provides us with a far more complete and accurate understanding of nature and ourselves than was available in any previous society. This gain in understanding has arisen from two sources: the use of the "scientific method", and the breaking up of our intellectual ...

Our current intellectual system provides us with a far more complete and accurate understanding of nature and ourselves than was available in any previous society. This gain in understanding has arisen from two sources: the use of the "scientific method", and the breaking up of our intellectual enterprise into increasingly narrower disciplines and research programs. However, we have failed to keep these narrow specialties connected to the intellectual enterprise as a whole. The author demonstrates that this lack of connection to the overall enterprise causes a number of difficulties. We have no viewpoint from which we can understand the relationships among the various disciplines. We lack a forum for adjudicating situations where different disciplines give conflicting answers to the same problem. We seriously underestimate the differences in methodology and in the nature of principles in the various branches of science. This provocative and wide-ranging book delineates these and other related difficulties, examines their sources in detail, and suggests solutions. The book erects three overviews of the complete intellectual terrain, creates a quantitative measure for the complexity of any system, and examines the important effects of the limitations of the human mind on scholarship.

This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of ...

This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Gödel on recent mathematical study.