A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space

Boris A. Rosenfeld

Sep 2012 · Studies in the History of Mathematics and Physical Sciences Book 12 · Springer Science & Business Media

About this ebook

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

Ratings and reviews

I have only browsed this, however it chronicles the development non-euclidean geometries remarkably well. Gauss' comments deciphered from his letters to friends reveals his warnings about the Gordian Knot.hidden all its quicksand. The book will become very popular as the Gaussian Knot will be cut in this decade revealing countless mathematicians which have tied up by it. Read this book to understand what is happening which will differentiate the lack of scientific method in mathematics from the coming theoretical mathematical physics revolution. The author displays a depth of knowledge which is presented in a compelling fashion that Leaves me unwilling to put this book down. I am a physicist who could not get enough mathematical theory. Gauss' genius will be in full display in this book as this generation of physicists pick up where Gauss left off. The sole of Gauss is in full display within these covers. Thank you Boris!