Poetry of the Universe: A Mathematical Exploration of the Cosmos | Astronomy Book for Science Lovers | Perfect for Students, Researchers & Space Enthusiasts

This book about the development of non-Euclidean geometry.It is a great book on its subject and a must read, though challenging, (the unreferenced footnotes at the back of the book- which are a great addition- does not help in reading this book), the effort is well worth it.One of the most important ideas contained in this book is on p. 192, which is a footnote to p. 104 in the main text. It is too long quote in full but the jest is:"Taken together with other efforts throughout the 1920's, both observational and theoretical, to try to establish first the reality and second the meaning of de Sitter's 1917 prediction of a redshift-distance relation, they constitute a body of work that makes all the more mysterious the myth of Hubble's sudden discovery of the relation in 1929."Having said that Osserman does not go where Morris Kline goes re: "Non-Euclidean Geometries and Their Significance," which is found in Kline's "Mathematics for the Nonmathematician" and "Mathematics- The Loss of Certainty," et. al., both are recommended.From the front cover piece of "Mathematics- The Loss of Certainty ... refutes the myth that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible," regarding the significance of the development of Non-Euclidean geometries in the 1800's. "For two thousand years the entire intellectual world accepted the Greek doctrine that the axioms of Euclidean geometry and of mathematics in general, were truths about the physical world, truths so clear and so evident that no one in his (or her) right mind could question them." ("Nonmathematician" p. 452-453).Kline also says: "Gauss had the intellectual courage to create non-Euclidean geometry but not the moral courage to face the mobs, for the scientists of the early nineteenth century lived in the shadow of Kant whose pronouncement that there could be no geometry other than Euclidean geometry ruled the intellectual world. Gauss's work on non-Euclidean geometry was found among his papers after his death." See also: Lobachevski; Bolyai and Riemann.Finally Kline again: "The implication of non-Euclidean geometry, namely, that man may not be able to acquire truths, affects all thought." ("Nonmathematician" p. 476).The point is, Osserman's book is a great exposition on the development non-Euclidean geometry.John Wheeler's sentence should also be included: "Matter and energy tell space how to curve and space tells them how to move," is in a lot of books on Gravity.