This is a great book!



It tells the dramatic story behind the story of the creation of non Euclidean geometry.



In that way it's about its subject in the same way that the Holy Grail stories are about the knights who sought it and not the Holy Grail itself.



Yes. You will get a coffee table understanding of the mathematics involved. About twenty three centuries ago the ancient Greek Euclid published his masterwork Elements in which he laid out five postulates for geometry. Most significant among them was postulate number five which said that two parallel lines would never meet.



From his perspective in ancient Greece, Euclid had apparently noticed that if you lay a piece of paper on a flat table and draw two parallel lines, they never meet. In his mind he must have imagined an infinitely flat table with infinitely parallel lines but still the same result...they never met.



The frustrating thing...as pointed out in this book...is that no one was able to actually prove Euclid's conjecture on the nature of parallel lines. For those unversed in such matters, mathematical proofs require an unmatched logical rigor. If social sciences set their bar at shoulder level and hard sciences set the bar at ceiling level then surely mathematics can be said to set the bar at the moon and beyond.



Needless to say, no one's proof of Euclid's fifth made the cut. And as it turned out it took until the nineteenth century before mathematicians were born would decided that the cut couldn't be made because the underlying postulate was unproveable. In this way, this book would be excellent reading next to Richard Kuhn's Structure of Scientific Revolutions.



In his book, Kuhn asserted and proved that scientific advance basically occurs "one funeral at a time." Kuhn said that new discoveries are first denied, then minimalized and only ultimately belatedly accepted and celebrated for the new truths they uncover. And in a serviceable way, this book shows each step of the process.



And beyond all that, this book shows how by challenging canon, renegade mathematicians were able to create a mathematical canvas upon which Einstein could actually come to paint his relativity where parallel lines can meet and surprising realities can come into being.

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