## review ì eBook or Kindle ePUB Õ John Stillwell

This book explores the history of mathematics from the Impossible PDFEPUB #195 the perspective of the creative tension between common sense and the impossible as the author follows the discovery or invention of new concepts that have marked mathematical progress Irrational. I uite enjoyed this book It deals with subjects in mathematics which were once considered impossible but which were later addressed in a surprising and fascinating voyage of intellectual discovery The first chapter on the irrationals is uite nice the concepts are explained nicely and clearly The second chapter about the imaginary and the complex numbers is uite nice too But I must say that I was left a bit disappointed herea yes there are very nice points about the geometry of complex number multiplication and corresponding rotationsb yes the mystical Euler's formula is there and it could not have been there ubiuitous as it is in mathematics and physics probably the most beautiful formula so far discovered formula which the physicist Richard Feynman called our jewel and the most remarkable formula in mathematics c yes the author also correctly points out that terms like complex and imaginary are very misleading BUT on the negative sidea the whole subject is treated only superficially in a small 20 page chapter and for example the fascinating subject of complex analysis is not even cursorily treated at least the Bezout's theorem is briefly mentioned b and while the author condemns terms such as imaginary and complex as misleading he fails to mention that complex numbers are real than real numbers in the sense that without complex numbers it is simply not possible to fully describe reality For example without complex numbers modern uantum mechanics would simply not be possible the wave function is a complex value function and when you multiply operators or state vectors you actually have to multiply complex numbers the matrix elements according to the rules of complex multiplication In uantum mechanics the determination of measurement outcome probabilities always include the suaring of absolute values of complex probability amplitudes defined by the wave function Complex numbers are simply fundamental for most predictions in modern science Chapter 3 on projective geometry is uite interesting although hardly mind blowing Chapter 4 about the infinitesimal is uite nice nothing new or revolutionary here but item 48 where with simple elegant trigonometric calculations and the application of geometric series the beautiful result that pi is encoded by an alternating seuence of fractions with odd denominators showing that the irrational transcendent pi has much to do with natural numbers as with geometry is really good Chapter 5 on curved space is really nice in particular 54 where the concept of Gaussian curvature is beautifully explained and where the beautiful Harriot's theorem later extended by Gauss is explained in a very nice manner Chapter 6 on uaternions is done very nicely as well but unfortunately it failed to really excite me as uaternions are not so cool any they have been at least partially superseded by other techniues in areas such as uantum mechanics however they still play an important role in calculations involving three dimensional rotations such as in three dimensional computer graphics Chapters 7 and 8 are pretty good Chapter 9 on the infinite is really nice It explains beautifully the concept of uncountable of potential versus actual infinity and the famous diagonal argument by Cantor is also explained But I did appreciate that the less famous but eually if no beautiful Harnack's theorem is explained as well it mind blowingly demonstrated that almost all real numbers are irrational and that almost all real numbers are transcendental contrarily to what intuition might drive us to believe Overall a nice and uite enjoyable book please note that it reuires at the very minimum high school maths if not preferably at tertiary level

### free download Yearning for the Impossible The Surprising Truths of Mathematics

Yearning for the Impossible The Surprising Truths of MathematicsUral context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape. Such a beautiful book

### John Stillwell Õ 3 summary

review Yearning for the Impossible The Surprising Truths of Mathematics Ô eBook or Kindle ePUB ☆ ❴Read❵ ➬ Yearning for the Impossible The Surprising Truths of Mathematics Author John Stillwell – Johns-cycling-diary.co.uk This book explores the history of matheAnd Imaginary Numbers The Fourth Dimension Curved Space Infinity and others The author puts these creations into a broader context involving related impossibilities from art literature philosophy and physics Yearning for PDF or By imbedding mathematics into a broader cult. I like this book uite a bit The writing is good but the metaphor becomes extended and forced The idea is that much of what we need to calculate things that have real existence comes from a consideration of mathematics thought to be impossible or irrational or imaginary It's very well done but I felt that I got it about halfway through I think it is time for me to read some shorter essays and popular excursions on mathematical topics