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The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
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The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions

3.87 of 5 stars 3.87  ·  rating details  ·  377 ratings  ·  36 reviews
According to string theory, we live in a ten-dimensional universe; but only four are accessible to our everyday senses. The remaining six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, shows that not only is geometry fundamental to string theory, i ...more
Paperback, 377 pages
Published March 6th 2012 by Basic Books (first published September 7th 2010)
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Mathematicians aren't really known for their writing skills. I mean come on, they scribble numbers, greek letters, and symbolic junk in general on a whiteboard expecting every layman to understand it. They even deviate from their own mathematical language and substitute conventional symbols for their own, then frown upon their colleagues if they fail to grasp the concept that they're talking about. But don't fret, The Shape Of Inner Space is written in plain english, and written well. It's about ...more
Yau proudly reviews how he came to discover Calabi-Yau spaces. I thought most of the high-level summaries of technical mathematical theorems were tedious and unenlightening.
Michael Connolly
Yau grew up in Hong Kong. He came to America as a young man and studied under Charles Morrey and S.S. Chern at the University of California at Berkeley. I was lucky enough to take classes from all three men when I was a student at Berkeley. Because my Ph.D. was in biophysics and not mathematics, I don't know enough math to read Yau's technical papers, so I appreciate having this plain-English explanation of his ideas. This book has no equations, but is still rather technical, and will be underst ...more
Laura Burroughs
Shing-Tung Yau gave me glimpses into the beauty of math that I never saw sitting in my high school and college classes. His enthusiasm and wonder at the elegance of universe resonates within the pages of his book.

But The Shape of Inner Space is for a narrow audience that consists of mathematicians, physicists, and nerdy types like me who don't mind slogging through some pretty cerebral stuff to glean a fuzzy, rudimentary, understanding of the interplay between geometry and string-theory.

Like mo
I wanted to really try and understand this book, but there were too many words and not enough graphic explanations of something that is inately ALL graphic. It is just too dificult to describe with words the detailed geometrical thinking that you need in order to keep up with the author. I love Geometry, but my natural ability for understanding 3-D modeling did not help me in understanding the higher dimensions talked about in this book. Exactly half-way through the book, I came to the realizati ...more
Daniel R.
An approachable book covering a range of complex and compelling topics in string theory and geometry. The book focuses on discoveries in geometry from the perspective of Shing-Tung Yau, a Fields Medal winner, and how the growing collaboration between mathematicians and physicists is advancing both fields. I didn't come away with a deep understanding of the topics covered in the book, I suspect a second or third reading would be required, but did come to appreciate the problems now being tackled. ...more
This book is written by famed Chinese-American mathematician Shing-Tung Yau, who did pioneering work in the mathematics of string theory.

I actually knew Prof. Yau when I was a graduate student at Stanford University in the 1970s. I chatted with him in Cantonese, and we also talked philosophy and religion from time to time. My thesis work was in a different field than this, but I have always followed his work. It was a pleasure to read this book that sets out so ably these important developments
The development of the concept of hidden spaces in string theory - A historical perspective

This is a fascinating story about the development of the mathematical concept of extra spatial dimensions known as Calabi-Yau spaces and its application in the string theory. The author speaks candidly, and describes his excitement at emerging new ideas in physics and mathematics, and how it progressed in string theory, and in the process changed his perspectives. Over the last 35 years this idea has shape
Yunjiang Jiang
I don't know how I ended up reading almost the entire thing. The book tries ambitiously to convey the essence of string theory, Kalabi-Yau conjecture, etc in a mere 300 page of layman's words, through the narrative of a professional writer and perhaps not even an amateur mathematician/physicist. One has to recall Richard Feynman being asked to explain half-spin Dirac-Fermi particles in a way that's understandable to a freshman class and responded famously after moments of pause that he found it ...more
Eric Wurm
I have in the past had trouble grasping string theory as a proto-science major and non-physicist. However, this is the best book on string theory I have ever read. Now, I'm not about to start spewing out equations that elucidate string theory to non-physicists. However, I feel I can explain the tenets and the consequences well even to someone that has never heard of it.

This is not only one of the best science books I have read, it is among the best books I have read. I feel like I have a glimps
I have read many popular science books and find them hit and miss when it comes to explaining advanced concepts. This book is by far the best book I've ever read on string theory. I love his geometric perspective on everything because that's how I think too. Even his digressions are great!

The more math you know, the more you will get out of this book. In my case I was very pleased that he connected some dots with math that had always been unclear to me from other popularizations of the topic.
While "The Shape of Inner Space" fails at being a popular science book, it succeeds at being what popular science books were meant to be, which is to share interesting ideas with you if you wrestle with it. It also pretends to be an autobiography of Yau but really succeeds at being a biography of the Calabi-Yau manifold. The first half was an absolute delight to work out, like mental LEGO collection, and I managed to learn some good math and physics along the way mostly with the help of Wikipedi ...more
David McAliley
This is not a light or easy read, but it has some great information. Very detailed about the process of development for the Calabi-Yau manifolds that are helping to explain the most intricate details of our physical universe.
THE SHAPE OF INNER SPACE is guaranteed to take readers places they've never been before, nor thought about before. That was certainly the case for me. Before I read this book, I had never heard of Calabi-Yau manifolds, and it had never occurred to me that someone could write an entire book on the subject--let alone a book as fascinating as this one. The authors did an exceptionally skillful job presenting complicated ideas from math and physics. I can't claim to have understood every single word ...more
I've never taken a physics course in my life, yet I "got" many of his explanations. The autobiographical part of the book was most appealing, detailing his impoverished childhood, how he dabbled in gang crime!, eventually turning to math, which saved him from violent street life. Also liked his poems- they made his enthusiasm for his subject matter obvious. Even if you have little scientific background, you will come away with some knowledge of the "manifolds" that (might) make up our universe. ...more
Alan Dean
Be warned: this is not for readers who are not familiar with the subject, but if you are at the point of saying "I'm bored with the same-old pop science books about particle physics" then this is an excellent next-step in your reading. Be warned though, there are some pretty heavy-duty parts. However, if you want to understand why particle physicists believe certain theories 'because of their beauty' then this will give you a glimpse into their inner eye and it is an astonishing vision.
would almost put this on my worldview shelf, but i can't say i actually understand it. it's about the six dimensional compact manifolds that are said to be the extra dimensions in our universe. highly speculative on the physics front. apparently it's super useful on the mathematics front, but i just simply can't grasp that. he says something like, "now we can describe these spaces and count the curves and tangent lines and shit!" and i'm like so?

but really interesting.
George Musser
It's very hard to assign a rating to this book. For people with a math or physics background, it should get five stars: it explains the math underlying string theory (and much besides) at a more intuitive level than textbooks or research papers typically do. But for the general reader, it deserves maybe two stars: it assumes a great deal of background and motivation to work through the topic.
Great read - it is slightly different from Brian Greene's string theory exposition, focusing more on mathematics - topology and geometry in particular, and hence a good complementary text for those reading Greene. While often the topics are inaccessible, those who have a little bit of ideas on differential equations, manifolds, analysis will be able to relate many ideas in it.
Ahmad Hazazi
This book basically is an autobiography books about the main author, Shing-Ting Yau. It's about his mathematical works the so-called "Calabi Yau manifold". This is one of the geometrical notions in mathematics that used to be the mathematical foundations of string theory. Well, what can I say it is worth to read for those who has a background in geometry.
Didn't read this in detail, but, turns out Yau here has ( had ) the same problem I did as a kid ( reading numbers backwards ) He asserts that only a mathmatician would ever have thought that the solution to the weird physical conundurms of QM etc would be due to higher dimenions of space. ( No , it's the very first thing everyone thought of )
Brett Peppler
This is another one of those science books thats turns into an autobiography to flush it out to 300 pages to justify it as a book. But... The science bits are incredible. I'm a string theory fan, but I'd never been introduced to string theory from a geometry perspective, which is a really intuitive way to do it.
Excellent book about Calabi-Yau manifolds and String Theory by the great Yau himself.
I think I needed a better background in math- in particular advanced geometry- to understand much of what Prof. Yau was talking about, although I did appreciate some of his explanations and how his work relates to string theory. Definitely not a book for the layperson.
Steve Schlutow
A good book, and not an easy read-I guess one could guess that from the title.. The book answered questions that I had, for example, why 10 dimensions? The authors answered it, and with visual geometry.. Again, I thought it was a very good book..
Read for science book club. Challenging - I'm glad I read it! We had a good conversation about the book, and I feel more comfortable about what I DO know and DON'T know about the geometry of string theory.
Scott Hotes
So far so good. I'm glad Yau is not using this as a vehicle to defend string theory, leaving that up to the physicists. Great insight into the world of research mathematics as a profession.

"shape of inner space" offers the possibility to understand the conjectures that founded the basics of string theory and the beauty of the math underlying it.
great opening chapters but then descends to levels of total insanity (which admittedly have a certain poignancy in their own right)
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S.S. Chern: A Great Geometer of the Twentieth Century Tsing Hua Lectures on Geometry & Analysis Surveys In Differential Geometry, Vol. 8: Lectures On Geometry And Topology Held In Honor Of Calabi, Lawson, Siu, And Uhlenbeck (2010 Re Issue) Chern: A Great Geometer of the Twentieth Century Gorenstein Quotient Singularities in Dimension Three

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