What do you think?
Rate this book
The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
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, it is also fundamental to the very nature of our universe.
377 pages, Paperback
First published September 7, 2010
132 people are currently reading
1977 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 53 reviews
February 27, 2015
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 glimpse at the universe at its smallest scale. The strange thing is that it took the writing of a mathematician, and not a physicist to get me there.
A word of caution: This book, even though it stimulates comprehension in its metaphors, is highly inaccessible even to someone who is a fan of theoretical physics. Many of the pages will seem like jargon or worse. However, the key points of this are accessible if you have the capacity. Be honest with yourself. If you have a tough time reading physics trade books, don't bother.
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 glimpse at the universe at its smallest scale. The strange thing is that it took the writing of a mathematician, and not a physicist to get me there.
A word of caution: This book, even though it stimulates comprehension in its metaphors, is highly inaccessible even to someone who is a fan of theoretical physics. Many of the pages will seem like jargon or worse. However, the key points of this are accessible if you have the capacity. Be honest with yourself. If you have a tough time reading physics trade books, don't bother.
October 23, 2012
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 understandable only to people who majored in math or physics as undergraduates.
The author is a mathematician, not a physicist. However, the mathematics that he discovered in the 1970s has been found to be extremely useful to theoretical physicists in the 1980s and 1990s. Yau's specialty is non-linear partial differential equations applied to differential geometry. His work has application to General Relativity and String Theory.
The author is a mathematician, not a physicist. However, the mathematics that he discovered in the 1970s has been found to be extremely useful to theoretical physicists in the 1980s and 1990s. Yau's specialty is non-linear partial differential equations applied to differential geometry. His work has application to General Relativity and String Theory.
February 17, 2014
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 shaped our thought on the nature of physical reality and involved an entire generation of theoretical physicists in research. This is partly autobiographical and hence makes it very interesting to read as he explains his odyssey. We get to read the contributions of leading physicists in this adventure; the growth of string theory as major force in theoretical physics. This is an outstanding book to read, but requires undergraduate level physics and strong interest in geometry.
A summary of this book is as follows: In string theory, the myriad of fundamental particle types is replaced by a single fundamental building block, a string. As the string moves through time it traces out a tube or a sheet (the two-dimensional string worldsheet), and different vibrational modes of the string represent the different particle types. The particles known in nature are bosons (integer spin) or fermions (half integer spin). By introducing supersymmetry to string theory both bosons and fermions could be accounted for, and with ten-dimensions, the mathematical requirements of string theory are completely satisfied. In addition, the anomalies and inconsistencies that plagued string theory are vanished. Until superstring theory came into existence, any predictions and calculations yielded nonsensical results, and were incompatible with quantum physics. The ten-dimensions consist of two sets four-dimensional spacetime we live in, and six-spatial dimensions in a hidden state in an invisible state because they are compactified to minute size. In this geometry, every point has a six-dimensional Calabi-Yau manifold in a compactified form, thus bringing physicists to the doorsteps of Calabi-Yau geometry.
Some physicists had originally hoped that there was only one Calabi-Yau manifold that would uniquely describe the hidden dimensions of string theory, but there are a large number of such manifolds each having a distinct topology. Within each topological class there are an infinitely large number of such Calabi-Yau manifolds. The Calabi-Yau space is further complicated by the fact that it has twisting multidimensional holes (about 500) running through the space. Another problem is; what makes the six-dimensions of space stable in a compactified form? It would be like constraining an inner tube with a steel belted radial tire. Just as the tire will hold back the tube as you pump air into it. All the moduli of the Calabi-Yau, both shape moduli and size moduli needs to be consistently stabilized. Otherwise the there is nothing to keep six hidden dimensions from unwinding and becomes infinitely large. It turns out that the D-branes of string physics can curb the tiny manifold's inclination to expand.
Some physicists have considered other types of spaces besides Calabi-Yau manifolds; they include non-Kahler compactification, and some non-geometric compactification postulates. In the beginning of the book , the author states : If Einstein's relativity is proof that geometry is gravity, string theorists hope to carry that notion a good deal further by proving that geometry, perhaps in the guise of Calabi-Yau manifolds is not only gravity but physics itself." In the latter part of the book the author takes a conciliatory mode by stating "Despite my affection for Calabi-Yau manifolds - a fondness that has not been diminished over the past thirty-some years - I am trying to maintain an open mind on the subject," ............."If it turns out that non-Kahler manifolds are ultimately of greater value to string theory than Calabi-Yau manifolds, I'm OK with that."
There are many success stories of mathematical reasoning; one such is the prediction of positrons by Paul Dirac. The biggest shortcomings of the Calabi-Yau space and the superstring theory and brane world is even though there is beauty and elegance in the setup but it still needs to make predictions which can be confirmed by the experiments. The results of LHC experiments so far have not resulted in satisfactory conclusions.
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 shaped our thought on the nature of physical reality and involved an entire generation of theoretical physicists in research. This is partly autobiographical and hence makes it very interesting to read as he explains his odyssey. We get to read the contributions of leading physicists in this adventure; the growth of string theory as major force in theoretical physics. This is an outstanding book to read, but requires undergraduate level physics and strong interest in geometry.
A summary of this book is as follows: In string theory, the myriad of fundamental particle types is replaced by a single fundamental building block, a string. As the string moves through time it traces out a tube or a sheet (the two-dimensional string worldsheet), and different vibrational modes of the string represent the different particle types. The particles known in nature are bosons (integer spin) or fermions (half integer spin). By introducing supersymmetry to string theory both bosons and fermions could be accounted for, and with ten-dimensions, the mathematical requirements of string theory are completely satisfied. In addition, the anomalies and inconsistencies that plagued string theory are vanished. Until superstring theory came into existence, any predictions and calculations yielded nonsensical results, and were incompatible with quantum physics. The ten-dimensions consist of two sets four-dimensional spacetime we live in, and six-spatial dimensions in a hidden state in an invisible state because they are compactified to minute size. In this geometry, every point has a six-dimensional Calabi-Yau manifold in a compactified form, thus bringing physicists to the doorsteps of Calabi-Yau geometry.
Some physicists had originally hoped that there was only one Calabi-Yau manifold that would uniquely describe the hidden dimensions of string theory, but there are a large number of such manifolds each having a distinct topology. Within each topological class there are an infinitely large number of such Calabi-Yau manifolds. The Calabi-Yau space is further complicated by the fact that it has twisting multidimensional holes (about 500) running through the space. Another problem is; what makes the six-dimensions of space stable in a compactified form? It would be like constraining an inner tube with a steel belted radial tire. Just as the tire will hold back the tube as you pump air into it. All the moduli of the Calabi-Yau, both shape moduli and size moduli needs to be consistently stabilized. Otherwise the there is nothing to keep six hidden dimensions from unwinding and becomes infinitely large. It turns out that the D-branes of string physics can curb the tiny manifold's inclination to expand.
Some physicists have considered other types of spaces besides Calabi-Yau manifolds; they include non-Kahler compactification, and some non-geometric compactification postulates. In the beginning of the book , the author states : If Einstein's relativity is proof that geometry is gravity, string theorists hope to carry that notion a good deal further by proving that geometry, perhaps in the guise of Calabi-Yau manifolds is not only gravity but physics itself." In the latter part of the book the author takes a conciliatory mode by stating "Despite my affection for Calabi-Yau manifolds - a fondness that has not been diminished over the past thirty-some years - I am trying to maintain an open mind on the subject," ............."If it turns out that non-Kahler manifolds are ultimately of greater value to string theory than Calabi-Yau manifolds, I'm OK with that."
There are many success stories of mathematical reasoning; one such is the prediction of positrons by Paul Dirac. The biggest shortcomings of the Calabi-Yau space and the superstring theory and brane world is even though there is beauty and elegance in the setup but it still needs to make predictions which can be confirmed by the experiments. The results of LHC experiments so far have not resulted in satisfactory conclusions.
January 14, 2014
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 most laypeople, I longed for more illustrations, but the ones Yau gives are powerfully explanative. I obviously can't comment on the accuracy or quality of Yau's body of work or his speculations about string theory. I will hope an expert will comment.
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 most laypeople, I longed for more illustrations, but the ones Yau gives are powerfully explanative. I obviously can't comment on the accuracy or quality of Yau's body of work or his speculations about string theory. I will hope an expert will comment.
March 18, 2014
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 realization that I no longer even had a general feeling for what the author was talking about. Up until then, I was able to at least keep up a vague understanding. Maybe I will try again later.
July 8, 2011
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.
January 26, 2018
I learned some stuff, but the author spent a lot of chapters patting himself on the back and I would have preferred a more general explanation of the mathematics of string theory rather than just 'look at all the stuff I'VE done'.
January 30, 2017
Karabiyard manifold
It's wonderful ,intriguing and difficult for me to read it.
It's wonderful ,intriguing and difficult for me to read it.
October 16, 2010
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. A worthwhile read if the topic is of interest.
January 16, 2012
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 in the field.
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 in the field.
March 3, 2016
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.
December 22, 2011
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.
March 12, 2021
Secondo la leggenda, Platone avrebbe fatto collocare sopra l’ingresso dell’Accademia ateniese un’iscrizione come questa: “Che nessuno entri ignaro della geometria”; una volta letto “La forma dello spazio profondo” potreste entrare nell’accademia di Platone. È come esplorare una caverna profonda e oscura dove la bellezza della matematica è capace di essere l’unica guida che possa venirci in soccorso.
Shing-Tung Yau e Steve Nadis ci raccontano una storia tremendamente complessa, in un diario, non un riassunto, un’incursione nella parte più intima e inaccessibile dell’Universo: le varietà di Calabi-Yau. Si tratta dela struttura portante della Teoria delle Stringhe, la teoria che più di ogni altra osa rivelare i misteri ultimi dell’Universo, la prima a riuscire nell’intento di quantizzare in modo coerente la gravità e quindi far parlare il microcosmo con il macrocosmo. Una teoria non ancora dimostrata, una teoria in fase di sviluppo e di ricerca, una teoria troppo bella per non essere vera, una teoria che ha dalla sua parte la matematica. Come affermava il fisico inglese Paul Dirac : “La bellezza matematica costituisce il criterio ultimo per decidere la linea di avanzamento della fisica teorica”.
Sembra impossibile che spazi più piccoli di quelli che si possono umanamente immaginare, siano in grado di esercitare un’influenza tanto profonda su ogni parte dell’Universo, al punto da diventarne un tratto distintivo e caratterizzante. Eppure è così.
Spesso si dice che la matematica sia il linguaggio della scienza o, quanto meno, il linguaggio della fisica: il che è certamente vero. Le leggi fisiche possono essere enunciate con precisione soltanto in termini di equazioni matematiche, piuttosto che a parole. Tuttavia pensare alla matematica soltanto come a un linguaggio non rende giustizia. È impossibile non meravigliarsi per “l'irragionevole efficacia della matematica nelle scienze naturali”. Come possono meri costrutti matematici, senza apparentemente alcun nesso con il mondo della natura, descriverlo con tanta precisione? È difficile dire perché idee fondamentalmente matematiche continuino a spuntare in natura. Richard Feynman trovava egualmente difficile spiegare perché tutte le leggi fisiche siano proporzioni essenzialmente matematiche. La chiave risolutiva di questi rompicapo potrebbe trovarsi nel nesso esistente tra matematica, natura e bellezza. Lo stesso scienziato affermava: “è difficile trasmettere a coloro che non sappiano di matematica una sensazione reale riguardo alla bellezza, alla più profonda bellezza della natura”.
In uno dei tanti aneddoti che Yau, professore emerito di Matematica presso l’università di Harvard, si concede tra le righe di questo libro, apprendiamo: “[...] avevo precisamente quella sensazione quando incontrai colei che sarebbe divenuta mia moglie, però è vero che non saprei da dove cominciare, se dovessi esprimere a parole quello che esattamente provai. Sia detto senza offesa per mia moglie: ho sperimentato qualcosa di simile, ho provato cioè quel vago senso di euforia che ci pervade e ci rende inquieti, quando a metà degli anni settanta dimostrai la congettura di Calabi”.
Leggete questo libro con estrema calma, non lo sovrapponete a nessun’altra lettura, non importa cosa e quanto ne capirete, di sicuro sarete grati, a Yau, a Calabi, alla natura.
Shing-Tung Yau e Steve Nadis ci raccontano una storia tremendamente complessa, in un diario, non un riassunto, un’incursione nella parte più intima e inaccessibile dell’Universo: le varietà di Calabi-Yau. Si tratta dela struttura portante della Teoria delle Stringhe, la teoria che più di ogni altra osa rivelare i misteri ultimi dell’Universo, la prima a riuscire nell’intento di quantizzare in modo coerente la gravità e quindi far parlare il microcosmo con il macrocosmo. Una teoria non ancora dimostrata, una teoria in fase di sviluppo e di ricerca, una teoria troppo bella per non essere vera, una teoria che ha dalla sua parte la matematica. Come affermava il fisico inglese Paul Dirac : “La bellezza matematica costituisce il criterio ultimo per decidere la linea di avanzamento della fisica teorica”.
Sembra impossibile che spazi più piccoli di quelli che si possono umanamente immaginare, siano in grado di esercitare un’influenza tanto profonda su ogni parte dell’Universo, al punto da diventarne un tratto distintivo e caratterizzante. Eppure è così.
Spesso si dice che la matematica sia il linguaggio della scienza o, quanto meno, il linguaggio della fisica: il che è certamente vero. Le leggi fisiche possono essere enunciate con precisione soltanto in termini di equazioni matematiche, piuttosto che a parole. Tuttavia pensare alla matematica soltanto come a un linguaggio non rende giustizia. È impossibile non meravigliarsi per “l'irragionevole efficacia della matematica nelle scienze naturali”. Come possono meri costrutti matematici, senza apparentemente alcun nesso con il mondo della natura, descriverlo con tanta precisione? È difficile dire perché idee fondamentalmente matematiche continuino a spuntare in natura. Richard Feynman trovava egualmente difficile spiegare perché tutte le leggi fisiche siano proporzioni essenzialmente matematiche. La chiave risolutiva di questi rompicapo potrebbe trovarsi nel nesso esistente tra matematica, natura e bellezza. Lo stesso scienziato affermava: “è difficile trasmettere a coloro che non sappiano di matematica una sensazione reale riguardo alla bellezza, alla più profonda bellezza della natura”.
In uno dei tanti aneddoti che Yau, professore emerito di Matematica presso l’università di Harvard, si concede tra le righe di questo libro, apprendiamo: “[...] avevo precisamente quella sensazione quando incontrai colei che sarebbe divenuta mia moglie, però è vero che non saprei da dove cominciare, se dovessi esprimere a parole quello che esattamente provai. Sia detto senza offesa per mia moglie: ho sperimentato qualcosa di simile, ho provato cioè quel vago senso di euforia che ci pervade e ci rende inquieti, quando a metà degli anni settanta dimostrai la congettura di Calabi”.
Leggete questo libro con estrema calma, non lo sovrapponete a nessun’altra lettura, non importa cosa e quanto ne capirete, di sicuro sarete grati, a Yau, a Calabi, alla natura.
May 15, 2024
(Currently reading)
Notes:
While this may be hard to accept, we've learned in the past century that whenever we stray far from the realm of everyday experience, our intuition can fail us. If we travel extremely fast, special relativity tells us that time slows down, not something you're likely to intuit from common sense. If we make an object extremely small, according to the dictates of quantum mechanics, we can't say exactly where it is. When we do experiments to determine whether the object has ended up behind Door A or Door B, we find it's neither here nor there, in the sense that it has no absolute position. (And it sometimes may appear to be in both places at once!) Strange things, in other words, can and will happen, and it's possible that tiny, hidden dimensions are one of them.
——————-
1.5-Let's picture our infinite, four-dimensional spacetime as a line that extends endlessly in both directions. A line, by definition, has no thickness.
But if we were to look at that line with a magnifying glass, as suggested in the Kaluza-Klein approach, we might discover that the line has some thickness after all--that it is, in fact, harboring an extra dimension whose size is set by the diameter of the circle hidden within.
———————
But ultimately, Kaluza-Klein theory was discarded. In part this was because it predicted a particle that has never been shown to exist, and in part because attempts to use the theory to compute the ratio of an electron's mass to its charge went badly awry. Furthermore, Kaluza and Klein-as well as Einstein after them--were trying to unify only electromagnetism and gravity, as they didn't know about the weak and strong forces, which were not well understood until the latter half of the twentieth century. So their efforts to unify all the forces were doomed to failure because the deck they were playing with was still missing a couple of important cards. But perhaps the biggest reason that Kaluza-Klein theory was cast aside had to do with timing: It was introduced just as the quantum revolution was beginning to take hold.
Notes:
While this may be hard to accept, we've learned in the past century that whenever we stray far from the realm of everyday experience, our intuition can fail us. If we travel extremely fast, special relativity tells us that time slows down, not something you're likely to intuit from common sense. If we make an object extremely small, according to the dictates of quantum mechanics, we can't say exactly where it is. When we do experiments to determine whether the object has ended up behind Door A or Door B, we find it's neither here nor there, in the sense that it has no absolute position. (And it sometimes may appear to be in both places at once!) Strange things, in other words, can and will happen, and it's possible that tiny, hidden dimensions are one of them.
——————-
1.5-Let's picture our infinite, four-dimensional spacetime as a line that extends endlessly in both directions. A line, by definition, has no thickness.
But if we were to look at that line with a magnifying glass, as suggested in the Kaluza-Klein approach, we might discover that the line has some thickness after all--that it is, in fact, harboring an extra dimension whose size is set by the diameter of the circle hidden within.
———————
But ultimately, Kaluza-Klein theory was discarded. In part this was because it predicted a particle that has never been shown to exist, and in part because attempts to use the theory to compute the ratio of an electron's mass to its charge went badly awry. Furthermore, Kaluza and Klein-as well as Einstein after them--were trying to unify only electromagnetism and gravity, as they didn't know about the weak and strong forces, which were not well understood until the latter half of the twentieth century. So their efforts to unify all the forces were doomed to failure because the deck they were playing with was still missing a couple of important cards. But perhaps the biggest reason that Kaluza-Klein theory was cast aside had to do with timing: It was introduced just as the quantum revolution was beginning to take hold.
This entire review has been hidden because of spoilers.
September 2, 2018
This book presents a point of view on the development of a large swathe of modern geometry from the perspective of co-author Shing-Tung Yau. Professor Yau is a famous mathematician whose path from a shop assistant to a leading authority in several areas of modern mathematics could inspire many young mathematicians. Yet there is a twist to this story. For decades Professor Yau was trying to set up a team of mathematicians to direct an attack towards Poincare Conjecture, one of the most famous problems in Mathematics, until Grigory Perelman got there alone. This was a great leap for humanity, but for Professor Yau the achievement of Perelman was also a disappointment. Professor Yau was criticized for his reaction and comments and it tarnished his reputation for years. In a way the book is an apology of Professor Yau where he carefully explains his view of Geometry as a field interconnected with Physics where every new theorem leads to new avenues of research in the quest for The Theory of Everything and every new model in Physics provides new methods leading to new results in Geometry. I would recommend the book as a necessary side reading for every student of Geometry as the book carefully explains the motivation behind the study of some of the most obscure and counter-intuitive mathematical objects.
July 17, 2017
A thorough read for all those looking for the beauty and truth in mathematical intricacy, and how far we have come in employing mathematical tools in understanding the deepest cores of nature, and the way physicality moves.
Significantly toned down on mathematical rigor though. A mathematically inclined reader many a times would find themselves looking for more of mathematically crisper description. The language and verbalization is flawless (credit to Steve Nadis). An entire book dedicated to Calabi-Yau manifold (credit to Shing-Tung Yau for sharing his expertise), and its historical background is simply irresistible: A much needed volume, especially for those looking to understand what advanced mathematics is, but not necessarily have a math background.
Read if you want to understand how mathematics is way much more than calculating.
Neeti.
Significantly toned down on mathematical rigor though. A mathematically inclined reader many a times would find themselves looking for more of mathematically crisper description. The language and verbalization is flawless (credit to Steve Nadis). An entire book dedicated to Calabi-Yau manifold (credit to Shing-Tung Yau for sharing his expertise), and its historical background is simply irresistible: A much needed volume, especially for those looking to understand what advanced mathematics is, but not necessarily have a math background.
Read if you want to understand how mathematics is way much more than calculating.
Neeti.
May 13, 2019
Prof Yau explains the book in a very delicate and simple language to understand for non-physicist. There might be some geometrical (mathematical) definitions for example manifold that would allow you to enjoy the book to the fullest.
Thank you Prof Yau. You've inspired me a lot by writing this book.
Thank you Prof Yau. You've inspired me a lot by writing this book.
September 13, 2025
It’s good pop science and pop math. Dense, but with attempts made to explain the ideas with pictures and analogies. Naturally Yau’s biases come through, regarding e.g. priority disputes. Nevertheless I found it informative and intriguing. String theory’s success in physics seems suspect, but its mathematical successes are certainly worth of our praise and study.
October 25, 2019
Fascinating trek through bits and pieces of contemporary topology and geometry. Their relationship with string theory is elaborated upon. The memoiresque component colors the book with the excitement personal narrative can lend. Excellent treatment of material for lay audience. Fun explorations.
February 9, 2019
Good book. Chunks of it still left me confused. String theory math is hard.
February 23, 2019
A somehow a semi-popular explanation of the latest phenomenal concept introduced in String theory about the nature of the inner most structure of physical reality
May 19, 2023
Read in 2018-2019. During my astronomy phase though I've never been great at understanding math so it was boring and hard to grasp for me at the time. Nevertheless an intriguing read!
November 11, 2024
What's a hole?
January 2, 2012
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 Wikipedia. I was out-grappled by the second half, for which I need some cross-training (astronomy and physics?) before I can do a round 2. This is of course a good reminder of my weak fundamentals, and motivation is never bad.
Feels like: a mathematical physics version of "In Search of Memory," which gave me an extremely similar experience.
Feels like: a mathematical physics version of "In Search of Memory," which gave me an extremely similar experience.
December 22, 2014
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 impossible, because "we do not really understand it". Same is probably true here. Notice the clear distinction here between understanding a concept versus understanding a hopelessly long mathematical proof. Ontologically there may be no difference between the two. In practice, however, for a subject sitting so closely to reality, physics has no mathematical excuses.
March 5, 2011
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, but I found the discussion totally inspiring. And the book left me with a new slant on the world--and, indeed, the universe--that I hope will stay with me for a long time.
August 24, 2016
The Calabi-Yau manifolds that I discovered ... my graduate student (..) ... the SYZ conjectured named after me ... Did I mention the Calabi-Yau manifolds named after me?
But actually the first 100 pages interested me, when Yau described the his research into the important work he did in differential geometry. But then came the string theory bit for most of the book which is just not interesting to me due to its crazy and unverifiable nature (not to bash the theory or the notion of hypothesizing things that are out of current technological scope to investigate, but I just found it dry.)
But actually the first 100 pages interested me, when Yau described the his research into the important work he did in differential geometry. But then came the string theory bit for most of the book which is just not interesting to me due to its crazy and unverifiable nature (not to bash the theory or the notion of hypothesizing things that are out of current technological scope to investigate, but I just found it dry.)
May 2, 2012
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. Just bleep over the sections you don't understand and move on to the next paragraph or page.
October 2, 2014
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.
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.
September 21, 2012
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.
Displaying 1 - 30 of 53 reviews