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The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry Illustrated Edition, Kindle Edition
Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems.
With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.
“The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe
“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe
“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
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Editorial Reviews
Review
"Fascinating, and an essential read for anyone interested in the history of modern mathematics.”—Peter Woit, Columbia University, Not Even Wrong
“Traces the remarkable arc of Yau’s life, from poverty and exile in Hong Kong to international renown as a Chinese-American mathematician and the first Chinese winner of the Fields Medal, often described as the Nobel Prize of mathematics.”—Science News
"A well-written and readable story of a very accomplished man’s life."—Mathematical Association of America Reviews
“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading. . . . [Yau’s] account of life in his natural home—mathematics—and his quest to uncover deep truths about nature proves to be a terrific read.”—Judith Goodstein, American Scientist
"Yau and Nadis dive into explanations of some extremely complicated math and do so with an enviable clarity and precision. The book also offers a compelling portrait of the intellectual life of a mathematician. The Shape of a Life frequently talks about the conferences and colleagues that inspired Yau and influenced his work, a welcome antidote to the stereotype of the solitary theorist locked away in his office.”—Physics Today
"Author Yau, who was awarded a Fields Medal in 1983 and other significant honors, tells in great detail the story of his life, and more importantly, his interpretation in personal terms of its events. . . . Mathematics majors from China may find this book particularly inspiring."—Paul J. Campbell, Mathematics Magazine
Finalist in the PROSE Awards mathematics category, sponsored by the Association of American Publishers
“Yau and Nadis’s The Shape of a Life opens a window into the fascinating mind and world of today’s equivalent of Apollonius of Perga, ‘The Great Geometer’ of antiquity.”—Mario Livio, author of Brilliant Blunders
"The interesting life of a remarkably influential modern mathematician."—Juan Maldacena, Institute for Advanced Study
“This book tells a fascinating story of a life lived between multiple cultures—China and the West, and mathematics and physics. Yau's journey from poverty in Hong Kong to the top levels of the mathematics world was not a simple one.”—Edward Witten, Institute for Advanced Study
"Candid, deep, and truly inspiring, The Shape of a Life is studded with unexpected insights into Yau's thinking. An extraordinary story about an extraordinary person."—Gish Jen, author of The Girl at the Baggage Claim: Explaining the East-West Culture Gap
“The remarkable story of one of the world's most accomplished mathematicians, Shing-Tung Yau, who has made profound contributions in pure mathematics, general relativity, and string theory. Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind's irrepressible spirit of discovery.”—Brian Greene, author of The Elegant Universe
About the Author
About the authors
Shing-Tung Yau is the William Caspar Graustein Professor of Mathematics at Harvard University, where he has served on the faculty since 1987. He is the winner of the Fields Medal, the National Medal of Science, the Crafoord Prize, the Veblen Prize, the Wolf Prize, and a MacArthur Fellowship. A member of the National Academy of Sciences, Yau has received honorary degrees from ten universities. He is also the director of six mathematical institutes in China and Hong Kong. Yau has written and edited more than twenty books and also edits numerous mathematics journals. He lives in Cambridge, Massachusetts.
Steve Nadis is a Contributing Editor to Discover Magazine and a Contributing Writer for Quanta. His articles have also appeared in Nature, Science, Scientific American, New Scientist, Popular Science, Technology Review, Nautilus, Wired, Air & Space, Omni, Sky & Telescope, The Atlantic, National Wildlife, Audubon, Archaeology, Environment, and other magazines. He is the coauthor of The Shape of Inner Space (Basic Books 2010), A History in Sum (Harvard University Press, 2013), From the Great Wall to the Great Collider (International Press, 2015), The Shape of a Life (Yale University of Press), and The Gravity of Math (Basic Books 2024). He has written or contributed to more than two dozen other books. He has has been a staff researcher at the Union of Concerned Scientists, a science journalism fellow at MIT, and a consultant to the World Resources Institute, the Woods Hole Oceanographic Institution, the Harvard Mathematics and Physics Departments, and WGBH/NOVA. A graduate of Hampshire College, Nadis lives in Cambridge, Mass.
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Customers appreciate the book's distinguished mathematicians, with one review highlighting the profound connections between topology and geometry. Moreover, the story receives positive feedback for its rich details of figures and events. Additionally, customers praise the author's dedication, with one review specifically mentioning the strong support from his parents.
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Customers appreciate the distinguished mathematicians featured in the book, with one customer highlighting their profound connections between topology and geometry.
"A moving account of the life of one of our greatest mathematicians who managed to overcome tremendous hardship with the help of a loving family that..." Read more
"...dedication of his parents, his chance pathway to America, his focus on geometry, and his extreme genius in processing math along with gifted insight..." Read more
"...this is a remarkable tale of the very successful life of a very remarkable mathematician...." Read more
"To find out some personal opinion of the famous and very accomplished mathematicians about himself and some of his friends." Read more
Customers enjoy the captivating story of the book, with one review highlighting its rich details of figures and events, while another notes its excellent descriptions of current topics.
"A moving account of the life of one of our greatest mathematicians who managed to overcome tremendous hardship with the help of a loving family that..." Read more
"...It makes us human, yet valuable, and make others realize they have the power to achieve and contribute, while it is normal to feel overloaded, lost..." Read more
"...But on the whole, this is a remarkable tale of the very successful life of a very remarkable mathematician...." Read more
"...His story includes the struggles and rivalries he has faced throughout his career including those with his mentor, colleagues, and former students." Read more
Customers appreciate the author's dedication, with one noting the strong support from his parents and another describing him as a good human being.
"...While a book on love, sacrifice dedication and a heart full of wonder it also describes the evolution of geometric analysis providing a glimpse of..." Read more
"...: his growing up in China in extreme poverty, the strong dedication of his parents, his chance pathway to America, his focus on geometry, and his..." Read more
"A good human being shared his life and his genius with those of us who aren't. Thank you Professor Yau!" Read more
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Uplifting and Profound.
Top reviews from the United States
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- Reviewed in the United States on July 7, 2019A moving account of the life of one of our greatest mathematicians who managed to overcome tremendous hardship with the help of a loving family that stressed education and held it to be its own reward. While a book on love, sacrifice dedication and a heart full of wonder it also describes the evolution of geometric analysis providing a glimpse of the profound connections between topology and geometry, and excellent descriptions of current topics relevant to modern math from minimal surfaces, Calabi-Yau manifolds and mirror symmetry to Ricci flow and an especially good description of the Poincare conjecture and its solution. The book is chalk-full of current mathematical genealogies and Yau himself has produced not only a large number of impressive geometers and mathematicians but also successful mathematical institutes, especially in China where he had to enlist the leaders of the communist party to overcome intrigue and political hurdles. The book is humorous, fun to read and is a must for anyone interested in the 'language of the world'.
5.0 out of 5 starsA moving account of the life of one of our greatest mathematicians who managed to overcome tremendous hardship with the help of a loving family that stressed education and held it to be its own reward. While a book on love, sacrifice dedication and a heart full of wonder it also describes the evolution of geometric analysis providing a glimpse of the profound connections between topology and geometry, and excellent descriptions of current topics relevant to modern math from minimal surfaces, Calabi-Yau manifolds and mirror symmetry to Ricci flow and an especially good description of the Poincare conjecture and its solution. The book is chalk-full of current mathematical genealogies and Yau himself has produced not only a large number of impressive geometers and mathematicians but also successful mathematical institutes, especially in China where he had to enlist the leaders of the communist party to overcome intrigue and political hurdles. The book is humorous, fun to read and is a must for anyone interested in the 'language of the world'.Uplifting and Profound.
Reviewed in the United States on July 7, 2019
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- Reviewed in the United States on February 7, 2021I heard of Prof. Yau from my math teachers in high school, which was the high school in Hong Kong Dr. Yau went to. My teachers talked about his academic achievements but none about his financial struggle and family misfortune, which was described in the book. After all, his life might start humble but get more and more glamourous, sprinkled with sweat or even tears, along the way.
Dr. Yau has made phenomenal contributions in the mathematics community all over the world, in particular US, China and Hong Kong, where he is mostly tied to, specifically in establishing advanced research centers for boosting high quality research. To do that, even a great talent (Dr. Yau does not like the word "genius") needs to work extremely hard (and must be passionate about what he is doing) to attain such achievements.
I am impressed that Dr. Yau has had opportunities to work with renowned mathematicians/scientists like Stephen Hawking, Roger Penrose…and many more.
There are lots of straight talks on people relationship that most people are shy of speaking out. Nevertheless, the non-constructive arguments or even feuds among scholars described in the book makes me feel a bit uncomfortable about the academic world. Even the ivory tower cannot get immune to politics.
Besides, in the book one can find the constructive blending of cultures - East meets West, Science meets Literature, Rational meets Sentimental.
Undoubtedly we the Pui Ching "monkey heads" (the nickname for Pui Ching's students) are proud of having Prof. Yau as an alumni.
- Reviewed in the United States on April 15, 2019I enjoyed reading Yau’s biography: his growing up in China in extreme poverty, the strong dedication of his parents, his chance pathway to America, his focus on geometry, and his extreme genius in processing math along with gifted insight in creating new math. His principal mentor in America was Shiing-Shen Chern (1911-2004) who “was one of the principal founders of modern differential geometry.” Yau’s primary focus was the relatively new field of “geometric analysis.”
In his lifetime, Yau was directly involved in a broad range of mathematics and interfaced with a wide cross section of important mathematicians. He was awarded the “Fields Medal” in 1982 (the Nobel prize of mathematics) and refers to at least 12 other Fields Medalists. He also had an interest in physics and contributed to general relativity and string theory. Nearly 500 people are referenced in this historical biography – about a quarter of which were Chinese and largely unknown to me. Fortunately, I did have some interest and familiarity with about 25% of the names; and that kept me involved in my reading so that it was hard to put the book down. He provides a cursory overview of the kind of math I enjoy reading.
Yau said, “ We are seeking theories and equations that can carry us forward on the path towards eternal truth. These ideas are more valuable than gold…”
Both Yau and Chern had a passion for mathematics and “wanted to boost the level of mathematics carried out on the mainland” of China to establish “a high-quality research environment” there. On the cumulating research on the Poincare conjecture, major progress was made by Richard Hamilton and also by Yau. I thought the topic was finally conquered by the Russian, Grisha (or Grigori) Perelman. He was awarded the Fields Medal in 2002 for this work but declined it as well as a million dollar Millenium prize. However, Yau now says that although Perelman made a major contribution to Ricci flows, the latter part of his proof leading to the Poincare conjecture is still not airtight and requires more study.
A possible downside to the book is its dwelling on raising money and choosing staff prospects in his many official leadership capacities. He also had a frequent need to defend himself against unjustified personal attacks by others, and there were prolonged conflicts with his “father figure,” Chern. There are many details of academic politics and turf wars that weren’t enjoyable (sociology of academia). It is interesting that he believes that this problem is much worse in China than in America and is a major impediment to promoting valuable research in China.
Although I generally liked the book, I believe that it is not for everyone; some significant familiarity with the mathematicians and their mathematics is needed as background.
- Reviewed in the United States on April 10, 2019From the moment I started reading the book, I could not leave it. I was touched by the way the authors, especially the main author, tell the story of this humble and poor Chinese boy who was not afraid to stand up for big challenges, starting with smaller ones and going up in complexity as he made progress. I could feel myself immersed in his life and many parts reminds me of my own life; I was not going through his life, but through mine, as I read chapter after chapter.
Life stories like this one is what the world need to keep inspiring us and the ones coming behind us. Telling the truth, the fears, the difficulties and how imperfect we can be in some cases help in destroying the myths around those who tend to surpass his/her peers. It makes us human, yet valuable, and make others realize they have the power to achieve and contribute, while it is normal to feel overloaded, lost or embarrassed.
My main lesson from this work is the search for good collaborators and friends that can be there for us when needed and viceversa. Despite few receive the prizes or the medals, we will always need of the "angels" working behind the scenes, supporting and pushing us outside of our comfort zone.
HIGHLY RECOMMENDED!
Top reviews from other countries
- NkReviewed in Canada on June 27, 2020
5.0 out of 5 stars The exceptional life story of one the mathematical giants of our time.
This unique and fascinating book is a first-person account of the exceptional life of one the true mathematical giants of our time. The book is candid, rich in content, multi-faceted and very inspiring. Parts of it are also very moving. I could not put it down, and do recommend it in the strongest possible terms.
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Dr. T.Reviewed in Germany on April 21, 2020
4.0 out of 5 stars S.-T. Yau, Emporer of Mathematics
Shing-Tung Yau ist Professor für Mathematik und Physik an der Harvard Universität, er erhielt 1982 die Fields-Medaille für den Beweis der Calibi Vermutung; Steve Nadis ist freischaffender Wissenschaftsschriftsteller und lebt in Cambridge (MA), bereits 2010 war er Yaus Koautor bei seinem Werk “The Shape of Inner Space“, das die Bedeutung der Calabi-Yau Mannigfaltigkeiten für die Stringtheorie behandelt. Diese Zusammenarbeit setzt sich nun in dem vorliegen Buch fort – Yaus Autobiographie.
Bereits während seines Studiums in Hong Kong fällt Yaus Begabung für Mathematik auf, seine Lehrer ermutigten ihn deswegen, im Ausland zu promovieren – und mit ihrer Unterstützung gelingt es, dass Yau ein von IBM gesponsertes Stipendium erhält, dass es ihm ermöglicht, ab 1969 in Berkeley ein Graduierten Studium zu absolvieren. Im ersten Semester belegte er Kurse in Algebraischer Geometrie, Differential Geometrie und Differentialgleichungen, beschäftigte sich ferner mit Gruppentheorie, Dynamischen Systemen, Automorphen Formen und Funktionalanalysis. Yau nutzte zudem jede noch verbleibende freie Minute, um in der Bibliothek zu arbeiten, hier verfolgte er auch die Arbeiten in den wichtigsten aktuellen mathematischen Journalen. Dabei stieß er auf ein Theorem von Reissman über Räume negativer Krümmung. Bald konnte er diese Ergebnis auf nicht-positiver Krümmung verallgemeinern, und sein erstes Jahr mit einer Arbeit von einiger Bedeutung beschließen. Es war an der Zeit einen PhD Betreuer zu wählen – Shiing-Shen Chern wollte ihn an die Riemannsche Vermutung setzen, da er Anzeichen sah, dass dieses Problem angreifbar sei. Aber Yau hatte sich bereits mit der Calabi Vermutung befasst und einen Plan erwogen, diese mit einem Gegenbeispiel zu widerlegen. Aber nachdem die Reissman Arbeit in den Annals of Mathematics erschienen ist, entscheidet Chern, diese Publikation als PhD Dissertation zu werten.
Yau ging 1971 als Postdoc ans Institute for Advancend Studies in Princeton, 1974 wurde er schließlich Professor an der Stanford Universität. Nach zahlreichen Fehlschlägen bei der Konstruktion von Gegenbeispielen, war er nun überzeugt, dass die Calabi Vermutung richtig sein müsste. Als Vorübung beschäftigte sich Yau mit der Monge-Ampere Gleichung, einer nichtlineare Differentialgleichung, deren komplexe Version im Herzen der Calabi Vermutung liegt. Der Beweis beruht auf der Abschätzung der (approximativen) Lösungen und ihrer Ableitungen bis zur dritten Ordnung. In einem ersten Durchbruch konnte Yau zeigen, dass alle diese Abschätzung aus der für die nullte Ordnung folgen; diese Lücke konnte Yau dann in wenigen Wochen füllen. Der Beweis der Calabi Vermutung war aber kein singulärer Erfolg, die Methode ließ sich mehr oder minder direkt auf andere Probleme übertragen, so dass sich dadurch noch fünf weitere Theoreme der algebraischen Geometrie beweisen ließen. Ein beachtlicher Erfolg für das noch junge Gebiet der geometrischen Analysis, dem sich Yau mit Eifer zugewandt hatte.
Neben der Calabi Vermutung hatte sich Yau aber bereits mit anderen Gebieten beschäftigt, mit minimalen Flächen, der Poincare Vermutung und dem Problem der Positivität der Energie in der Relativitätstheorie, das er gemeinsam mit seinem Doktoranden Richard Schoen für drei Dimensionen lösen konnte. Er erhielt daraufhin eine Einladung von Stephen Hawking, um mit ihm den physikalisch interessanten vier- dimensionalen Fall zu diskutieren.
Um endlich mit seiner Frau ein gemeinsames Heim zu gründen, ging Yau 1984 nach San Diego. Mit Richard Hamilton diskutierte er dessen Arbeiten zum Ricci Fluss. Hier trifft auch der Yau Schüler Gary Horowitz mit Andrew Storminger aufeinander, gemeinsam mit Philip Candelas erkennen sie die Bedeutung von Calabi-Yau Mannigfalten für die Stringtheorie. Yau nimmt sich des Problems der Abschätzung der Anzahl solcher Räume an, und konstruiert diverse Beispiele, insbesondere physikalische interessante Fälle mit Euler-Zahl -6. Aber die Fakultätsmitglieder in San Diego folgen nicht Yaus Vorstellung für die weitere Entwicklung des Fachbereichs, darum folgt Yau 1987 einem Ruf an die Harvard Universität.
Brian Green und Ronan Plesser stoßen auf die sogenannte ‘mirror symmetry‘ von Calabi-Yau Räumen, mit deren Hilfe konnte Candelas die Anzahl der 3- Kurven auf einer Quintic bestimmen. Diese Symmetrie ist das erste Beispiel einer Dualität in der Stringtheorie. Yau begann sich für dieses Thema zu interessieren. Ḿit Strominger und Zaslow gelangt er zur sogenannten SYZ Vermutung, die sie zwar nur für Spezialfälle beweisen können, die aber die mirror symmetry de-mystifiziert.
Yau ist aber nicht nur ein einflussreicher Wissenschaftler, sondern auch ein begnadeter Wissenschaftsorganisator und politiker; er organisierte zahlreiche Konferenzen zur Mathematik und Stringtheorie. Als Chief Edtior des Journal of Differential Geometry gelingt es ihm, dass Michael Freedman, Clifford Taubes und Simon Donaldson ihre preiswürdigen Arbeiten hier publizieren, ebenso wie Ed Wittens “Supersymmetry and Morse Theory“. Ebenso ist Yau Gründungsdirektor des Center of Mathematical Sciences and Applications (CMSA), einem interdisziplinären Institut der Harvard Universität.
Schließlich hat sich Yau intensiv bei der Reorganisation der mathematischen Forschung in China engagiert, die Zuge der Kulturrevolution auf anwendungsorientierte Bereiche eingeschränkt wurden war. Eines der vielen Früchte seiner Arbeit, ist die Gründung des Mathematical Sciences Center der Tsinghua Universität, das 2014 in Yau Mathematical Sciences Center (YMSC) umbenannt wurde. Nicht genug, ist Yau auch Visiting Professor des Departments of Mathematics der Chinesischen Universität Hong Kong (CUHK).
Das wissenschaftliche Werk von Shing-Tung Yau ist sicherlich der Hauptanlass für das Entstehen dieses Werkes, dabei steht aber die Ideengeschichte der Entdeckungen, das Zusammenspiel mit Schülern und Kollegen und die Rolle verschiedener wissenschaftlicher Programme im Vordergrund, die eigentlichen mathematischen Resultate werden hingegen in der Regel nur am Rande erwähnt. Aber ein wesentlicher Beitrag zu dem Buch, machen auch Yaus persönliche Erinnerungen aus, insbesondere an seinen Vater, dem er die Verwurzelung in der chinesischen Kultur und die Liebe zur chinesischen Literatur verdankt. Etwas verstörend sind die zahlreichen Bezüge auf Zerwürfnisse mit Yaus ehemaligen Mentor Chern, dessen Adepten wohl Zwist zwischen Chern und seinem mittlerweile berühmten Schüler zu säen versuchten.
Ausführlich geht Yau auch auf die Aufregung ein, die 2006 ein Artikel im New Yorker von Sylvia Naser (Autorin von ‘A Beautiful Mind‘) und David Gruber ihm eintrug – ‘Manifpld Destiny‘ wurde von einer Fotomontage eingeleitet, die Yau zeigt, der nach der um Perelmans Hals hängende Fields Medaille schnappt. Hintergrund war, dass Gregori Perelman 2002/03 – wie aus dem Nichts – drei kurze Preprints mit seinen Ergebnissen zum Ricci Fluss veröffentlicht, mit denen sich die Poincare Vermutung beweisen lies. Für diese Leistung wurde Perelman 2006 die Fields Medaille angetragen, die er aber ausschlug. Etwa zu dieser Zeit hielt Yau einen langen Vortrag zum Poincare Problem auf der Strings Conference in Peking, in dem er sich freute mitzuteilen, dass es seinen Schülern Xi-Ping Zhu und Huai-Dong Cao gelungen sei, viele Lücken in den oft skizzenhaften Beweisen Perelmans zu schließen.
Das Buch eröffnet einen großartigen Einblick in das Schaffen und Werk von Shing-Tung Yau, einem der hervorragendsten Mathematiker der Gegenwart, der sein Leben unermüdlich dem weiteren Fortschritt seines Fachgebiets widmet – The Emperor of Math nannte Dennis Overbye ihn in einem NY Times Artikel. Den beiden Autoren ist eine flüssige Darstellung gelungen, wenn man von einigen arkanen Verzweigung in Yaus Schüler Genealogie und Paper Genesis absieht. Leider ist das Buch auch etwas spartanisch ausgestattet, sämtlich Verweise auf Originalarbeiten sind lediglich in Prosaform im Text enthalten, eine Bibliographie fehlt hingegen.
- mcpickettReviewed in Australia on January 14, 2025
5.0 out of 5 stars Great biography
A really interesting and very well written biography even if the maths goes over your head
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MarceloReviewed in Brazil on November 11, 2019
5.0 out of 5 stars Biografia de Yau.(Calabi-Yau Manifolds)
Muito bom, conta a vida de um Medalha Fields e na leitura vemos várias interações com vários Matemáticos famosos. pra quem estuda Geometria Diferencial é uma leitura imperdível.
- AlokReviewed in India on May 21, 2019
5.0 out of 5 stars Absolutely Loved the book
Absolutely Loved the book