出版社: Princeton University Press
副标题: Portrait of a Problematic Vocation
出版年: 2015118
页数: 464
定价: USD 29.95
装帧: Hardcover
ISBN: 9780691154237
内容简介 · · · · · ·
What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twentyfirst century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop cult...
What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twentyfirst century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.
Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party?
Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
作者简介 · · · · · ·
Michael Harris is professor of mathematics at the Université Paris Diderot and Columbia University. He is the author or coauthor of more than seventy mathematical books and articles, and has received a number of prizes, including the Clay Research Award, which he shared in 2007 with Richard Taylor.
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庾子山 (Focus on science.)
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought wi... (1回应)20150526 20:03
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?—David Hilbert, Paris 1900尽管希尔伯特认为历史告诉我们科学的发展是连贯的，我们如今已经不相信这种连贯性。并且，即便揭开未来的面纱，我们也未必知道我们的目标何在。我们今天大多相信科学的发展是由一连串的范式革命构成的。数学也是如此，如克罗内克所说的，新现象会推翻旧假说并且以新假说取而代之。但数学中的变化剧烈程度要小，因为数学不必为适应新发现而调适自身，而是可以改变旧的假说或者改变我们所认为可以接受的标准。康托尔说数学之为自由学问，其题中之义在是。史学家Jeremy Gray认为职业自治（professional autonomy）是数学现代主义的标志。前现代的数学家的想象受限于数学哲学和数学科学之间的关系。在Gray看来，没有职业自治性，数学的现代转向就不会发生。现代主义之成为主流，是因为它恰当表述了数学家所在的新处境：数学被吸纳到现代研究型大学的结构（从而形成职业数学家的国际群体），数学的目标和主题的新形式得以形成。如果本书是关于什么的话，那么本书是关于过一种数学家的双重人生是何种感觉：一方面数学家在这种职业自治之中的生活，只需要向同事负责；另一个是更广阔的世界中的生活。要解释数学家到底做什么是一件很难的事情，正如David Mumford所说的：“作为一个职业数学家，我已经习惯于生活在一种真空之中，这种真空的周围是那些以对数学一无所知而自豪的人。”这种困难使得后面的问题不被问出来：什么是数学家的目标？为什么要做数学？为什么做数学？这个问题一般有三个回答，其中两个明显是错的。第一个是数学没有实际应用，第二是数学能确定地证明真理。这两者不论有多少可信度，都不无法为纯数学——不旨在解决特定范围的实际问题的数学——的提供驱动力。两者都在数学之外寻求数学的驱动力，并且暗示着，数学家要么是失败的工程师，要么是失败的哲学家。第三个理由是美学的，其经典表达见于哈代。但这个理由仍旧受到贫乏和自我陷溺的责难，而数学之被容忍，不过是因为它有可能的实际用处和大学仍需要数学来训练真正有用的公民。本书一开始主要是讨论为什么做数学，但鉴于一本数学书不讨论何谓数学是说不通的，所以也讨论何谓数学。又因为本书是为无数学训练背景的人写作的，因此更多是关于“作为一种生活方式的数学”。本书并不追求得出定论，而是如 Herbert Mehrtens所说的，以“如何做数学”来说明“数学是什么”。1回应 20150526 20:03 
庾子山 (Focus on science.)
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to e...20150526 17:10
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to establish a reliable basis for future comparisons. I have no such obligation because I am not trying to establish anything; my knowledge of the relevant literature is secondhand and extremely limited in any event; and the allusions in the middle chapters do nothing more than provide an excuse to suggest that an exclusive reliance on the western metaphysical tradition (including its antimetaphysical versions) invariably leads to a stunted account of what mathematics is about. In the same way, the occasional references to sociology of religion or to religious texts are NOT to be taken as symptomatic of a belief that mathematics is a form of religion, even metaphorically. It rather expresses my sense that the way we talk about value in mathematics borrows heavily from the discourses associated with religionThe expositions of mathematical material in the “Dinner Party” sequence are as scholarly as anything in the book, but it seemed to me that to maintain a serious tone in the dialogues that follow would make them impossibly stilted. Why this is the case inevitably raises the question of just how seriously mathematics is to be taken. My confusion on this point is such that I sincerely can’t tell whether or not the question itself is a serious one. The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2. I can assure the reader who finds this unconvincing that my intentions, at least, are serious.One of the author’s alter egos in the dialogues repeatedly invites the reader to think of a number neither as a thing nor as a platonic idea but rather as an answer to a question. Outside the fictional dialogues, I wouldn’t put a lot of energy into defending this way of thinking—not because it’s wrong but because the kind of number theory with which the book and its author are concerned cares less about the numbers themselves than about the kinds of questions that can be asked about them. The habit of questioning questions, rather than answering them, pervades contemporary pure mathematics.The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2.回应 20150526 17:10

庾子山 (Focus on science.)
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to e...20150526 17:10
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to establish a reliable basis for future comparisons. I have no such obligation because I am not trying to establish anything; my knowledge of the relevant literature is secondhand and extremely limited in any event; and the allusions in the middle chapters do nothing more than provide an excuse to suggest that an exclusive reliance on the western metaphysical tradition (including its antimetaphysical versions) invariably leads to a stunted account of what mathematics is about. In the same way, the occasional references to sociology of religion or to religious texts are NOT to be taken as symptomatic of a belief that mathematics is a form of religion, even metaphorically. It rather expresses my sense that the way we talk about value in mathematics borrows heavily from the discourses associated with religionThe expositions of mathematical material in the “Dinner Party” sequence are as scholarly as anything in the book, but it seemed to me that to maintain a serious tone in the dialogues that follow would make them impossibly stilted. Why this is the case inevitably raises the question of just how seriously mathematics is to be taken. My confusion on this point is such that I sincerely can’t tell whether or not the question itself is a serious one. The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2. I can assure the reader who finds this unconvincing that my intentions, at least, are serious.One of the author’s alter egos in the dialogues repeatedly invites the reader to think of a number neither as a thing nor as a platonic idea but rather as an answer to a question. Outside the fictional dialogues, I wouldn’t put a lot of energy into defending this way of thinking—not because it’s wrong but because the kind of number theory with which the book and its author are concerned cares less about the numbers themselves than about the kinds of questions that can be asked about them. The habit of questioning questions, rather than answering them, pervades contemporary pure mathematics.The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2.回应 20150526 17:10 
庾子山 (Focus on science.)
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought wi... (1回应)20150526 20:03
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?—David Hilbert, Paris 1900尽管希尔伯特认为历史告诉我们科学的发展是连贯的，我们如今已经不相信这种连贯性。并且，即便揭开未来的面纱，我们也未必知道我们的目标何在。我们今天大多相信科学的发展是由一连串的范式革命构成的。数学也是如此，如克罗内克所说的，新现象会推翻旧假说并且以新假说取而代之。但数学中的变化剧烈程度要小，因为数学不必为适应新发现而调适自身，而是可以改变旧的假说或者改变我们所认为可以接受的标准。康托尔说数学之为自由学问，其题中之义在是。史学家Jeremy Gray认为职业自治（professional autonomy）是数学现代主义的标志。前现代的数学家的想象受限于数学哲学和数学科学之间的关系。在Gray看来，没有职业自治性，数学的现代转向就不会发生。现代主义之成为主流，是因为它恰当表述了数学家所在的新处境：数学被吸纳到现代研究型大学的结构（从而形成职业数学家的国际群体），数学的目标和主题的新形式得以形成。如果本书是关于什么的话，那么本书是关于过一种数学家的双重人生是何种感觉：一方面数学家在这种职业自治之中的生活，只需要向同事负责；另一个是更广阔的世界中的生活。要解释数学家到底做什么是一件很难的事情，正如David Mumford所说的：“作为一个职业数学家，我已经习惯于生活在一种真空之中，这种真空的周围是那些以对数学一无所知而自豪的人。”这种困难使得后面的问题不被问出来：什么是数学家的目标？为什么要做数学？为什么做数学？这个问题一般有三个回答，其中两个明显是错的。第一个是数学没有实际应用，第二是数学能确定地证明真理。这两者不论有多少可信度，都不无法为纯数学——不旨在解决特定范围的实际问题的数学——的提供驱动力。两者都在数学之外寻求数学的驱动力，并且暗示着，数学家要么是失败的工程师，要么是失败的哲学家。第三个理由是美学的，其经典表达见于哈代。但这个理由仍旧受到贫乏和自我陷溺的责难，而数学之被容忍，不过是因为它有可能的实际用处和大学仍需要数学来训练真正有用的公民。本书一开始主要是讨论为什么做数学，但鉴于一本数学书不讨论何谓数学是说不通的，所以也讨论何谓数学。又因为本书是为无数学训练背景的人写作的，因此更多是关于“作为一种生活方式的数学”。本书并不追求得出定论，而是如 Herbert Mehrtens所说的，以“如何做数学”来说明“数学是什么”。1回应 20150526 20:03

庾子山 (Focus on science.)
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought wi... (1回应)20150526 20:03
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?—David Hilbert, Paris 1900尽管希尔伯特认为历史告诉我们科学的发展是连贯的，我们如今已经不相信这种连贯性。并且，即便揭开未来的面纱，我们也未必知道我们的目标何在。我们今天大多相信科学的发展是由一连串的范式革命构成的。数学也是如此，如克罗内克所说的，新现象会推翻旧假说并且以新假说取而代之。但数学中的变化剧烈程度要小，因为数学不必为适应新发现而调适自身，而是可以改变旧的假说或者改变我们所认为可以接受的标准。康托尔说数学之为自由学问，其题中之义在是。史学家Jeremy Gray认为职业自治（professional autonomy）是数学现代主义的标志。前现代的数学家的想象受限于数学哲学和数学科学之间的关系。在Gray看来，没有职业自治性，数学的现代转向就不会发生。现代主义之成为主流，是因为它恰当表述了数学家所在的新处境：数学被吸纳到现代研究型大学的结构（从而形成职业数学家的国际群体），数学的目标和主题的新形式得以形成。如果本书是关于什么的话，那么本书是关于过一种数学家的双重人生是何种感觉：一方面数学家在这种职业自治之中的生活，只需要向同事负责；另一个是更广阔的世界中的生活。要解释数学家到底做什么是一件很难的事情，正如David Mumford所说的：“作为一个职业数学家，我已经习惯于生活在一种真空之中，这种真空的周围是那些以对数学一无所知而自豪的人。”这种困难使得后面的问题不被问出来：什么是数学家的目标？为什么要做数学？为什么做数学？这个问题一般有三个回答，其中两个明显是错的。第一个是数学没有实际应用，第二是数学能确定地证明真理。这两者不论有多少可信度，都不无法为纯数学——不旨在解决特定范围的实际问题的数学——的提供驱动力。两者都在数学之外寻求数学的驱动力，并且暗示着，数学家要么是失败的工程师，要么是失败的哲学家。第三个理由是美学的，其经典表达见于哈代。但这个理由仍旧受到贫乏和自我陷溺的责难，而数学之被容忍，不过是因为它有可能的实际用处和大学仍需要数学来训练真正有用的公民。本书一开始主要是讨论为什么做数学，但鉴于一本数学书不讨论何谓数学是说不通的，所以也讨论何谓数学。又因为本书是为无数学训练背景的人写作的，因此更多是关于“作为一种生活方式的数学”。本书并不追求得出定论，而是如 Herbert Mehrtens所说的，以“如何做数学”来说明“数学是什么”。1回应 20150526 20:03 
庾子山 (Focus on science.)
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to e...20150526 17:10
One of the most exciting trends in history of mathematics is the comparative study across cultures, especially between European (and Near Eastern) mathematics and the mathematics of East Asia. These studies, which are occasionally (too rarely) accompanied by no less exciting comparative philosophy, is necessarily cautious and painstaking, because its authors are trying to establish a reliable basis for future comparisons. I have no such obligation because I am not trying to establish anything; my knowledge of the relevant literature is secondhand and extremely limited in any event; and the allusions in the middle chapters do nothing more than provide an excuse to suggest that an exclusive reliance on the western metaphysical tradition (including its antimetaphysical versions) invariably leads to a stunted account of what mathematics is about. In the same way, the occasional references to sociology of religion or to religious texts are NOT to be taken as symptomatic of a belief that mathematics is a form of religion, even metaphorically. It rather expresses my sense that the way we talk about value in mathematics borrows heavily from the discourses associated with religionThe expositions of mathematical material in the “Dinner Party” sequence are as scholarly as anything in the book, but it seemed to me that to maintain a serious tone in the dialogues that follow would make them impossibly stilted. Why this is the case inevitably raises the question of just how seriously mathematics is to be taken. My confusion on this point is such that I sincerely can’t tell whether or not the question itself is a serious one. The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2. I can assure the reader who finds this unconvincing that my intentions, at least, are serious.One of the author’s alter egos in the dialogues repeatedly invites the reader to think of a number neither as a thing nor as a platonic idea but rather as an answer to a question. Outside the fictional dialogues, I wouldn’t put a lot of energy into defending this way of thinking—not because it’s wrong but because the kind of number theory with which the book and its author are concerned cares less about the numbers themselves than about the kinds of questions that can be asked about them. The habit of questioning questions, rather than answering them, pervades contemporary pure mathematics.The position of this book is that what we understand as pure mathematics is a necessarily human activity and, as such, is mixed up with all the other activities, serious or otherwise, that we usually associate with human beings. The three chapters in part 2 try to make this apparent by depicting mathematicians in unfamiliar but recognizably human roles: the lover (or theorist of love), the visionary, and the trickster. Modes of mathematical seriousness come in for extensive examination throughout the book, especially in the final chapter of part 2.回应 20150526 17:10
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订阅关于Mathematics without Apologies的评论:
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0 有用 aTician 20180929
相比于数学本身，数学家的个人生活、数学家群体的社群活动简直太无聊。数学行为与数学内容相比完全不值一提，即使前者因为更易被外人理解而被赋予兴趣。
0 有用 L 20190108
expelled my fears and anxieties. beyond grateful to have encountered such a book at an early stage of my career. not a book for dilettantes.
0 有用 AG 20150601
内容大多都是介绍和科普一些有趣的当代数学和当代数学家的内容，许多是关于数论的。里面的 how to explain number theory at a dinner party 值得一看。
0 有用 L 20190108
expelled my fears and anxieties. beyond grateful to have encountered such a book at an early stage of my career. not a book for dilettantes.
0 有用 aTician 20180929
相比于数学本身，数学家的个人生活、数学家群体的社群活动简直太无聊。数学行为与数学内容相比完全不值一提，即使前者因为更易被外人理解而被赋予兴趣。
0 有用 AG 20150601
内容大多都是介绍和科普一些有趣的当代数学和当代数学家的内容，许多是关于数论的。里面的 how to explain number theory at a dinner party 值得一看。