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This volume includes topics such as: invariants of strongly pseudoconvex CR manifolds; the integral formulas of the Pontrjagin characteristic forms on an oriented differentiable manifold; the construction of tensor fields and connections on the frame bundle; and cellular manufacturing systems. ... Read more

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Slutsky is perhaps the Russian/Ukrainian economist most quoted by mainstream economists today, although his fame in the West rests on only two articles that were initially translated into English. Moreover, Slutsky’s work is still employed in economics textbooks today, and he is the only Russian/Ukrainian person to be so honoured. This is the first book in English devoted to assessing Slutsky’s contributions to economics and to their links with his influential work in pure mathematics and statistics.

Whereas previous scholars who have written on Slutsky have done so exclusively from either a ‘history of economics’ or a ‘history of science’ approach, Barnett argues that the two strands must be tied together as he examines Slutsky’s wide range of research interests and traces the connections between them. Barnett utilizes the full range of Russian archival and published sources and offers new translations into English of some of Slutsky’s currently unknown works in economics. Barnett provides the first detailed overview of the context and immediate influence of Slutsky’s life and work, both within Russia and outside of it.

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`The authors attempt succesfully to give a balanced picture of Chuquet's achievements and his limitations. Thus the book presents a well-documented and thoroughly elaborated research work.' Mathematical Reviews (1986) ... Read more

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Observes the lives of nine women mathematicians and their particular contributions in the areas of number theory, calculus, topography, and abstract algebra. ... Read more

Customer Reviews (5)

short and sweet
This was assigned as part of a 'women in math' class at my uni.I love hearing about these women's lives.I also love the exercises at the end of each biography.They are very simple so that even non-math majors can grasp the fundamental concepts of each chapter.As a math major, it's kind of relaxing to do these exercises.I do believe this book encourages an interest in mathematics.

Great Book
This book is very well written.It has wonderful information about the lives of these women and the activities are very creative and really promote a fun understanding of math.They require only a basic understanding of math concepts, yet can be taken to higher levels too.

Could have been better
This book could be a good starting place for those interested in reading about women mathematicians, but Perl places too much emphasis on these women as wives as mothers.For instance, the greater part of Grace Chisholm Young's biography was dedicated to her role as mother and wife. Only a short amount of Young's biography was dedicated to her math research and publications. I found this very disturbing,and, honestly quite an insult to these outstanding and courageous women. I also think it sends the wrong message to those women aspiring to be career mathematicians, that no matter how much you accomplish as a mathematician, you will always be thought of first as a wife and mother.

More on this needs to be written.
The book contains fascinating details of the lives of the very few womenin history with careers in Mathematics. It should be updated or extended totwo volumes to include the work of more recent women mathematicians.Woulddo well to include interviews with living women now working in thisfield.The end of each chapter includes examples of the type of work eachwoman was interested in, with exercises and activities. Good resource book

More on this needs to be written.
The book contains fascinating details of the lives of the very few womenin history with careers in Mathematics. It should be updated or extended totwo volumes to include the work of more recent women mathematicians.Woulddo well to include interviews with living women now working in thisfield.The end of each chapter includes examples of the type of work eachwoman was interested in, with exercises and activities. Good resource book ... Read more

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From the reviews of Vols. I-III:

"Since their publication in 1986 J-P. Serre's Collected Papers have already become one of the classical references in mathematical research. This is on the one hand due to the completeness of the collection (132 items) and on the other, of course, due to the beautiful and clear expositions of Serre's papers and their influence on mathematics.

As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published. [...]

The author's notes at the end of each volume giving corrections and important recent progress as well as improvements of the main results represent a highlight of this collection. The mathematical community definitely looks forward to further volume(s) of Serre's outstanding work."

Zentralblatt MATH

Customer Reviews (1)

WARNING: this does not come in the advertised size
The actual size of this book is roughly 10 x 7 inches, about half an inch longer and wider than the other three volumes on amazon (it also does not have the folded cover pages)! Confusingly, it does have the same ISBN as the volume of the advertised size (available elsewhere). ... Read more

Product Description

From the reviews of Vols. I-III:

"Since their publication in 1986 J-P. Serre's Collected Papers have already become one of the classical references in mathematical research. This is on the one hand due to the completeness of the collection (132 items) and on the other, of course, due to the beautiful and clear expositions of Serre's papers and their influence on mathematics.

As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published. [...]

The author's notes at the end of each volume giving corrections and important recent progress as well as improvements of the main results represent a highlight of this collection. The mathematical community definitely looks forward to further volume(s) of Serre's outstanding work."

Zentralblatt MATH

Product Description

"Extremely readable recollections of the author... A rare testimony of a period of the history of 20th century mathematics. Includes very interesting recollections on the author's participation in the formation of the Bourbaki Group, tells of his meetings and conversations with leading mathematicians, reflects his views on mathematics. The book describes an extraordinary career of an exceptional man and mathematicians. Strongly recommended to specialists as well as to the general public."

EMS Newsletter (1992)

"This excellent book is the English edition of the author's autobiography. … This very enjoyable reading is recommended to all mathematicians."
Acta Scientiarum Mathematicarum (1992)

Customer Reviews (5)

The recollections of a great mathematician
The title is a little misleading since there is not much math in the book, but a lot of personal stories about the intellectual life and travels of A. Weil. Through them we can glimpse his personality and thus the book will be interesting to mathematicians and historians of mathematics. The reader can detect a completely undogmatic mind, skeptical about justice and politics and with a rather ironic sense of humour. His stay in jail for not reporting for duty at the start of WWII was one of his most productive periods.

He recalls, but he is not able to give a concrete date, the day when H. Cartan and he founded Bourbaki. One of the funniest anecdotes is when Cartan receives a call from a Greek whose name is Bourbaki thinking it is a joke, but they become friends and he is even invited to some of their meetings.

A. Weil was not only an outstanding mathematician but a man of a wide culture and a polyglot. He studied sanskrit to read the great books of Indian literature and spent a couple of years in India. Another interesting story is when he is taken by a Russian spy in Finland and he is saved in extremis from execution by a chance meeting of Nevalinna with the chief of police.

He eventually moved to the US, although the first years must have been very frustrating teaching at second rates colleges where when he provided a proof the students would ask: "Is it going to be in the exam?"

The book ends in the fifties when he is appointed a professor at the University of Chicago after a stay in Sao Paulo.

To sum up, a fascinating personality that had a fascinating although not always easy life.

Light reading!
There is only a small number of autobiographies by mathematicians. Andre Weil was a giant in math. His autobio, written late in life, is fun to read. Weil has strong opinions that may perhaps not appeal to all. Even so, the book light reading, agreeing or not; and it fun too. For me it was a page-turner. To others perhaps a little pompous. Judge for yourself. While perhaps self-absorbed, I think Weil in his autobio gives personal and fresh insight into the tumultuous period in history, between the two World Wars in Europe, as it relates to math. The main part of the book covers Weil's life before he came to the US.
Weil had a monumental impact on math, and he also wrote some lovely history of math books, --number theory; and then of course some specialized books, that are corner stones in math, but not especially easy to read, at least for beginners. But Andre Weil is a central figure in math. His younger sister Simone Weil was an author and philosopher, and a political activist on the left in French politics in the 1930ties. She died young.

Light reading!
There is only a small number of autobiographies by mathematicians. Andre Weil was a giant in math. His autobio, written late in life, is fun to read. Weil has strong opinions that may perhaps not appeal to all. Even so, the book light reading, agreeing or not; and it fun too. For me it was a page-turner. To others perhaps a little pompous. Judge for yourself. While perhaps self-absorbed, I think Weil in his autobio gives personal and fresh insight into the tumultuous period in history, between the two World Wars in Europe, as it relates to math. The main part of the book covers Weil's life before he came to the US.
Weil had a monumental impact on math, and he also wrote some lovely history of math books, --number theory;and then of course some specialized books, that are corner stones in math, but not especially easy to read, at least for beginners. But Andre Weil is a central figure in math. His younger sister Simone Weil was an author and philosopher, and a political activist on the left in French politics in the 1930ties. She died young.

Quite some autocensorship
Weil did indeed lead a colorful life, and he certainly was a dominant figure in maths. But if one writes an autobiography, he should be honest when speaking both of his best and his worst. Unlike this, Weil strictlyrestrains from the reader the chapters of his life which he is not so proudof. I will name just two. First, in the book his wife (with a young sonfrom her previous marriage) simply occurs in his life, and the reader isnever told how and where they met, and who was the husband she abandonedbecause of this acquaintance (I here only comment that it was anotherFrench mathematician of the period, and earlier a friend of Weil, but he isnot mentioned anywhere in the story). And second, his evading the militaryservice; surely, most of us do not want to die, but to explain that we donot want to serve because we have a hinduistic view of the World is anoverused trick (though perhaps it was not overused in those times). One sodevoted to that view would definitely not feel at home in Princeton. Inaddition, in his well-known style Weil is extremely critical of theprofessional qualities of practically everyone, with exception of his"family" - the Bourbaki. Most of the textbooks by other peoplewere awful, the knowledge of most other people catastrophicallyincomplete.

Still, there are some interesting facts for those who want toknow what a life of a mathematician can involve, and two stars are justlyearned. Perhaps this would have been a better book has it been written morein the spirit of Hardy's Apology, omitting the family matters and focusingon what the title promises.

Excellent!
Weil led a colorful, fascinating life.He became a well-known mathematician at an early age, and mastered several languages.Additionally, he traveled around the world, and narrowly escaped execution. His autobiography allows the reader to come to know him for himself,rather than for his work.If the reader pays close attention, he/she willsee his subtle humor, which is cleverly woven in to his life story. ... Read more

Product Description
Fascinating accounts of the lives and accomplishments of history’s greatest mathematical minds--from Pythagoras to Georg Cantor. Charming anecdotes about Descartes, Euler, Pascal, many more, as well as accessible discussions of their contributions to mathematical thought. 30 diagrams. Bibliography.
... Read more

Customer Reviews (8)

Not what I expected.
I dontated this book.Hopefully someone will like it but I didn't.It is boring.

Good Historical Reference
This happened to be just what I was looking for:info on some of the more prominent mathematicians in history, in a short readable format.Not written as a necessarily easy, novel-like read, but definitely worth adding to my library.

One of the Best Books I've Ever Read
I am a high school math teacher and picked this book out of one of my cupboards for some lame "read during school" promotion (It's not like they ever have "do math during school" promotions...).I found the book difficult to put down.The book is filled with intriguing information at several levels; the math, the biographies, the drama, etc.Terrific book.

A really awesome book.
I've read Of Men and Numbers twice and have enjoyed the book immensely. It's so interesting and sometimes funny, and Jane Muir paints a great picture of the twelve most famous mathematicians that ever lived. Many mathematics books can be technical when presenting a story, but not in Of Men and Numbers. The writing is so simple that Jane Muir made the book extremely accessible for anyone and even for the kids. There are legends associated with many of the famous mathematicians, and they are all contained in this book. Before I read Of Men and Numbers for the first time, I had no idea of the men, only just their names associated with special numbers, proofs, etc., and afterwards, I felt my knowledge enriched by the colorful sketch of each man's biography. Of course, as I use the word "men," there is no biography of a female mathematician because the title Of Men and Numbers implies its omission. All in all, I greatly recommend Of Men and Numbers to anyone regardless of her/his interest in mathematics.

E. T. Bell clone - shares his regrettable style
It is a pity that Jane Muir seems to have modeled her book on "Men of Mathematics" by E. T. Bell.Like him, she "embellishes" her biographies to the point of sacrificing historical accuracy.Unfortunately (from my point of view) she also shares some of Bell's anti-Christian sentiments.For example, in the section on Blaise Pascal, she portrays Pascal as a mentally ill religious lunatic.Naturally, in the section on Evariste Galois, the great mathematician Cauchy is made out to be a fool and a bigoted religious fanatic while Galois (a very unstable, self-destructive character if there ever was one) is made out to be the martyred hero! ... Read more

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The biography of mathematician Laurent Schwartz in the context of his century. Aims to provide readers with a sense of the import of his work and his achievements, and his extraordinary abilities as a thinker and mathematician. Also documents the scholar's commitment to social causes such as the civil rights movement and the Vietnam war. Softcover. ... Read more

Customer Reviews (1)

Grappling is the word
This book is as fascinating to anyone interested in mathematics as any other mathematician's biography, with the extra asset of his life being deeply imbedded in 20th century history. While it gives a most interesting account of the French and international mathematical world during the second half of the century (especially on Bourbaki and, of course, on the distributions), it also tales the story of a "committed" (formerly trotskist) intellectual who valued his struggle for decolonization as highas his mathematical work. ... Read more

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Arthur Cayley (1821--1895) was one of the most prolific and important mathematicians of the Victorian era. His influence still pervades modern mathematics, in group theory (Cayley's theorem), matrix algebra (the Cayley-Hamilton theorem), and invariant theory, where he made his most significant contributions. Yet Cayley's life has been overlooked by historians, who have lavished far more attention on lesser figures. Mathematician and biographer Tony Crilly, the world's leading authority on Cayley, rectifies this oversight with the first definitive account of his life.

Born in England, Cayley spent his childhood in St. Petersburg, where his father was a commercial agent. After returning to England in 1828, Cayley received a first-rate education. As an undergraduate at Trinity College in Cambridge, he was named "Senior Wrangler," the top mathematics student of his year. After graduating, he found himself at the vanguard of the revolution in British mathematics which included William Rowan Hamilton, George Boole, and James Joseph Sylvester. At the same time, needing a reliable income, he trained for the bar and became a barrister at Lincoln's Inn in 1849. Though a successful lawyer, Cayley devoted all his free time to mathematics and confirmed his reputation as one of the era's leading minds with a procession of brilliant articles on key aspects in pure mathematics. Only after 1863, when he was appointed to the Sadleirian Chair at Cambridge, could he fully pursue mathematical investigations, and he continued to publish influential papers until his death.

Comprehensive and elegantly composed, this biography makes clear the scope of Arthur Cayley's prodigious achievements, firmly enshrining him as the "Mathematician Laureate of the Victorian Age."

Customer Reviews (1)

A mathematical biography
You'll enjoy this book more if you're not mathematically knowledgeable because that's the audience it's written for. More than half the text deals with Cayley's mathematics but when the author feels it necessary to explain that a determinant is "a technical name given to a formula used to extract a single number from a spatial array", you can't expect deeper math topics to be treated with more than a superficial gloss. As a mathematician, I was disappointed in this book. ... Read more

Product Description
Mathematicians and scientists have been closely tied to many famous disasters. The Challenger explosion, the failure of the Mars Orbiter, and the Kansas City Hyatt Regency walkway collapse all involved thinking errors. This book presents the ten things our future mathematicians and scientists must know to prevent these kinds of tragedies from occurring. Because science and mathematics instruction is often dominated by facts and calculation, children are rarely exposed to these important concepts. Over 50 stories are included that show children the strong connections between mathematics and science and the real world.

a)Sister Elizabeth Kenny discovered an effective treatment for polio, but it was ignored by the medical establishment for 30 years.

b)Engineers tried to stop the Challenger launch because of concerns that the o-rings might fail in the cold temperatures. They were ignored.

c)Dr. Semmelweis discovered why thousands of women who gave birth at hospitals were dying and a simple way to stop the deaths. His colleagues ignored his discovery and thousands of women continued to die.

d)How a simple design mistake led to 114 deaths when a walkwaycollapsed at the Kansas City Regency Hotel.

Questions are included at the end of each chapter to test the reader’s understanding of each concept. ... Read more

Customer Reviews (8)

Liberal propoganda disguised as a math book
This book is extremely simplistic and written in a cartoon style.The author's liberal bias is not only evident, it's the purpose of the book.The intended audience is young, naive teachers with a very weak or no background in math or science and with no background in economics, i.e. gullible neophytes who can be conned into believing anything by someone with just a bit more knowledge.From that starting point, the author plays on the reader's emotions to "teach" false economics and encourage readers to think along politically correct lines and buy into left wing agendas.The book is filled with so much politically correct nonsense and economic fallacies that any usefullness is lost.The books primary intent is not to make mathematicians and scientists critical thinkers. Rather, it's to encourage mathematicians and scientists to place multiculturalism and other goals of the far left as central in their pursuits.

Fun and Informative Book of Math and Science Facts - Recommended!
This book is not written in an overly serious manner and some readers might be put off by the cartoon Albert Einstein and assorted mice that add commentary throughout the sections, but the underlying mathematical and scientific principles are indeed important for all students to understand.

My sister (an ex-NASA engineer) recommended this book for my fairly advanced 8th grade son, but I was a little put off because at first glance it seemed that this book was way below his level. Interestingly enough, I was hooked after the first few sections and ended up reading all of the way through in one sitting. It refreshed some science and math facts I had long forgotten (like how to calculate the size of the Earth) and actually taught me some historical things I didn't know.

Students will also benefit from the questions asked at the end of each section and the answers are in the back of the book.

This is a surprisingly enjoyable and informative book that really should be on any future science and math oriented student's reading list. Adults will also likely enjoy it, especially Chapter 7 which covers lying with statistics.

Recommended!

CFH

If you started high school, this may be a little advanced
Well, I'm feeling a little critical, as I was expecting something that was more advanced. This book is written at a basic grade 9 level. Entertaining, for sure. And I am sure there is a niche audience who will find it useful, mostly those adults who didn't go far in school and who want to understand the tricks played in the lay press to promote a product. It might open a teenager's eyes to critical thinking. But if you finished high school you may be little disappointed. Any scientist will have learned these lessons a thousand times over....

Great tool with specific purpose
This book is quite handy, though a bit depressing if you think about it. There are 10 themes, each with 4 or 5 examples. The last 3 pages of the theme include Zaccaro's traditional math problems, including Level 1, Level 2, and and Einstein level. Each example includes about 3 questions for discussion, most of which are thoughtful and interesting.

If you're looking for a math workbook, this isn't it. If you're looking for some interesting reading, thoughtful questions, and a bit of math, this book is it.

I find, however, that to make the examples meaningful to my 4th and 5th grade students, I'm pulling in internet images and video clips to supplement. I'm also being selective about which examples I share, trying to use those that are most interesting and relevant to them.

This book is more of a tool/resource/guide. It's definitely not a math practice.

This should be required reading for everyone!
I ordered this terrific book for my 12 year old daughter who is an absolute math & science fiend (she reads science books for the fun of it) and flipped through it when it arrived to check it out. Well, I quickly became engrossed in the stories and the lessons inherent within the stories and immediately started noticing things within my environment which had been pointed out in the book. This book is amazing and should be read by everyone; not just aspiring mathematicians and scientists. All existing and future managers need to read it in order to realize that what they want is sometime vastly different from what is possible or even safe.

Zaccaro even includes several discussion questions at the end of each chapter which makes this book ideal for the classroom. I will be sharing this title with my daughter's math & science teachers from now on because I believe this book to be extremely important to our children's education. ... Read more

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Here, in this first biographical study of James Joseph Sylvester, Karen Hunger Parshall makes a signal contribution to the history of mathematics, Victorian history, and the history of science.

A brilliant Cambridge student at first denied a degree because of his faith, Sylvester came twice to America to teach mathematics, ultimately becoming one of Daniel Coit Gilman's faculty recruits at Johns Hopkins in 1876 and winning the coveted Savilian Professorship of Geometry at Oxford in 1883. He held professorships of natural philosophy, worked as an actuary, was called to the bar, and taught mathematics to cadets training for engineering and artillery posts in the British Army. During his long, distinguished career he also edited England's Quarterly Journal of Pure and Applied Mathematics and established the American Journal of Mathematics, the first sustained mathematics research journal in the United States.

Situating Sylvester's life within the political, religious, mathematical, and social currents of nineteenth-century England, Parshall penetrates the myth of this venerated figure, revealing how he lived, the choices he made and why, how the world in which he lived affected him -- and how he affected that world. The story of Sylvester's life sheds light on the evolution of mathematical thought. It also examines the ways in which mathematics may be done and what factors may shape a mathematician's ideas. Parshall explores the development of academic professionalization, nineteenth-century mathematical culture, and the emergence of modern algebra as a mathematical discipline. She highlights the human side of what many view as that most arcane and otherworldly of intellectual endeavors, mathematics, which indeed answers to such diverse factors as religion, ego, and depression.

Product Description
The first of four volumes in the landmark Lives and Legacies Oryx Press series, Scientists, Mathematicians, and Inventors profiles approximately 200 men and women who changed the world by leaving lasting legacies in their fields. It fills a gap in the biographical reference shelf by offering far more than basic facts about a scientist's life and work--each entry describes not only the immediate effects of the individual's discoveries, but their impact on later scientific findings as well. Each entry contains a timeline listing important dates in the biographee's life as well as a bibliography of the most important works on the subject. A master timeline chronicling major events in scientific exploration and an annotated general bibliography are also included. ... Read more

Customer Reviews (1)

Excellent
One of the best and most concise books detailing scientists and engineers that have changed the world.If you have a friend or relative that is into science, buy them this book. ... Read more

Product Description
Writing in 19393, the historian of mathematics Herbert Turnbull, described John Pell as ' a mysterious figure' and commented: 'he may well prove to be an unsuspected genius, for his manuscripts appear to survive, unexamined, in the British Museum.'Turnbull's expectations were pitched a little too high: although Pell was a man of unusual intellectual abilities, and one of the leading mathematicians of his day. His work does not merit any use of the term 'genius'. The term 'mysterious', on the other hand, was well deserved; and no less mysterious is the fact that the great majority of Pell's voluminous manuscripts have remained almost entirely unexamined for more than sixty years after Turnbull published those comments. This first full-length biography of John Pell (1611-1685) by Malcolm and Stedall reconstructs the life and times of this central and enigmatic mathematician and scholar. The text consists of over 600 pages and is presented in three parts: Part 1 "The Life of John Pell (1611-1685)" is a thoroughly researched new account of Pell's life; Part 2 "The Mathematics of John Pell" explores Pell's contribution to mathematics; and Part 3 "The Pell-Cavendish correspondence" is the first complete edition of Pell's correspondence, with detailed annotations.For historians of mathematics and science, philosophers, social and political historians and early modern intellectual historians, this superb work of scholarship is essential reading. ... Read more

Customer Reviews (1)

Correction
This is just a comment from one of the authors. Ever since this book was published, Amazon has listed it as a 'Royal Microscopy Society Handbook'. !? It is not a handbook, it is not about microscopy, and it has nothing to do with the Royal Microscopy Society. The publishers have repeatedly asked Amazon to remove these false details, but they are still there. You may think this book is special-interest only, but, believe me, it isn't as specialized as that. Yours sincerely, Noel Malcolm (Ignore the star rating I give -- they just won't print this without one.) ... Read more

Customer Reviews (1)

Wonderful look at mathematics, the times & the author
A Fantastic Book -- this 400+ page manuscript nicely mixes mathematical science with a historical view of the development (1930's through early 1980's) of mathematical research in the United States.This book is highlyreadable, extremely enjoyable and quite straightforward with details andopinions.One gets a first hand insight into how the author approached hisresearch, his career, and his life.Halmos has always been a brilliant andskillful writer but his contributions have mostly been in the technicalarena; this time he has provided a volume we can all enjoy.I found itdifficult to put this book down once I began its reading. ... Read more

Product Description
In 1957 Stephen Smale startled the mathematical world byshowing that, in a theoretical sense, it is possible to turn a sphereinside out. A few years later, from the beaches of Rio, he introducedthe horseshoe map, demonstrating that simple functions could havechaotic dynamics. His next stunning mathematical accomplishment was tosolve the higher-dimensional Poincaré conjecture, thus demonstratingthat higher dimensions are simpler than the more familiar three. In1966 in Moscow, he was awarded the Fields Medal, the most prestigiousprize in mathematics.

Smale's vision and influence extended beyond mathematics into two vastly different realms. In 1965 in Berkeley, he initiated a program with Jerry Rubin of civil disobedience directed at ending the Vietnam War. And as a mineral collector, he accumulated a museum-quality collection that ranks among the finest in the world. Despite these diverse accomplishments, Smale's name is virtually unknown outside mathematics and mineral collecting. One of the objectives of this book is to bring his life and work to the attention of a larger community.

There are few good biographies of mathematicians. This makes sense when considering that to place their lives in perspective requires some appreciation of their theorems. Biographical writers are not usually trained in mathematics, and mathematicians do not usually write biographies. Though the author, Steve Batterson, is primarily a mathematician, he has long been intrigued by the notion of working on a biography of Smale. In this book, Batterson records and makes known the life and accomplishments of this great mathematician and significant figure in intellectual history. ... Read more

Customer Reviews (2)

Biography of an Unusual Mathematician
Batterson's book is the only book length biography of Stephen Smale, a Field medalist (1966), who made major contributions to topology and dynamical systems. In the first half of the book, Smale is depicted as a brilliant mathematician who had a relatively humble beginning and was a relatively late bloomer as well.Atheme that runs through the book and one that predominates the middle part of the book is Smale's social activism. The last one-third of the book deals with a variety of topics - Smale interests in minerals and photography, his adventures trips (e.g. climbing mountains, sailing) and "other people" (family members, students and his involvement in a gender discrimination lawsuit filed a by a junior colleague). The book ends with a chapter with anassessment of Smale contributions and stature as a mathematician as well as his departure to take up an appointment in Hong Kong. Personally, I found the book to be fairly uneven - I particularly enjoyed reading the early chapters on Smale's coming of age as a creative mathematician.The middle part dealing his social activism was for me less enjoyable - partly due the extensive effort made to explain the socio-political events in the 1960s. These narratives distract the readers away from Smale mathematical work during this period but are essential as they provide the social-political environment within which Smale's activism was prominent. The last few chapters seemed to be a few chapters thrown together to cover topics that were left out earlier.The fact that I had such a mixed view of the book is probably not due to the author's writing ability but more to Smale's unusual character - very few mathematicians are known for their brilliance as well as for their active commitment to social issues.

A marvelous book
This book not only provides a useful description of some of the theory at a level technical enough to be satisfying, but also gives a fascinating view into the life and thinking of a Field's Medal winner (1966).Who would have guessed that the future Field's Medal Winner received a C in Calculus II and Physics and that he had a B- average Jr. year at the University of Michigan?And perhaps particularly heartening to those who have been through the graduate school experience, that he was less favored than Munkries and received an ultimatum from the chairman to improve (and that in graduate school, according to Raul Bott, Smale sat in the back and it wasn't clear he was always paying attention). But, of course, Smale more than redeems himself resulting in a storied career and a reputation that surpasses the boundaries of his specialties.This is a marvelous book. ... Read more

Product Description
Nobel Laureate Eugene Wigner once wondered about "the unreasonable effectiveness of mathematics" in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that -- mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is "a product of human thought that is independent of experience," how can it so accurately describe and even predict the world around us?

Mathematicians themselves often insist that their work has no practical effect. The British mathematician G. H. Hardy went so far as to describe his own work this way: "No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." He was wrong. The Hardy-Weinberg law allows population geneticists to predict how genes are transmitted from one generation to the next, and Hardy's work on the theory of numbers found unexpected implications in the development of codes.

Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them. ... Read more

Customer Reviews (40)

Maths in nature or in the mind
Excelent book with a tremendous amount of information, cultural, historical and philosophical, all presented in an easy to read and understand text which is also amusing.

My take on the subject
It's always disturbed me how relatively SIMPLE equations describe how things "work". If everything about nature is so complex, WHY do simple math relationships seem to apply?

We've formulated these equations and "pretend" to understand nature, but we really don't know much -- from not knowing exactly what makes up an atom, to not knowing what gravity is (just it's effects), to our lack of knowledge about the universe (just a bunch of guesses posed as facts). And don't get me started on "The Field" (see Lynne McTaggart book)

So, if "God" is a mathematician, he's being pretty coy.

Oh yeah, this is SUPPOSED to be a book review. Livio did a nice job conveying the
history of the development of math and the players involved. The discussion around
whether math is discovered (the God angle) or invented sometimes got tiresome, hence I
chose between a 3 and 4 rating.

Fascinating historical overview of Mathematical ideas
Is God a Mathematician examines the philosophical question of whether mathematical rules/theories are something that exist in nature and researchers just uncovering it, in a manner which is similar to theories in physics, or is mathematics is abstract mind games that people invent. In case of the latter, another question arises as to how can these abstract mind games, or mathematical inventions describe the physical world in such unreasonable accuracy.

As this is a very deep philosophical question, I hope that prospective readers are not really expecting to get a Yes/No answer to the mystery of the universe (like the number 42 in the Hitchhiker's guide to the galaxy). What they will find in the book is some discussions from different points of views, and how various mathematical discoveries through the course of history, changed the common beliefs about these types of questions.

The book is divided to 9 chapters, in which the first introduce the topic, the next six of them are devoted to a chronological history of math and physics, while the last two provide a deeper discussion on the main questions. The historical description is very well written. The author introduces the main thinker/researcher with some biographical information, then describes his discoveries and discusses their implication on the "math as discovery/invention?" question. The historical description is very broad and takes you from the early days of Descartes, Pythagoras, Plato, Archimedes and Geminus, via renaissance thinkers like Galileo, Descartes, Newton, Bernoulli, and logicians like Russell, De Morgan, Frege, Boole and of course Kurt Godel. I personally found this chronological outline fascinating.

In term of the main question, that is mainly dealt with in the last two chapters of the book, the author present some discussion and philosophical ideas from both sides of the discussion and conclude with fascinating examples of how extremely abstract mathematical ideas, turned up to be very applicable in the future to various physical domain.

Another small point of the writing, I think Dr. Mario Livio's writing provides a great example of how a popular science book should be written. The writing style and explanation are very simple to understand yet accurately deliver the underlying message in a way that anyone can enjoy it. I recommend the book to everyone who is interested in the history of mathematical ideas and the main question of the text.

The Answer is Probably Yes
Galileo is credited with the observation that the laws of nature are written in the language of mathematics.In this thought-provoking and entertaining book, Mario Livio takes a fresh look at how mathematics seems mysteriously to rule the cosmos.He first re-states Einstein's question of how it came to be that the idealized principles of mathematics apply to brute physical reality and highlights Eugene Wigner's famous remark about the "unreasonable effectiveness of mathematics in the natural science."He then expresses the further question of whether mathematics is an inherent property of things and thus waiting to be discovered, or instead an invention of the human mind. Although these philosophical questions are among the most interesting out there, Livio deals chiefly with showing how mathematics permeates the history of science and the study of nature. No, Mr. Livio does not answer the question of whether God is a mathematician, but maybe he does not have to; given the way mathematics governs the cosmos the answer is probably yes.

Well, is God a mathematician?
Maybe. Or maybe not. One conclusion is certain from this book: the author does not really tackle this exact question as his main theme. His big question for the reader, rather, is: has mathematics been discovered, or has it been invented? His answer turns out to be, "yes." Sometimes he argues for the one idea, sometimes for the other, either way strongly. God, perhaps, has to rule on the case, but Mario Livio certainly does not propose this! The "Plato" approach he speaks about at length takes the "discovery" side of the debate. Oddly enough, to this reviewer the amount of time spent on Mr. Plato probably muddled the story line, rather than clarifying. Nevertheless, "Is God a Mathematician?" flowed smoothly and satisfyingly.

When treating a topic like a history in mathematics, an author could take on a theme and pick among hundreds of personages to flesh out the theme. One has the feeling that Dr. Livio did just that. Fortunately, his book gets credit for being both interesting and informative, thus worth reading. He does a fine job spelling out some technical topics for the world of us amateur, non-doctoral people. Much of the book sets up more like an anthology. The bad part: harder for the reader to keep the chapter threads connected. The good part: if you do not like a particular personage's story, you can skip to the next. Something gets lost, of course, but it may have been partially lost anyway.

For theists looking for a deity's ownership of mathematics, the author's answer is not really there. For those without religious belief, the answer would not matter anyway. So, forget the title words and enjoy the book for its stories. You might also be able to figure out the "Plato" part in more detail than did this reviewer.
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