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Customer Reviews (10)

The most interesting book I've ever read!
I CANNOT believe the intellectual insight described in this book.

I am a Mathemetician Master's school graduate from CSULB and USC and have been tested to have exceptional mathematic ability.
You would think with my background, I could breese through this book. (albeit, as a mathemetician, I might be bored reading the book!)
Quite the opposite. This book is NOT about Mathematics. It is about why SCIENTISTS (mathemeticians as an example) hate ambiguity so much that they "create" never-before-invented solutions to resolve that ambiguity. This book also explains the process of solving those problems.

This book explains why and how our human scientific itellect has evolved. AMBIGUITY is the impetus. SOLVING the ambiguity is the goal and "engine" for evolution.

Without the existence of ambiguity, contradiction, and paradox, we humans would never have raised our combined intellect beyond "nature" or "God".

To me, the "ah ha" teachings in this book MUST become a classroom experience for young scientific minds that leads them to look for ambiguities in their life and motivates them to solve them.

Not an easy read, but an interesting one nonetheless
Mathematics is a fascinating subject. I am not a mathematician, but deal enough with it in my chosen profession to be constantly amazed by how logical the application of mathematics to proving a theorem or analyzing an algorithm turns out to be. But wait ... is it really logical? Or does it merely seems so and what is actually happening is that the author of the said proof is using creative tricks and techniques from the mathematical tool box to somehow tie everything up with a nice red bow-tie? In this book, the author argues that mathematics is creative more than algorithmic, and that mathematicians use a good dose of ambiguity mixed with equal parts of contradiction and paradox to create mathematics. Now, I shall point out that the term "ambiguity" here does not mean vagueness, rather it refers to a central truth that is perceived in two self-consistent but mutually incompatible contexts. The author takes the reader on this journey of ambiguity, paradox and contradiction on the way to discovering a lot of interesting mathematics. There is a section on counting numbers and cardinality, complete with Hilbert's Infinity Hotel; there is an interesting section on how to approach geometry through Euclid's Elements, and so on. I don't suppose that this is the sort of book you would pick up for a plane ride -- contemplating the philosophy of mathematics at 35,000 feet is enough to induce stupor. But if you are interested in the field and still remember the Central Limit Theorem from Calculus-I or Series and Sequences from Calculus-II, then you will definitely enjoy this book. I know I did.

Mathematical Philosophy
I would classify this book as a Mathematical Philosophy Book. The author definitely places Philosophy more than the hard-core Mathematics, so don't be disappointed if the reader's main goal is on Math.
Overall this bookis a great book, but definitely not for the weaker math students. It brings you to the higher platform to look down on Math issues in a pensive way - ie "Switch on the light" à la Andrew Wiles.

This book should be best read not in sequential manner, because of the writing style of the author which is quite verbose.

Some chapters are very well written:
Chap 8: (Pg 363) Obstacles to Learning Mathematics : Many great ideas and truths are hidden behind the math theoretical structures, unfortunately in the university math profs emphasize more on structures and leave the poor students to find out the 'beauty' of truth themselves - because 'Beauty' is not tested in Exams :(
Chapter 4: Paradoxes of Infinity. The "Cantor Set" Construction example is very refreshing.
Chapter 5: on "Quotient Space" (X/R) is excellent.
I also like the Isomorphism ideas (Pg 216-217): as Isometry (in Geometry), homeomorphism (in Topology), besides various isomorphism in Groups, Rings, Fields...

In summary, this book will elevate your math philosophical thinking like a Mathematician.

Extremely simpleminded
This is yet another naive rehash of the same old pop-math clichés. Since Byers knows nothing about mathematics beyond the meat-and-potatoes undergraduate curriculum, he has to use dishonest tricks to make these tired topics seem interesting. One time-tested trick is to claim that every single theorem is "surprising". For example, "we usually forget how surprising" it is that logic can be applied to geometry (p. 219). Only eight pages earlier we were surprised that the natural numbers have the same cardinality as the even numbers. And only four pages later we are surprised again, this time that there are infinitely many primes (p. 223). And so it goes. What a thrilling ride! Another underhand trick is to make completely unsubstantiated claims as to some mysterious metaphysical importance of every mathematical concept, e.g., "the notion of countable infinity captures something quite fundamental about the human nature and limits of what human beings can know" (p. 165).

Stylewise, Byers' amateur prose is made all the more unbearable by his obnoxious habit of putting at least four or five words per page in quotation marks for no apparent reason. We learn, for example, of a conjecture which "seems" true (sic, p. 281); elsewhere we study "infinity", "zero", and the notion of continuity, which means that f(x) gets "close" to f(a) when x gets "close" to a (sic, p. 239).

Byers' pathetic use of footnotes is a parody of scholarship. For example, the claim that "Poincaré call[ed] Cantorism a disease" (p. 286) is backed up by a footnote saying "Gardner (2001)" with no page reference. This is Gardner's "Colossal Book of Mathematics", obviously a deeply unscholarly source, and a colossal one at that. In this case, of course, Byers could not have provided the original reference because there is none. Poincaré never made this statement in print; and even if he did make it informally he was most likely referring to the paradoxes of set theory and not Cantor's transfinite numbers, as Byers would have known if he had not done his research at a high school library.

Bits of interesting mathematics mixed with unremarkable philosophy
I suspect that Prof. Byers is an excellent mathematics teacher and I very much enjoyed the snippets of mathematics in this book.However, most of the book was devoted to philosophy, which I found to be at least one of the following: (1) repetitive, (2) unoriginal, or (3) wrong.Repetitive for sure.Unoriginal in that he repeats many of the points made more eloquently and clearly by folks like Lakatos (though Byers does do a good job of giving credit where it is due).Wrong in the philosophy of mind, as in the section toward the end of the book where he tries to argue (a la Searle?) that machines can't think, and that computers might be able to write proofs but they can't do the inherently creative aspects of mathematics.It's very strange to me to run into a mathematician who holds these kinds of mystical views about minds, that they are not machines!

I feel like this would make a truly excellent 50 page book, with just a few of the key philosophical points clearly explained and illustrated with some of the excellent mathematical examples in this book.It could even be expanded -- but with more of Byers' mathematical illustrations, not his philosophical ramblings.

If I focused just on my favorite 50 pages of this book, it would get at least four stars; but the other 300 pages average it down to two. ... Read more

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She is best known for her curve, the witch of Agnesi, which appears in almost all high school and undergraduate math books. She was a child prodigy who frequented the salon circuit, discussing mathematics, philosophy, history, and music in multiple languages. She wrote one of the first vernacular textbooks on calculus and was appointed chair of mathematics at the university in Bologna. In later years, however, she became a prominent figure within the Catholic Enlightenment, gave up the academic world, and devoted herself to the poor, the sick, the hungry, and the homeless. Indeed, the life of Maria Agnesi reveals a complex and enigmatic figure -- one of the most fascinating characters in the history of mathematics.

Using newly discovered archival documents, Massimo Mazzotti reconstructs the wide spectrum of Agnesi's social experience and examines her relationships to various traditions -- religious, political, social, and mathematical. This meticulous study shows how she and her fellow Enlightenment Catholics modified tradition in an effort to reconcile aspects of modern philosophy and science with traditional morality and theology.

Mazzotti's original and provocative investigation is also the first targeted study of the Catholic Enlightenment and its influence on modern science. He argues that Agnesi's life is the perfect lens through which we can gain a greater understanding of mid-eighteenth-century cultural trends in continental Europe.

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The name Bourbaki is known to every mathematician. Many also know something of the origins of Bourbaki, yet few know the full story. In 1935, a small group of young mathematicians in France decided to write a fundamental treatise on analysis to replace the standard texts of the time. They ended up writing the most influential and sweeping mathematical treatise of the twentieth century, Les élements de mathématique. Maurice Mashaal lifts the veil from this secret society, showing us how heated debates, schoolboy humor, and the devotion and hard work of the members produced the ten books that took them over sixty years to write. The book has many first-hand accounts of the origins of Bourbaki, their meetings, their seminars, and the members themselves. He also discusses the lasting influence that Bourbaki has had on mathematics, through both the Élements and the Seminaires. The book is illustrated with numerous remarkable photographs. Readership Students, mathematicians, and historians interested in the group of mathematicians known as Bourbaki. ... Read more

Customer Reviews (3)

Balanced overview of rebarbative biographees
This is a very solid overview of the Bourbaki school, though obviously nothing like a full-fledged biography or monograph. The treatment is slightly more sophisticated than what you might find in a series of Scientific American articles (e.g., the author is confident that readers won't be scared off by an occasional integral sign or 2x2 matrix). I read the French edition, so I can't comment on the translation, though I was abashed to learn that the French adjectival form is not "bourbakien," as I might have guessed, but "bourbachique".

One of the main virtues of the book is that it's frank enough to include many thoughtful criticisms of the Bourbaki style and content. For example, although the Bourbaki were dedicated to following an axiomatic method, they ignored Gödel's incompleteness theorem, aside from an occasional dismissive reference. (That theorem shows that if you start from a system of axioms, you can't deduce all "mathematical truths" from them -- i.e., you can run across some statements that are consistent with the axioms but that cannot be deduced from them). The Bourbaki also ignored category theory, even though one of its inventors (Samuel Eilenberg) was a member of the group for a while. Today category theory is the dominant framework for describing the fundamental structures of mathematics. The Bourbaki also disdained so-called applied mathematics, including probability theory and dynamics, for its lack of "purity," even though it has yielded much mathematical fruit in the past 50 years. (Indeed it represents much of the lasting glory of French mathematics, e.g. the work of Fourier, Legendre, Lebesgue, Henri Poincaré and even Jacques Hadamard, whose seminars were a role model for the Bourbakis' and who supervised the PhDs of two of the group's founding members.) In short, the Bourbaki seem to have ignored or disdained rather lots of stuff. The bourbachique closed-mindedness ultimately contributed to the obsolescence of their approach.

The book's candor is also a bit of a flaw. By the end of the book the members of the group come across as the dogmatic, elitist clique their contemporaries accused them of being. They do seem to have been a livelier bunch in person than what I'd expected from their impersonal, austere, diagram-less presentation of mathematics. But while having a sense of humor was a prerequisite for being invited to join, the examples of their humor are for the most part sophomoric, and occasionally mean-spirited. Readers who already weren't Bourbaki fans might feel vindicated after reading this book; I can't vouch for what their fans might feel. Overall a quite interesting, but not uplifting, brief intellectual biography.

Despite Obvious Flaws, it's a colorful book, providing a clear look at rather common mathematical values and beliefs
For values and beliefs for a large group of mathematicians, this is a helpful book.For Bourbakian values and beliefs have been, by and large, adopted by the academic masses, alas. (expression of a Bourbakian value and a Bourbakian belief from p.75 "basic concepts are treated as abstract entities whose nature and concrete meaning are insignificant") Still, it's a nice tourist guide, even has lots and lots of color snaps.

But the text just reads and feels odd. It might just be due to some weaknesses in the text's translation from the French. All the same, sometimes I have no idea what is being written about or why.

For example, on page 41 I read "the fundamental theorem of algebra, which states that any polynomial with real coefficients has at least one complex root (in other words, there is a complex numer x that makes the expression equal to zero)" WHAT?!?!?!?!?!?! Not only useless, it's nonsense. The basic thought on complex numbers and polynomials with real-valued coefficients is the following. If any polynomial equation with real coefficients has a complex number z as a root, then the complex conjugate of z is also a root of the polynomial equation.

Interesting for fans of Bourbaki's texts
This is very interesting for fans of any of Bourbaki's mathematics texts.It has photos of many of the members taken at their meetings, and information about how the group operated.You'd never know it from the final product, but their original goal was to write a calculus book!Several of the founding members had just begun teaching, and they were unhappy with the standard French calculus text of the day--a multivolume work by Goursat that they considered out of date.They decided to write a little bit of background material on algebra and general topology, and somehow ended up with the books we all know and love.
The book also describes the personality quirks of the members, and has some commentary on the contents of the various texts of Bourbaki.It doesn't explain technical details like why Bourbaki chose to define integrals the way they did.
If you didn't major in math, this book probably won't interest you. ... Read more

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Presents biographies of women from the nineteenth and twentieth centuries who pursued their interests in mathematics. Each chapter includes different mathematical activities. ... Read more

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A companion to "Mathematical Apocrypha," (published in 2002)this second volume of anecdotes, stories, quips, and ruminations about mathematics and mathematicians is sure to please.It differs from other books of its type in that many of the stories are from the twentieth century and many about currently living mathematicians.A number of the best stories come from the author's first-hand experience.The writing is lively, engaging, and informative.There are stories the reader may wish to share with students and colleagues, friends, and relatives.The purpose of the book is to explore and to celebrate the many facets of mathematical life.The stories reveal mathematicians as intense, human, and sympathetic.They should resonate with readers everywhere.This book will appeal to students from high school through graduate school, to faculty and to mathematical scientists of all stripes, and also to physicists, engineer, and anyone interested in mathematics. ... Read more

Customer Reviews (1)

Plausible and entertaining stories about mathematicians as people
Mathematics is one of the oldest, perhaps even the oldest, areas of scholarly endeavor. While it provides the core of much of the functioning of human society, one area that is often neglected is the mythology of the discipline. In this book, his second about the unsubstantiated lore of mathematics, Steven Krantz demonstrates that while mathematicians are somewhat different than the rest of humanity, they are still human.
Mathematicians demonstrate arrogance, humility, insecurity, jealousy, pettiness, conceit, eccentricities, fear, insanity, incompetence and genius, just like all other people. However, some of these traits are more common and more pronounced in mathematicians than in other groups.
Krantz captures all of this in this set of stories about mathematicians as people, there is only a rare mention of actual mathematical formulas or principles. As the title implies, these stories are not necessarily true, although in most cases, only mathematical historians will be able to refute any of them. For they all possess the one trait that an apocryphal story must have, plausibility.
... Read more

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This book traces the history of the MIT Department of Mathematics one of the most important mathematics departments in the world through candid, in-depth, lively conversations with a select and diverse group of its senior members. The process reveals much about the motivation, path, and impact of research mathematicians in a society that owes so much to this little understood and often mystified section of its intellectual fabric, exemplified by names like Euclid, Newton, Euler, and Goedel.

At a time when the mathematical experience touches and attracts more laypeople than ever, such a book contributes to our understanding and entertains through its personal approach.

From the book:
The usual thing is there were these Thursday colloquiums at MIT or Harvard, and even the mathematicians from Brown would come. They would invite some speaker to give a mathematical talk. And afterward there was a dinner and a party in somebody's house. If it was in one guy's field, he would make the party. So that's how they socialized. They couldn't socialize with people who'd talk about tomatoes or clothes or something; they had to talk to people who understood the values they had, which were mathematical values. They're attracted to mathematics like a drug addict is attracted to drugs. They can't stay away from it.;
--Fagi Levinson ... Read more

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Well done book of interviews of MIT mathematicians
If you are interested in people who do math, the history of mathematics, or have taken any math at MIT, this book is probably for you.

An intriguing look at mathematics and the men behind it
Though never in the eye of popular culture, these men kept society advancing with their minds. "Recountings: Conversations with MIT Mathematicians" is a collection of interviews and anecdotes from the geniuses of MIT who have pursued mathematics as their life's careers and obsessions. These men have been responsible for major scientific advances throughout history and picking their minds in a volume that's more interesting than one could think math class could ever be. "Recountings" is an intriguing look at mathematics and the men behind it.
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Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes.'...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées) ... Read more

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Read Stillwell
I wish to draw attention to Stillwell's article "Number Theory as a Core Mathematical Dicipline". Stillwell says: "My suggestion is that mathematics, from kindergarten onwards, should be built around a core that is interesting at all levels, capable of unlimited development, and strongly connected to all parts of mathematics. My paper attempts to show that number theory meets these requirements, and that it is natural to build modern mathematics around such a core." The rest of the paper is a wonderful display of beautiful number theory with deep connections with all major areas of mathematics. Naturally there are connections with algebra, and "this is not surprising, because most basic commutative algebra is derived from Gauss's Disquisitiones Arithmeticae via Dirichlet and Dedekind". For example, a "wonderful constellation of results comes from forming the product of elements in an abelian group in two ways", for instance Fermat's little theorem: a^(p-1)=1 mod p when gcd(a,p)=1. This is because the list a,2a,...,(p-1)a mod p must be a permutation of 1,2,...,(p-1) mod p since all elements are nonzero and unequal (since a is invertible), so a*2a*...*(p-1)a=1*2*...*(p-1) mod p, i.e. a^(p-1)*1*2*...*(p-1)=1*2*...*(p-1) mod p, i.e. a^(p-1)=1 mod p. There are also connections with complex numbers. Since (a+bi)(c+di)=(ac-bd)+(ad+bc)i, the multiplicative property o absolute value reads (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2, which is a classical number theoretic identity apparently know to Diophantus when he said things like "65 is naturally divided into two squares in two ways, namely into 7^2+4^2 and 8^2+1^2, which is due to the fact that 65 is the product of 13 and 5, each of which is the sum of two squares". Now, 13 and 5 in turn are sums of two squares "because" they are primes of the form 4n+1, which is a theorem most easily proved by factorisation in Gaussian integers, i.e. m+ni. The theory of Gaussian integers is largely identical to that of ordinary integers since there is a notion of quotient and remainder from which we get an Euclidean algorithm and from there we prove unique factorisation etc. For ordinary quotient and remainder we need to know, when dividing by x, that multiples of x come within a distance x of any number. With the Gaussian integers we need to know that multiples of m+ni get within abs(m+ni) of any complex number, which is geometrically clear since the multiples of m+ni make a square lattice with side length abs(m+ni). So number theory is apparently also connected with geometry. An even better illustration of this is Diophantus's parametrisation of Pythagorean triples. Primitive Pythagorean triples (a,c,b) correspond to rational points on the unit circle (a/c,b/c) and these in turn correspond to lines through (-1,0) with rational slope t, so we find them by solving y=tx+t and x^2+y^2=1, which gives x=(1-t^2)/(1+t^2) and y=2t/(1+t^2). This rationalisation of the circle also pays of in calculus by showing us how to rationalise integrands like sqrt(1-x^2). Indeed, Bernoulli explicitly credited Diophantus for the substitution he used to turn the integrand for the arc length of a circle into 1/(1+t^2) from where the infinite series of pi follows by geometric series expansion and term-by-term integration. As Bernoulli also recognised, number theory also explains why integrands like sqrt(1-x^4) cannot be rationalised. Assume it can, sqrt(1-x^4)=y, square both sides and multiply up denominators to get Z^4-X^4=Y^2. the impossibility of this when X,Y,Z are integers was essentially proved by Fermat, by infinite descent, and polynomials behave sufficiently like integers for us to be able to mimic his proof in the polynomial case. ... Read more

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"I Want To Be A Mathematician" is an account of the author's life as a mathematician. It tells us what it is like to be a mathematician and to do mathematics.It will be read with interest and enjoyment by those in mathematics and by those who might want to know what mathematicians and mathematical careers are like.Paul Halmos is well-known for his research in ergodic theory, and measure theory.He is one of the most widely read mathematical expositors in theworld. ... Read more

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Thank you Mr. Halmos, for having wanted to be a mathematician...
I don't think my words of praise would do justice to this wonderful book. Halmos has strong opinions almost about everything and the way he talks about his examples are very wise. You don't need to be a would-be mathematician to enjoy the book. If you have ever wondered or invested some time in the world of mathematics, science and academia, Halmos provides you a very good account. If you are more than interested in math or maybe thinking about pursuing a Ph.D. this book will be much more valuable for you.

There are so many parts to be quoted from the book but I prefer to start a Wikiquote page for Halmos and pour sentences there. Halmos may not be one of the greats (according to his words) such as Euler, Gauss, Riemann, etc. but he is probably the greatest writer of such books.

All along the book I had a feeling: it was more like a frank and witty dialogue between me and the great mathematician (and lecturer) who had been there and done that. I kept on asking questions and Halmos kept on giving answers.

Thank you Mr. Halmos, for having wanted to be a mathematician, having been one of the best and having written such a nice book on what it was all about. ... Read more

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In the 17th century, the small but culturally and intellectually eminent city of Basel was the home of one of the most prominent mathematical families of all time, the Bernoullis, and their friend, protege, and master Leonhard Euler. The author chronicles their lives and achievements at a time when modern analysis and its applications to physics burst on the scene and created a methodological framework for modern science. Written for young adults, this book conveys the excitement of a scientific culture that impacts our life to this day and will serve as an inspiration to gifted young people to devote their lives to scientific pursuits. ... Read more

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Customer Reviews (21)

To reiterate:a terrible book
This book reads like a bunch of 7th grade book reports about various individuals and topics strung together in roughly chronological order.Its character studies are shallow, the writing is bland, and its exposition of key ideas are embarrassingly shallow.I got it for $2 to try out my new Kindle.The good news is that the Kindle is fantastic.What an awful book though.

Just plain poorly written
As tempting as it may seem, do not get roped into reading this book.Admittedly, I purchased this book based solely on the blurb written on the back and my interest in mathematics.However, the story, as presented by Aczel, is not as intriguing as it obviously could be.In all honesty, reading the Wikipedia article on Nicolas Bourbaki is a much more worth-while experience.

The writing style is at once dull and long-winded.Ideas are repeated over and over again and far too much time is spent on topics only cursorily related to Bourbaki and its mathematics.When any detail is presented at all it is done so without exposition, without any real attempt to educate the reader.

The book literally reads like a poorly written high-school paper.

It's An OK Read If You Have Interest In The Subject
A moderately entertaining read.Aczel takes us behind the development of strutural mathematics as well as the Bourbaki group of French mathematicians - both the history and the personalities.There is precious little on art, candidly, and the mathematics is also quite light - focusing on set theory and the development of "New Math".Rather, it reads more like a biograpghy of a couple of the Bourbaki - Weil and Groethendieck, and not a real riveting one at that.The premise is interesting enough, and the book is OK if you have interest in the subject, but it is not Aczel's best work.

Better than the Reviews
I have The Mystery of the Aleph, The Riddle of the Compass, Fermat's Last Theorem, and even Complete Business Statistics. I like his writing, but was dissuaded by the extreme negativity of the reviews on this site. Finally, I decided to trust my gut. I enjoyed and profited from his version of Bourbaki. However, I think he may be out on a limb equating Grothendieck with Einstein.

The Artist and the Mathematician

This book gives the impression that the Bourbaki group alone discovered and laid bare the mathematical structures studied in modern mathematics and originated the idea of founding the edifice of mathematics upon set theory. There is no mention of all the controversies and work done on the foundations and structures of mathematics prior to Bourbaki. For all the talk about Bourbaki and their investigation and championing of mathematical structures, the book says virtually nothing about what a mathematical structure is or looks like, or how the Bourbaki approach or the nature of their conception of mathematics differed from what preceded them, except to say they were rigorous and built mathematics upon set theory.

There is some mathematical terminology in the book, but no mathematics. The content is mostly biographical, with Andre Weil and Alexandre Grothendieck getting, in the final count, the most attention. The Bourbaki group's first meeting, in December of 1934, isn't mentioned until chapter seven, eighty pages in. From page 81 to page 127 the subject is Bourbaki, then the book shifts topic and is about Roman Jakobson, Claude Levi-Strauss and the rise of structuralism, including Roland Barthes, Jaques Lacan and others. The author claims that Bourbaki's structrual view of mathematics, their focus on mathematical structures and the structure of mathematics, is a major source, along with the linguists Sausurre and Jakobson, of what became, in the literary and sociological fields, Structuralism. The author displays no critical thought in these pages, and the presentation is superficial and misleading throughout.

For the mathematically adventurous, Leo Corry's book Modern Algebra and the Rise of Mathematical Structures places Bourbaki in historical context. See especially chapter 7, Nicolas Bourbaki: Theory of Structures, which is also available online as a .pdf file.
... Read more

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Norman Levinson (1912-1975) was one of the most respected mathematicians throughout the world and one of the most beloved in the Cambridge, MA community. This collection of his Selected Papers bears witness to the profound impact Norman had on research in mathematical analysis with applications to problems in science and technology. Levinson's originality is reflected in his fundamental contributions to complex, harmonic and stochastic analysis, to linear and nonlinear differential and integral equations, and to analytic number theory, where he made significant advances toward resolving the Riemann hypothesis up to the end of his life. The two volumes are divided by topic, with commentaries by some of those who have felt the impact of Levinson's legacy: B. Conrey, B. Levitan, J. Moser, J. Nohel, M. Pinsky, A. Radakrishnan, R. Redheffer, D. Sattinger, H. Sussman, and E. Zeidler. Personal tributes from H. McKean, W. T. Martin, B. Kostant and Levinson's wife Fagi honor the memory of this remarkable man. ... Read more

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Richard Brauer (1901-1977) was one of the leading algebraists of this century. Although he contributed to a number of mathematical fields, Brauer devoted the major share of his efforts to the study of finite groups, a subject of considerable abstract interest and one that underlies many of the more recent advances in combinatorics and finite geometries.The 120 papers collected in this volume were first published between 1926 and 1979. Brauer's mathematical impulse was remarkably steady, and his papers are equally distributed between those written before his fiftieth year and those written thereafter, including a number of contributions that were published after his formal retirement as Perkins Professor of Mathematics as Harvard in 1971.The papers are grouped into six sections following an autobiographical preface written for this collection. The first section contains twenty papers on the theory of algebras and is introduced by Oscar Goldman. The seventy-four papers on finite groups make up the second and largest section, which spans all three volumes. The final four sections complete the third volume and represent Brauer's contribution to Lie groups, number theory, polynomials and equations, geometries and biographies of Artin and Thompson. ... Read more