The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed

by Amir D. Aczel

Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s and continued to be published through most of the twentieth century, was a direct product as well as a major force behind an important revolution that took place in the early decades of the twentieth century that completely changed Western culture.

Pure mathematics, the area of Bourbaki’s work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture.

The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century — both in mathematics and in other areas — were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke — because Bourbaki, one of the foremost mathematicians of his day — never existed.

Genres: Mathematics, Nonfiction, History, Science, Biography, Art, Science Nature

272 pages, Hardcover

First published January 1, 2006

About the author

Amir Aczel was an Israeli-born American author of popular science and mathematics books. He was a lecturer in mathematics and history of mathematics.

He studied at the University of California, Berkeley. Getting graduating with a BA in mathematics in 1975, received a Master of Science in 1976 and several years later accomplished his Ph.D. in Statistics from the University of Oregon. He died in Nîmes, France in 2015.

Reviews

[Anome · Rating 2 out of 5]

After reading a review of this book, I went to Amazon and ordered it, as well as the American Mathematical Society's book on the subject. I often feel sorry for Aczel, since, starting with [i]Fermat's Last Theorem[/i], he has generally given the impression of writing the second best book on any subject. At least with his book on Bourbaki, there isn't really any competition. Yet.

The AMS book is remarkably dry, and spares the personal details in favour of the facts. Aczel's book, on the contrary, is a little too...well, wet. After the first few chapters, I'm now familiar with the intimate details of the lives of many of the conspirators and influences of Bourbaki, but he still hasn't actually gotten to who or what Bourbaki was. Every time he introduces a new figure, he goes rambling off into their personal history, leading to a labyrinthine narrative that at a couple of points had me confused as to which person he was talking about.

After reading this book, and the AMS one, I feel there is still a need for a readable account of the Bourbaki movement.

[Jafar · Rating 3 out of 5]

In the 1930’s, a group of top French mathematicians who thought that the math of their day was sloppy, decided to rewrite the entire math and bring rigor, abstraction, generality, and structure to it. They picked on an old college prank and decided to publish their work under the name of Nicolas Bourbanki, a mathematician from the Republic of Poldevia! For a few decades, this group, with a few generations of members, became immensely influential in how math was taught and done all over the world. Then they fizzled out and disappeared for various reasons – mostly because they achieved what they set out to do. Rigor became name of the game in math and the group lacked the vision, leadership, and motivation to do anything else.

This book is Bourbanki’s story. I found the story quite interesting given that I’d never heard of it. However, I liked the book less that its story because I thought Aczel was trying to over-dramatize for the sake of attracting the lay reader. The French anthropologist Claude Lévi-Strauss (“the father of structuralism”) asked the founding member of Bourbanki to model and solve a problem for him regarding some strange marriage customs of aboriginal Australians. Aczel picks up on this story to claim that the whole structuralism movement in anthropology, linguistics, psychoanalysis, literary theory, etc. was inspired by Bourbanki’s ideas of structures – a very far-fetched claim – and he adds a few chapters covering these subjects.

Bourbanki erected the entire mathematics on the foundation of set theory, ignoring Russell’s Paradox and Gödel’s Incompleteness Theorem that showed that set theory wasn’t airtight rigorous and had holes in it. Then chaos and fractals and catastrophe theories came along and showed that you can do math without structures. In social sciences, structuralism gave way postmodernism. And… rest in peace Bourbanki.

[Adam · Rating 4 out of 5]

I feel my impression of this book is different enough to warrant writing a review. I actually quite enjoyed this book. Many of the other reviewers are certainly on point with saying this book is poorly organized. I feel that is very true, I also feel that Aczel attempts to cram too many topics into a single book to its detriment.

If you work in the Mathematical field at all, it's likely you've come across the name Bourbaki at some point, even if you're a more modern mathematician. Famous for being the name of a group that wrote as a single individual, they are considered one of Mathematics' power house groups. I think Aczel did a good job in giving us a sort of inside look into the group for the lay reader. I found the story of Alexandre Grothendiek absolutely enthralling and I probably could have just read a biography on him. I had heard of him before this book, naturally, but I didn't realize he had such an incredible background story. I truly enjoyed reading about the mathematicians prior to World War II, which prompted the creation of the group and their struggles through the war. I feel like that's one of the more overarching points behind the book, to give Bourbaki's story and relay it's overarching goals in mathematics. I really liked reading about the interrelations of the Artists, Philosophers, and Mathematicians involved in Paris' Café scene and I felt that, very much, worked into the spirit of Bourbaki. I loved seeing how the Art and Philosophy influenced the mathematics and vice versa.

Unfortunately, I feel like the book gets pretty side tracked when it starts talking about Linguistics and Anthropology with Levi-Strauss. I feel like that sort of got forced into the narrative and broke the story up a bit too much for me. At a certain level I understand why it was inserted before Grothendiek's chapter covering his post-Bourbaki narrative and Bourbaki's demise, but I felt like it was too much to me and I didn't find the topic as interesting.

I realize some of the narrative is written for "dramatic effect", which is usually okay, but when it covers Weil's story at the beginning and ends with a cliff hanger... then doesn't continue until more than halfway through the book is kind of a bit much. This made it feel even more erratic and I can understand why some readers would mark this down.

Amidst this disorganization is a really good story about the famous mathematician Alexandre Grothendiek and the super group Bourbaki. I found both of these aspects very memorable and if you can focus on that excellent material, it really makes this book worthwhile.

[Michael · Rating 1 out of 5]

A remarkably dull book about remarkably interesting things, this reads like a set of carefully written initial notes that somehow bypassed the part where the book itself was written and edited and somehow just shot out onto the shelves, printed and bound and with a misleadingly intriguing cover. If you want to learn about the Bourbaki group and its place in modern thought, you would almost surely be better off browsing the relevant Wikipedia articles.

[Jimmy Tarlau · Rating 3 out of 5]

Sometimes you read a book and you can't quite remember why you picked it up or what it is about. I started reading this book thinking it might have something to do with a disappearance (which it does) or a scientific/suspense thriller regarding an imaginery mathematician (kind of). Actually it is the history of a group of French mathematicians who decided that Math needed to be more rigorous. It based its math on set theory and was a major factor in the mathematic 'movement' in the last part of the 20th century. It had its relations with structuralism (which I know very little about) and the works of Claude Levi-Strauss. I liked reading about the history of the different mathematicians and their lives during WW II but some of the material on structuralism in antrhopology, pscychology, and literature were lost on me.

[J. · Rating 3 out of 5]

I was primarily reading this to better understand what Bourbaki was, and I guess this book explained that. But it didn't do a great job at explaining why structuralism became so important. Structuralism seems natural, from a mathematical perspective, but I was unable to see--and Aczel didn't explain to me--what it was useful for in psychology, anthropology, etc. Also, I found the layout of the book a little confusing, and I think it could be rearranged to more effectively tell the story.

[Marie · Rating 3 out of 5]

Poorly written, but a interesting historical exploration of Bourbaki and associated mathematicians.

[Bob · Rating 3 out of 5]

Summary: The story of the Bourbaki, named after the greatest mathematician who never existed, who led a revolution in the emergence of the “new math,” introducing a new rigor into the field.

When I was in middle school, we were introduced to “the new math.” One of the things I was always curious about was why the first thing we did was learn about sets. I was reminded of this when I read this book, which explained why sets were foundational to the approach.

This is the story of Nicolas Bourbaki, who convened a group of mostly French mathematicians around him, creating a tremendously productive group that in its day revolutionized the practice and teaching of math. Aczel introduces us to the key figures in this group–Andrew Weil (who later solved Fermat’s Last Theorem and brother of philosopher Simone Weil), Laurent Swartz, Henri Cartan, Claude Chevally, Jean Delsarte and Jean Dieudonne. We are also introduced to Alexandre Grothendieck, perhaps the most brilliant and also eccentric of them.

The most striking thing we learn is that the group formed around a mathematical joke upon which Weil built. Nicolas Bourbaki never existed except as a made up identity that reflected the collective effort of this group to rehabilitate and revolutionize mathematics in France that had fallen into the backwaters of German mathematics and science. These mathematicians met regularly and forged a consensus on how math would be practiced and taught in France that resulted in the prolific production of texts, revolutionized not only math education throughout the world, but touched a variety of other disciplines. Their approach was founded on set theory. They emphasized math in the abstract, focusing on mathematical proofs and rigor.

They were trying to articulate the structure of mathematics and this led to interesting interactions with pioneering anthropologist Claude Levi-Strauss, child psychologist Jean Piaget, linguistic theorists, and even writers including Italo Calvino. Aczel traces how structuralism for a time replaced existentialism in philosophy until the turn to the post-modern.

During the war Weil fled to America and stayed there, and gradually, his influence in Bourbaki waned. In the early 1950’s Alexandre Grothendieck joined for a time. His brilliance both stimulated the work of the Bourbaki and led to his departure as he recognized the weakness of set theory as a basis for Bourbaki, trying and failing to convince them of the idea of categories. Grothendieck differed from the Bourbaki, preferring to work alone.

The parting spelled a turning point for both. While Bourbaki continued to have a spreading influence for a time, it was more on the basis of past work. Grothendieck went on to do innovative work for a time, and directing students into significant problems. He held a position at the IHES, a French version of the Institute for Advance Study. Then he became more engaged in political and environmental causes, and when his efforts failed in these areas, he retreated to the Pyrenees, where his whereabouts remained unknown. After this work was published, he died in 2014 in Saint-Girons, Ariège.

The title of this work is a bit of a puzzle. Apart from a chapter on cubism, Braque, and Picasso, and its connections to antecedents to the Bourbaki, this is not a book about artists, unless this is a contrasting reference to Grothendieck and Weil, which was opaque to this reader. I found the organization of the book a bit labyrinthine. Nevertheless, it was an intriguing account of a movement in mathematics I’d never heard of. It was fascinating to see how productive this group was for a period and yet how significant the human factors were in the ultimate fate of Bourbaki.

[Lelna Gwet · Rating 4 out of 5]

Waaaaay too much content, though all equally fascinating in their own right. As someone who has a natural inclination to draw connections between mathematics and the cognitive sciences, I found this to be a very interesting account that encompassed an arguably important moment in history for all of those disciplines.

However, the book lacks clear organization. If I was not already naturally fascinated by the different intersections presented, I would have stopped reading after the first few chapters; it was extremely confusing to identify and follow the direction of the book. Also, structuralism was not very clearly defined to begin with. So, Aczel's attempt to stress the importance of structuralism in mathematics, linguistics, anthropology, and psychology was a bit lost on me (with a quick Google search between chapters, I was able to kinda-ish clarify my confusion in order to carry on in the story).

In the end though, I definitely enjoyed the story overall and the biographical pieces of Alexandre Grothendieck & André Weil. Additionally, the bibliography exposed me to more literature for further follow-up.

[Anabelian · Rating 5 out of 5]

A good overview of the development of structuralism as a movement at large and its interplay with Bourbaki's ideas. Also contains a heartfelt biographical sketch of Alexander Grothendieck.

[Vishaka Datta · Rating 2 out of 5]

I picked up this book with much enthusiasm to learn about the mathematical world in which the Bourbaki group rose to prominence. the stories of the members of the gropu, and an exploration of the ideals that led to their approach to mathematics. In my engagement with mathematical history so far, its pretty clear the Bourbaki group played a huge role in the way mathematics is done, and in particular, the now common emphasis on abstraction and some semblance of formal rigour in proving mathematical results. This wasn't how people approached mathematics before the World War II.

The book starts off rather well and paints in broad brush-strokes the early lives and upbringing of Andre Weil and Alexander Grothendieck. The author notes the stark differences between their upbringing; Weil was the son of diplomats, who pulled out all stops to give their son the best education that money could offer. A prodigy of sorts, Weil would climb through the mathematical world quickly and find himself as a full rank professor and the head of the mathematics department at the Aligarh Muslim University at the age of 23. Weil's travels through Europe brought him in contact with top mathematicians across Europe. Grothendieck was prodigious by any stretch of imagination, only, his teenage years were spent in concentration camps and refugee camps in nearly complete isolation from the mathematics community. The remaining mathematicians covered in the book - Schwartz, Dieudonne, Chevalley, Cartier -- get a quick introduction.

Grothendieck and Weil's life stories make for interesting reading, but unfortunately, I felt the book went downhill from there for me.

The author then discusses the genesis of the Bourbaki group, and goes on to proclaim that Bourbaki championed the idea of structuralism in mathematics, an approach which took root in linguistics according to the author. But what is structuralism? What is the structuralist view of ideas in linguistics? Or in mathematics? How does it differ from other approaches to linguistics or mathematics? The book falls short rather badly here. Instead, one keeps encountering the same single sentence description of structuralism over and over.

In a rather interesting chapter on anthropology, where the author discusses a meeting between Andre Weil and Levi-Strauss that led to some ideas from group theory being applied to studying marriage relations in tribes studied by Levi-Strauss. Here, again, the book falls short in explaining just what structuralism means, and how it took anthropology by storm. The artist that the book title refers to is Pablo Picasso, and the lone chapter on structuralism in art again fails to motivate what made Picasso's approach revolutionary. So in a sense, the book is as much about structuralism in general as it is about Bourbaki, neither of which is treated to a satisfying depth in the book.

An appreciation for pure math and art are rather difficult topics to convey to a popular audience. For instance, Rebecca Goldstein manages it with aplomb in her book on Kurt Godel, although it helped that she was a philosopher herself. One can't help but feel that more could have been done to convey the importance of the Bourbaki project to change the way mathematics was taught and researched. More coverage of the impact (and criticism) of Bourbaki would have been a welcome addition. Same goes for structuralism.

The concluding chapters of the book deal with Grothendieck's dramatic disappearance from the world. Personal interviews with the mathematicians or friends who knew him would have made the story far more relatable. For instance, I found an account on Grothendieck written by his collaborator , Pierre Cartier (a fellow Bourbaki) to be quite moving in its treatment of Grothendieck's life. Grothendieck seems like a rather singular figure in the history of mathematics, and science in general, and his rise to the top of the mathematical world and subsequent withdrawal ends up sounding like a rather cliched story of sorts in the book.

The book serves as a good introduction to Bourbaki perhaps, and also has a useful reference list, but you would really need to look elsewhere for a better account of Bourbaki.

[Book O Latte · Rating 4 out of 5]

Pada masa pertengahan abad 20, nama Nicolas Bourbaki dikenal sebagai matematikawan hebat yang menelurkan banyak buku penting di berbagai bidang matematika seperti aljabar, topologi, teori himpunan, dan lain-lain.

Namun Nicolas Bourbaki, si matematikawan hebat itu, sebenarnya tidak pernah ada.

Nama tersebut adalah nama samaran dari sekumpulan matematikawan (rata-rata dari Perancis) yang awalnya bergabung untuk memperbaharui textbook matematika yang pada saat itu (pasca Perang Dunia I) sudah ketinggalan jaman.

Buku ini mengisahkan kemunculan grup Bourbaki, tokoh-tokohnya, dan hubungan serta pengaruhnya terhadap budaya kemasyarakatan di Perancis pada saat itu dan selanjutnya. Ini yang tersirat dari judul buku "The Artist and the Mathematician". Di dalamnya diceritakan tentang awal abad 20 yang penuh 'pendobrakan'. Einstein mendobrak cara pandang terhadap geometri semesta. Picasso, Braque dan kubisme mewakili cara pandang baru di dunia seni. Intinya, zeitgeist atau semangat era itu adalah meninggalkan cara lama dan menempuh cara baru.

Pasca Perang Dunia I, dengan semangat membangun yang baru, Paris dan terutama kafe-kafenya menjadi pusat pemikiran dan kreasi yang dinamis, tempat bertemunya para ilmuwan, filsuf, penulis, dan seniman.
Dunia matematika di Perancis saat itu dirasa tertinggal dari Jerman, karena perang telah merenggut banyak matematikawan muda yang harus ikut angkat senjata.
Para matematikawan di beberapa universitas di pelosok Perancis yang bertanggung jawab atas kurikulum, dengan inisiatif dari Andre Weil dan Henri Cartan, bertemu di sebuah cafe di Paris dan bersepakat untuk membentuk grup Bourbaki.

Tokoh grup Bourbaki yang paling banyak diceritakan di buku ini adalah Andre Weil (salah satu pendirinya) dan matematikawan jenius Alexander Grothendieck (anggota generasi ketiga).

Selanjutnya diceritakan bagaimana para anggota grup menyusun struktur kurikulum pengajaran matematika, bagaimana perkembangan grup sampai bubarnya.

Diceritakan juga hubungan karya grup Bourbaki dengan teori strukturalisme dari antropolog Claude Levi Strauss, bagaimana pengaruhnya terhadap linguistik, psikologi, dan ekonomi.

Buku ini awalnya cukup menarik ketika membahas sejarah pendirian Bourbaki dan tokoh-tokohnya, tetapi entah kenapa banyak pengulangan di bagian menuju akhir ketika menerangkan tentang strukturalisme. Dan yang saya tangkap tentang hubungannya dengan seni (yang dijadikan judul) malah kurang kuat. Agak maksa gitu.

Ada dua hal yang terlintas di pikiran saya waktu membaca buku ini. Yang pertama adalah tentang perang.
Eropa saat itu memiliki banyak sekali anak-anak muda brilyan yang, seandainya tidak ada perang, bisa jadi membawa kemajuan besar bagi ilmu pengetahuan, di Eropa khususnya dan dunia pada umumnya. Namun perang menghancurkan mereka.
Di buku Logicomix, Bertrand Russell berkata "Begitu banyak peristiwa besar yang menjadi besar justru karena tidak rasional. Dan tidak ada yang lebih irasional daripada perang."

Yang kedua adalah betapa serunya kafe-kafe di Paris pada saat itu, penuh dengan obrolan intelektual yang kreatif dan penuh semangat. Saya jadi membayangkan, mungkin dulu anak-anak muda idealis generasi bung Karno dan bung Hatta, mendiskusikan pendirian negara, pendidikan bangsa dll, sambil ngopi-ngopi di warung.

Saya jadi ingat waktu berkunjung ke kota kecil Princeton dan numpang berteduh di kedai kopi di Nassau Street (waktu itu hujan besar). Di dalamnya penuh akademisi, entah mahasiswa atau dosen dengan laptop dan buku masing-masing, membaca jurnal, mengerjakan paper, obrolannya seputar ilmu. Tepat pada saat itu kafe itu jadi pusat pemikiran juga (ya habis kafenya di depan kampus sih, pantaslah isinya begitu).

Kalau kafe-kafe sekarang juga dijadikan tempat ngobrol intelektual idealis kreatif seperti itu, asyik juga ya. Batas akademik dan publik jadi lebur, seperti Paris awal abad 20.

- dydy-

[Nathan Albright · Rating 5 out of 5]

It takes this book a while to get to its point. As a fond reader of matters mathematical [1] and historical, and as someone with a somewhat downbeat view of the goodness of humanity as a whole, I expected that when I read the book I would read about a fraudulent attempt on the part of someone to pretend to be a genius mathematician that gullible people happened to believe. At any rate, I expected that the author would begin talking about Nicolas Bourbaki fairly quickly, given the fact that his name appeared as part of the title of the book, and certainly as part of the hook to draw the reader's interest. What, a world-famous and genius mathematician never existed? Say what? However, the author, himself an accomplished and excellent historian of mathematics, most famous for his book on Fermat's Last Theorem that is on my lengthy list of books that I want to read, decides to delay the reveal of who Nicolas Bourbaki is and why he never technically existed, and why that matters. Although the payoff is delayed, it is a worthwhile one, and so those readers who are as puzzled as I was upon starting this book should be encouraged that it will all make sense eventually, even if the book is definitely a slow starter.

The contents of this book definitely cross over the border from ordinary into deeply mysterious, examining aspects of biography, religion and philosophy, military history, linguistics, as well as the history of mathematics. The book opens with the mysterious of one Alexandre Grothendieck, a Jewish mathematician who grew up in France of foreign ancestry who was said to have worked with Nicolas Bourbaki, before retreating into obscurity and voluntary exile and solitude, going entirely "off the grid" as it were, discussing his personal history as a refugee seeking to escape Hitler's final solution. The author then turns to a short biography of another French Jewish mathematician named Andrè Weil, whose attempts to avoid service in the French military ended up leading to jail and nearly execution for desertion in the run-up to World War II. Then the author examines the flight of another French Jewish mathematician from the German wehrmacht in World War II. On the 59th page of the roughly 200 page book the author asks the obvious question: Who was Nicolas Bourbaki? At this point the author goes back and gives context, discussing the career of General Charles Bourbaki in mid-1800's France, famous for his loyal service to the French nation and his escape into Switzerland and captivity after the disaster of the Franco-Prussian War. Then the author looks at art history and the relationship between cubist and surrealist art and the mathematics of the 20th century, showing how a group of French mathematicians formed an anonymous/pseudonymous commune as a way of influencing the course of world mathematics by their approach to structuralism with its dependence on set theory. At this point the author's mystery has been revealed and a more straightforward discussion of the rise and fall of structuralist philosophy, from its peak influence in the 1950's and 1960's, its influence on the pioneering anthropology work of Levi-Strauss, and its gradual decline after the rise of postmodernism.

Aside from the fact that this book is an intriguing and insightful multidisciplinary history that deals with a wide variety of fields with skill and polish, there is an intriguing and deep irony in this book that students of philosophy will find of great interest. Rather, there is a whole host of ironies. For one, the author is at pains not to relate the Jewish origin of the mathematicians of the Nicolas Bourbaki collective with their struggles of faith in the aftermath of the Holocaust. For another, a great part of the decline of this collective came about with the decline of nationalist mathematics as a whole, as well as the aftermath of the Vietnam War and the rise of the radical left, for which several of the mathematicians gave their enthusiastic support. Additionally, the author speaks often about the contradictions inherent in the set theory that formed the philosophical underpinnings of structuralism, but comparatively little time talking about the fact that the entire philosophy of postmodernism is self-refuting [2]. These ironies demonstrate that mathematics is of great importance in the larger culture even if many people shy away from the strangeness and difficulty of intense and deep study in mathematics.

[1] See, for example:

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

https://edgeinducedcohesion.wordpress...

[2] Although the matter is too lengthy to be discussed in full here, it is worthwhile to note that postmodernism believes there is no absolute truth, although the statement that there is no absolute truth is itself an absolute truth. Likewise, this worldview comes with the point of view that there is no possibility of conveying what is understood by one person to another, but postmodern philosophers write lengthy and weighty tomes in which it is possible for the reader, albeit only an unusually patient and longsuffering one, to understand what the author is getting at. The fact that postmodern philosophers claim to be teachers of absolute truth and communicate through lengthy books gives the lie to their claims that there is no truth nor any possibility of communication between human beings. It would be hard to imagine a philosophical view that was more entirely self-defeating.

[Dan Cohen · Rating 2 out of 5]

I didn't really like this book. It's a history of the Bourbaki phenomenon, in which a group of mathematicians issued publications in the name of an imaginary mathematician (Bourbaki). This it does do, although the narrative is a little confusing and annoying as the first few chapters dance around this purpose. But vast tracts of the book are really devoted to the concepts and history of Structuralism. I accept that the Bourbaki phenomenon was intimately connected with Structuralism but I wasn't looking for a book on Structuralism and found the discussion of it largely boring.

The book makes repeated claims for the importance of the Bourbaki movement and for the greatness of (at least one of) the mathematicians that drove it, but these claims are not really illustrated.

I would only recommend this book to someone as interested in Structuralism as in mathematics.

[Marissa Fandel · Rating 4 out of 5]

a fun foray into a very niche segment of the history of mathematics. i really enjoyed the context given that positioned Bourbaki's innovations in theoretical math with applications in the humanities, particularly poetry, psychology, and sociology. anyway, it's not math heavy, not too heady, and gives you some glossy eye dreaming about creating New.

[Anton Isopoussu · Rating 2 out of 5]

A reasonably well informed book about the history and impact of the Bourbaki group.

The book wasn't well written at all but it's sufficiently short and dense in interesting tidbits to breeze through regardless.

[Rebeka · Rating 2 out of 5]

Ένα ενδιαφέρον βιβλίο για να μάθει κάποιος ποιος ήταν επιτέλους αυτός ο Μπουρμπακί. Οι πληροφορίες που δίνει είναι απλά ενημερωτικές και δεν θεωρείται, για μένα τουλάχιστον, λογοτεχνικό στην κατηγορία της μαθηματικής λογοτεχνίας.

[Antoine · Rating 4 out of 5]

A cool introduction to the secret french mathematical group Bourbaki which helped to push for enormous rigor in mathematics. The book is all over the place and delves into many irrelevant rabbit hole though.

[Alyssa Gutierrez · Rating 3 out of 5]

He'll always try to stop me, that Nicolas Bourbaki
He's got no friends close, but those who know him most know He goes by Nico He told me I'm a copy
When I'd hear him mock me, that's almost stopped me

[Simon Yoong · Rating 2 out of 5]

Did not enjoy this book. It lacks the wit and ability to interest me.

[Emily · Rating 3 out of 5]

Found this in a little free library. The story was interesting but the author struggled to fill an entire book with it.

[Aran · Rating 4 out of 5]

Bona font, bastant útil pel treball d’història.

[William Bies · Rating 3 out of 5]

This popular book for the educated public by the science writer Amir Aczel is part recreation, part serious intellectual history; it should be read to open the reader’s mind to connections between ideas, without going into any great, or even sufficient, depth. Bourbaki was a French general from the nineteenth century who achieved some distinction during engagements in the Crimean war. In the 1930’s, a group of young and ambitious French mathematicians began writing under this pseudonym. Theirs was a movement towards abstraction, generality and rigor that, in the middle decades of the twentieth century, would come to characterize modern mathematics. Aczel spends the first few chapters giving pocket biographies of several of the major contributors, then settles into an exposition of the group’s program and its ties to the Zeitgeist, which he identifies somewhat cursorily with the revolutions in physics going under the names of relativity and quantum theory and, more convincingly, with the advent of cubism at the hands of Braque, Picasso and Duchamp. These painters turned away from the neoclassical strictures of the nineteenth-century academy to a focus on the interrelationships among the elements of the painted subject, conceived according to novel concepts of spatial and temporal organization. In mathematics, the Bourbaki group issued a series of austere textbooks that refounded the disciplines of set theory, topology, algebra and analysis thoroughly along axiomatic lines and emphasized the structural aspects of each field. In due course, they persuaded most of the mathematical community to approach its investigations in their abstract spirit, which is very different from what prevailed in earlier centuries when the stress was on concrete calculations and formulae. Anyone who has encountered the so-called ‘new math’ in elementary school would have had a taste of the Bourbaki style. In the final chapters, Aczel draws out the active connections between Bourbaki in mathematics and other avenues of French intellectual life after the second world war, such as Claude Levi-Strauss’ structuralism in anthropology, the linguistics of Troubetzkoy and Jakobson, the psychology of Piaget and Lacan and the literary circle known as Oulipo. He closes with a brief account of the demise of structuralism and of Bourbaki in the late 1970’s and the abandonment of his mathematical career by the greatest of the Bourbakians, Alexandre Grothendieck. While Aczel’s is a reasonably solid account of the history of his subject, one wishes he had lived up more to the promise of his title: the artist and the mathematician. For Grothendieck, at least, was a brilliant and consummate artist of ideas. After early pioneering work on functional analysis and topological groups, in the 1960’s Grothendieck, acting on a suggestion from Pierre Cartier, set out on his own and revolutionized the field of algebraic geometry with his theory of schemes, presented in his monumental Elements de geometrie algebrique. The scheme-theoretic approach effects a profoundly beautiful and fruitful union between commutative algebra and traditional algebraic geometry (along the lines of the speculative Italian school from the preceding century, which now receives an adequate theoretical foundation). Along with the contemporaneous advent of sheaf theory and homological algebra (from which derive the most powerful ideas surrounding all this work), the rise of Grothendieck’s scheme theory defines modern mathematics at its finest and most inventive. If ever there was a harmonious interplay between art and mathematics, it is here we may best seek to catch a glimpse of it. To the everlasting beauty of mathematics, which no moth, no flame, no crooked will and no cosmic catastrophe can mar!

[Lawrence · Rating 3 out of 5]

For a popular mathematics book, I found The Artist and the Mathematician pretty bizarre. It started out as if it were going to be a history of the group of twentieth-century French mathematicians known as Bourbaki, with a focus on onetime member Alexandre Grothendieck, who simultaneously was one of them and, Aczel indicates, somewhat transcended them. It ended up cutting a far broader swath than that, as Aczel's narrative about Bourbaki's history transformed into an explication of (what he interprets as) its effects, via structuralism, on culture at large. The fact that the excursions into structuralism somewhat secretly compose a large portion of The Artist and the Mathematician is only one of the strange things about it.

Really, I found Aczel's book alternately inspiring and extremely frustrating. The best parts, such as the recounting of Grothendieck's politically radical family origins, or Jacques Lacan's fusion of structuralism and the theories of Freud, unlocked my imagination greatly. On the other hand, it was intensely offputting to read through one of the longest chapters in the book, "Claude Lévi-Strauss and the Birth of Structuralism" — during which phrases like "the idea of structure" are repeated like mantras — without getting any clear idea of what "structures" are actually supposed to be, possibly because the relevant mathematics is approached through baby steps — and then, on top of that, to encounter the following passage, a few chapters later:

"In 1957, Pierre Cartier made an amazing observation. He understood that a ringed space locally isomorphic to a ringed space of the form Spec(A) — the set of all prime ideals of a commutative ring A — should be considered as a generalization of an algebraic variety. Cartier told Grothendieck about this idea, and the latter began to develop the foundations of algebraic geometry based on Cartier's generalized notion of algebraic variety, now known as a scheme."

It seems like it was flown in from a completely different book. Overall, indeed, The Artist and the Mathematician gave me the sense of being composed (perhaps as its cover might indicate!) of a lot of separate works collaged together. In addition, I also didn't see a lot of internal evidence within the book to substantiate Aczel's grand claims for Bourbaki's influence, however interesting his recounting of what some of that purported influence might be. I do very much appreciate his ambition in this book — I just find it bizarre that he failed so greatly in getting something unified out of it.

I still have no idea who the artist or the mathematician is.

[Dan · Rating 2 out of 5]

I fought my way through the entire book, and there were some rewards, but generally the book is poorly organized and strays from its ostensible subject matter.

From the title one would expect a book about the fictitious mathematician Nicolas Bourbaki, a construct of a group of real-life French mathematicians, who really did publish a large body of influential mathematical texts in the 20th century, and that story is there but it's somewhat tangled and buried in rubbish. I believe the author was experimenting with applying cubism to narrative and the results were unsatisfactory.

The first part of the book presents disjointed and partially overlapping accounts of the lives of various real mathematicians who contributed to the creation and works of Bourbaki, but this part is unclear in its organization and does not present a clear overall picture. Then there are several chapters on structuralism (a central element of Bourbaki's work) in mathematics, anthropology, linguistics, psychology, and literature. These were okay but one chapter would have sufficed for the non-mathematical exploration. The book concludes with a pretty well-written account of the demise of Bourbaki and the withdrawal from Bourbaki and the rest of society of Alexandre Grothendieck, a brilliant mathematician who might have ensured the Bourbaki group's continued relevance if he had stayed with the group.

[Harry]

"At the end of 1957, his mother died. Grothendieck, who had been exceptionally close to his mother and greatly admired both her and his father, underwent a shock, which caused him to leave mathematics for a few months. He returned to mathematical research in 1958, and soon afterwards married a woman named Mireille, who had been a close friend of his mother and was several years older than he. Eventually he would have three children with her.
In 1957, Pierre Cartier made an amazing observation. He understood that a ringed space locally isomorphic to a ringed space of the form Spec(A)--the set of all prime ideals of a commutative ring A--should be considered as a generalization of an algebraic variety. Cartier told Grothendieck about this idea, and the latter began to develop the foundations of algebraic geometry based on Cartier's generalized notion of algebraic variety, now known as a scheme."

enjoyed this book like I would enjoy reading wikipedia biographies of 20 mathematicians in a row, except with more redundancy and less continuity

[AC · Rating 3 out of 5]

Some interesting history, but it definitely could have been a shorter book and accomplished the same thing. Of late, Aczel's books have started to suffer a lot from this--unnecessary diversions (sometimes paragraphs, sometimes entire chapters) whose sole effect seems to be to ensure the book goes over 200 pages--as if the substance of the material is somehow diminihsed if it only runs 180 pages. He could have lost 90% of the 40+ pages of the history structuralism and still gotten his point across. The fact is, there just wasn't enough about Bourbaki to make a book this long (without delving too much into detailed mathematics), but that wasn't going to stop him from having a 200+ page book. Still, Aczel is again in fine form drawing together a wealth of information from the history of science and mathematics and presenting them in a way that is both informative and enjoyable.

[Belacqua · Rating 2 out of 5]

Unfortunately this doesn't quite live up to expectations. Too chatty when it comes to biographical details of too many people, while Nicolas Bourbaki and their contributions get only skin deep coverage. Let alone giving the layperson at least some grasp of what the mathematics was about. Still interesting as Azcel tries to place Bourbaki within in the general context of cultural history - an approach that would deserve a more skilful execution as it is a somewhat unique, promising point of view. I had the impression that Azcel had a great idea but was lacking knowledge, eloquence, and courage to pursue it. So he pads it out with platitudes and anecdotes. But it still is an acceptable and accessible read as well as a colourful portrait of the era.

[Fernando del Alamo · Rating 3 out of 5]

Este libro trata de la historia de Nicholas Bourbaki, matemático que no existió, sino que fue un grupito de matemáticos franceses encabezados por Andre Weil. El nombre lo habían tomado de un general retirado, aunque hicieron más bromas on todo ello.

Habla de las vidas y aventuras de algunos de ellos, enfatizando a Alexander Grtthendieck. Por otro lado, dice y vuelve a decir que el grupo introdujo el estucturalismo matemático. El problema es que no defiene muy bien lo que es y eso hace que quien no conoce exactamente la definición tenga que buscarla en fuentes externas.

No ha sido del todo de mi agrado. Puede ser interesante para matemáticos que conozcan bien el estructuralimo matemático, para conocer el carácter y las circunstancias de los que lo impulsaron.

[Trenchologist · Rating 3 out of 5]

Interesting topic, one that resonates even today, the history of it well-covered, but felt greatly redundant to me. Perhaps in part because of my already established familiarity with Structuralism, a founding principle of the actions & ideas explored in the book. But it's also somewhat because of the book itself, where things were covered again, then again, then mentioned another time. Wanted to know more about Grothendieck (a real person who fits into the whole scheme), truth told, and I think Aczel realized somewhere in the writing process that here was the better story, and so ended up dividing the book's attentions between B. and G. -- not entirely to its benefit. Also, I'm still not sure who the artist was or maybe was supposed to be.