Founder of the Secret Society of Mathematicians

Anti-Globalism suggests an article at Science News on the passing of Henri Cartan, one of the founding members of a strange and influential group of French mathematicians in the twentieth century. "In the 1930s, a group of young French mathematicians led an uprising that revolutionized mathematics. France had lost most of a generation in the First World War, so the emerging hotshots in mathematics had few elders to look up to. And when these radicals did look up, they didn't like what they saw. The practice of mathematics at the time was dry, scattered and muddled, they believed, in need of reinvention and invigoration... Using the nom de plume Nicolas Bourbaki (after a dead Napoleonic general), they wrote a series of textbooks laying out mathematics the right way. Though the young mathematicians started out only intending to write a good textbook for analysis..., they ended up creating dozens of volumes which formed a manifesto for a new philosophy of mathematics. The last of the founders of Bourbaki, Henri Cartan, died August 13 at age 104... Two of his students won the Fields medal..., one won the Nobel Prize in physics and another won the economics Nobel."

Comments

Remove the stone of shame...

[Anonymous Coward]

Attach the stone of triumph!

secret?

[bfields]

"Secret society" is a bit over the top! I always had the impression it had the feeling more of a running joke; from the article:

In the 1950s, Ralph Boas of Northwestern University wrote an article for the Encyclopaedia Britannica on Bourbaki, explaining that it was the pseudonym for a consortium of French mathematicians. The editors of the encyclopedia soon received a scalding letter signed by Nicolas Bourbaki himself, declaring that he would not allow anyone to question his right to exist. In revenge, Bourbaki began spreading the rumor that Ralph Boas himself didn't exist, and that B.O.A.S was an acronym of a group of American mathematicians.

Though it wasn't *just* a joke--they wrote a lot of very serious mathematics!

You meant the wrong way

[Anonymous Coward]

Bourbaki books are the most boring books you can buy. Avoid them at all costs. If you want to study mathematics, there are much better books.

Their motto is to never explain anything. These makes these books completely unreadable. Mathematics the right way ccroding to them is:
--no example: examples are evil being that stray us from the true path of pure abstraction.
--never mention any applications: are you nuts ? mathematics must remain pure. Applied mathematics are the spawn of the devil. If it serves some purpose, it's not mathematics anymore.
--Don't draw anything. Drawings are tools of the devil. 2D domains and geometrical figures should only exists as pure abstraction.
--The less explanations, the better: only idiots needs explanations.
--Never rewrite a theorem for the sake of clarity: having 20 references to other theorems
(usually in another volume) in a 5 lines proof
is better for clarity (don't even write the name of the Theorem you refer to, a true mathematician knows them by volume and page number).

And better they add insult to the injury in the preface: "no prerequisite knowledge of math is needed to read this book". Yeah whatever.

Re:You meant the wrong way

[killmofasta]

Umm. I have a few texts from the late 1800s, and they are absolutly completely worse. Bourbaki's is the abstraction. ( I have their volume on abstract algebra, that I referred to while I was taking that graduate level course. Theirs is a terse work, much more accurate, and well though out. ) A few Springer-Verlag texts are worse also.

Re:You meant the wrong way

[msuarezalvarez]

Indeed. And the much more literary style that was deemed acceptable before resulted not only in inaccuracy but in gross errors.

Bourbaki's work is an amazing feat, which nowadays can be appreciated maybe only with a considerable amount of historical perspective---mostly because it was extremely successful: it set (maybe by using an elaborate, laborious, hyperbole that is, among many other things, a display of love for the subjects treated) standards against which mathematical writing was (and is!) compared, if not jugded, and the student of today has the false impression that the textbooks he reads today are of the same kind as those that were read at all times, simply because he does not know history.

The effort spent in coming up with clear, precise definitions, detailed proofs, even with usable notation, is easy to disparage once one can enjoy its benefits.

Re:You meant the wrong way

[porpnorber]

I think perhaps you weren't born to be a mathematician. I seriously wish that some of my profs would have STFU'd about the applications and focused on the proofs and proof techniques. If you are studying biology, do you really want half your class hours devoted to what plants look nice in a garden? (Maybe you do, but if so, study gardening instead.) If you are studying software architecture, should the textbook assume that what you really care about is, I don't know, writing keyboard scanners? (Again, you might, but then why not buy a different book?) And do you want your general psych class turned into a course on methods of military indoctrination? It doesn't matter the field, I think we'd benefit from a lot less focus on applications and a lot more on mastery of content. Mathematics most of all, because the cultural content of mathematics is the collection of tools for thinking about pure problems, abstracted from any problem domain. Indeed, the best advances in mathematics come, it seems to me, from abstracting internal mathematical tools away from their original mathematical focus, and thereby making them available to the whole subject, and not just one small field.

As to issues with how theorems are referred to, I think this brings us to the root of the Bourbaki phenomenon. The cult of personality is not so productive in a field whose content is supposedly objective, and naming results after people is a barrier to objectivity in understanding and a barrier to communication. My girlfriend is Chinese. Do you suppose she knows, or cares, about Green's theorem or Taylor series, under those names? But five seconds with a pencil and paper and we are in sync.

Mathematics is not automotive mechanics and it is not pop music! And—I don't mean to be rude here, in making a cultural observation—that was a particularly hard lesson for French academia in particular—though for France we needed to write "it is not the civil service and it is not religion."

Re:Imagine their meetings!

[CRCulver]

Imagine them finding an equation to discover the solution for all the problems of the world, and then the awkard silence as it turns out to be 42.

from Straight Dope

[mbius]

The following examples may help to clarify the difference between the new and old math.

1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?

1970 (Traditional math): A logger sells a truckload of lumber for $100. His cost of production is $80. What is his profit?

1975 (New Math): A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100 and each element is worth $1.

(a) make 100 dots representing the elements of the set M

(b) The set C representing costs of production contains 20 fewer points than set M. Represent the set C as a subset of the set M.

(c) What is the cardinality of the set P of profits?

1990 (Dumbed-down math): A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Underline the number 20.

1997 (Whole Math): By cutting down a forest full of beautiful trees, a logger makes $20.

(a) What do you think of this way of making money?

(b) How did the forest birds and squirrels feel?

(c) Draw a picture of the forest as you'd like it to look.