# Founder of the Secret Society of Mathematicians

#### kdawson posted more than 6 years ago | from the as-only-the-french-can-do-it dept.

103
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."*

## Remove the stone of shame... (5, Funny)

## Anonymous Coward | more than 6 years ago | (#24812341)

Attach the stone of triumph!

## For anyone wondering what that refers to... (0, Flamebait)

## dwalsh (87765) | more than 6 years ago | (#24814085)

Don't worry, it isn't funny.

(Simpsons parody of the Stonemasons)

## Re:For anyone wondering what that refers to... (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24814195)

## Re:For anyone wondering what that refers to... (1)

## Zacobi (1118955) | more than 6 years ago | (#24814223)

Don't worry, it isn't that funny any more.

(Simpsons parody of the Freemasons)

Fix'd

## Their biggest achievement (0)

## Anonymous Coward | more than 6 years ago | (#24812371)

They made Steve Guttenberg a star.

## Re:Their biggest achievement (0)

## Anonymous Coward | more than 6 years ago | (#24812527)

## Re:Their biggest achievement (4, Funny)

## 4D6963 (933028) | more than 6 years ago | (#24812633)

They made Steve Guttenberg a star.

Who??

## Re:Their biggest achievement (1)

## Rod Beauvex (832040) | more than 6 years ago | (#24814319)

## Re:Their biggest achievement (0)

## Anonymous Coward | more than 6 years ago | (#24816517)

It's from a song in an epsiode of the American primetime cartoon "The Simpsons." Basically it was about a secret society modelled after the Freemasons called the Stonecutters that manipulated world events. Their drinking song included references to these acts of manipulation, of which making Steven Guttenberg a star was one.

## Imagine their meetings! (0)

## Bragador (1036480) | more than 6 years ago | (#24812379)

Imagine a bunch of mathematicians, meeting secretly and proving under the light of the torches that a solution existed for all the problems of the world... and yet, not knowing what the solution was.

Priceless

## Re:Imagine their meetings! (2, Funny)

## Anonymous Coward | more than 6 years ago | (#24812685)

The He-Man-Godel-Hating Club!

## Re:Imagine their meetings! (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24819373)

The first rule of the He-Man-Godel-Hating Club is

you do not talk about the He-Man-Godel-Hating Club!## Re:Imagine their meetings! (2, Funny)

## KDR_11k (778916) | more than 6 years ago | (#24822351)

The first rule of clubs is that whenever anyone mentions any club you claim that its first two rules match those of the Fight Club!

## Re:Imagine their meetings! (1)

## unitron (5733) | more than 6 years ago | (#24826977)

The first rule of club rules is ... ah, never mind.

## Re:Imagine their meetings! (5, Funny)

## CRCulver (715279) | more than 6 years ago | (#24812919)

## Re:Imagine their meetings! (2, Funny)

## laejoh (648921) | more than 6 years ago | (#24817031)

Imagine wanting to write it down but finding that the margin of the book you're using is way too small...

Besides, the solution for (and cause of) all the problems of the world is beer!

## Thees Matematics... (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24812441)

## secret? (5, Funny)

## bfields (66644) | more than 6 years ago | (#24812447)

"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:

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

## Re:secret? (3, Funny)

## DeadDecoy (877617) | more than 6 years ago | (#24813801)

Mwahahaha this plan is brilliant. Now if only I could get with a girl and spread my brood upon the world.

## Re:secret? (1)

## Whiteox (919863) | more than 6 years ago | (#24815157)

I have hear that Hans Delbrook was also a member.

## And it all came down to this (2, Insightful)

## El Yanqui (1111145) | more than 6 years ago | (#24812453)

## when things don't add up & everything's 'secre (-1, Offtopic)

## Anonymous Coward | more than 6 years ago | (#24812483)

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## Re:when things don't add up & everything's 'se (3, Funny)

## Anonymous Coward | more than 6 years ago | (#24812625)

Oh, Anonymous Coward, how I love your posts. The complete disregard to logic, spelling and grammar appearing in every topic has become my warm security blanket. You are the nougat center of my candybar and I will henceforth use random caps keys while starting all sentences with a lowercase letter - or better an ampersand - as a show of the esteem I hold you in.

& sINCE yOU post this in every topic perhaps you might want to edit the oRIGINAL.

pS, I work for the gOVERNMENT and we are tracking you. yOU should quit doing that thing with anime porn or yOU"LL go blind.

## You meant the wrong way (5, Insightful)

## Anonymous Coward | more than 6 years ago | (#24812493)

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 (4, Insightful)

## msuarezalvarez (667058) | more than 6 years ago | (#24812679)

## Re:You meant the wrong way (0, Redundant)

## fluch (126140) | more than 6 years ago | (#24812731)

I can just second this.

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24813293)

## Re:You meant the wrong way (5, Informative)

## killmofasta (460565) | more than 6 years ago | (#24813085)

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 (5, Interesting)

## msuarezalvarez (667058) | more than 6 years ago | (#24813291)

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 (3, Insightful)

## Alomex (148003) | more than 6 years ago | (#24813657)

There were no gross errors found by the Bourbaki group. This is why their horrible formal writing style died out: it increased the pain of writing without the gain of the previous waves of math formalization.

## Re:You meant the wrong way (1)

## goose-incarnated (1145029) | more than 6 years ago | (#24813403)

## Re:You meant the wrong way (4, Informative)

## PiNtoS (1318793) | more than 6 years ago | (#24812699)

Bourbaki books are the most boring books you can buy. Avoid them at all costs.

This is a bit extreme. While they're certainly not the best books to begin learning a subject, they're great reference books. They're well written, (generally) correct, and what's more, they've got some seriously elegant proofs. And from what I recall, they do have some diagrams (e.g., their commutative algebra book).

## Re:You meant the wrong way (1)

## Guignol (159087) | more than 6 years ago | (#24812981)

Either way, this should not be modded insightful but troll or maybe flamebait.

## Re:You meant the wrong way (1, Informative)

## Anonymous Coward | more than 6 years ago | (#24813117)

Better books:

Walter Rudin: Complex and Real Analysis (splendid book for students, great explanation of measure theory),

functional analysis from same author is good too.

Kato: Perturbation theory (very good book but quite hard, wait till graduate).

Brezis: functional analysis (french): a little abstract but short. Some early chapters are a little boring.

Yosida: functional analysis (haven't had time to finish it, so my opinion on it is not set).

Hormander: Series on linear operators are a reference. Very long.

Adams: Sobolev Spaces: very useful to know the theorems in non standard situations, the proofs are instructive even though you might not need know them.

Kallenberg: probability. I'm no probabilist but the first chapters are very well organized and written in a consitent manner.

The worst of these books is infintely better than any book by Bourbaki. Stop your idolatry of these mathematicians. Bourbaki is just a group cult writing awful books.

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24813949)

Not a single book you mention is about algebra/number theory. Maybe you are more interested in using mathematics than in abstract proofs - in that case these books are simply the completely wrong ones, and your opinion on them will be as low as mine about 90% of all books concerning numerical mathematics.

## Re:You meant the wrong way (2, Insightful)

## lysergic.acid (845423) | more than 6 years ago | (#24814025)

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24814189)

I don't know about the 1930. Maybe there were the best books at those times. But by today's standard they suck and should not be recommended to students.

They're outdated and best left to historians. Besides, the group continues to

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24813237)

=> I will love those books! (QED)

Now, the real question. Are the books in the public domain yet? For every revolution, the followers have to have their little book freely available. History has show this! (Sorry about the Marx reference)

## Re:You meant the wrong way (5, Insightful)

## porpnorber (851345) | more than 6 years ago | (#24814245)

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

reallywant 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 aboutpureproblems, abstracted from any problem domain. Indeed, the best advances in mathematics come, it seems to me, from abstracting internal mathematical tools away from their originalmathematicalfocus, 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:You meant the wrong way (4, Insightful)

## Scott Carnahan (587472) | more than 6 years ago | (#24815325)

The idea that career choices are predetermined at birth is a popular romantic view (cf. the human literary corpus of epics and fairy tales about Chosen Ones), but there is essentially no hard evidence for its validity, and I think it devalues the richness and variability of life experiences. Also, I don't think we should exclude people from mathematics just because they don't like the sort of dry abstraction you find in Bourbaki texts. There are plenty of reasonably successful mathematicians who are more comfortable learning things when they have an example or application in mind. For example, Timothy Gowers [wikipedia.org] wrote two [wordpress.com] posts [wordpress.com] on his blog, suggesting that exposition is improved by starting with examples to motivate an idea.

From a practical standpoint, I don't think we should try to change teaching methodology too much at a time, because there are almost always weaknesses in revolutionary plans that don't show up at the thought experiment stage. More abstractly, I think people tend to learn content better when it is motivated with a useful context. Exactly where this balance should be struck is still a contentious issue (see math wars [wikipedia.org] ), but I don't think Bourbaki is the answer. Even among pure academics, we value theoretical work by some notion of applicability. We say that etale cohomology is a good theory, not because it lets you think abstractly about pure stuff (although it does), but because you can use it to prove hard quantitative statements like the Weil conjectures, the Adams conjecture, and many theorems in representation theory.

## Re:You meant the wrong way (1)

## porpnorber (851345) | more than 6 years ago | (#24815601)

I don't, in fact, disagree with you very intensely, and yes, perhaps I spoke too strongly. I do think that there is a real current trend

awayfrom teaching subjects according to their own self-determined core values andtowardswhat politicians and industrialists would like, and I truly believe this to be short-sighted, damaging, and not particularly justified by education theory, historical experience, or much else. That's not quite the same as me wanting to launch into untested didactic waters without a lifeboat. And while I agree that 'not born to it' may have been a careless choice of words, I think the genetic and early childhood components are undeniable, and often wish we could get back to the state before technical bookshops filled up with XYZ for Dummies, as if being a Dummy in a field were something to be proud of; because yes, there are those with talent and there are those with determination and they are not always the same people, but equally there are those with neither, and they are not going to succeed at a thing. It remains that for someone to be so unable to relate to Bourbaki (not merely, 'hm, I don't learn well this way,' or 'interesting in historical context but not the way of the future,' or 'not really a textbook but a technical movement masquerading as a textbook' but 'everybody stay away at all costs!'), leads me to believe that, well, this person will have a lot more fun doing something applied.And I say that as someone who (a) has themselves learned that they have more fun in computing than in pure maths and (b) is very interested in alternate technical developments, alternate methods of presentation, and, well, finding new and different items for the mental toolkit.

Of course Bourbaki isn't the 42. But if someone in the field doesn't respect it, well, that's a little like a biologist dissing Darwin and telling people not to pay attention to him. Yes, mathematicians get to criticise Bourbaki and biologists get to criticise Darwin. They can and they should, or they won't get very far (and indeed wouldn't get much respect from Darwin or Bourbaki). But let's consider the context and the technical meat when we do it, rather than descending to the level of "Five Reasons Bourbaki Is The Worst Thing You'll Ever Read."

## Re:You meant the wrong way (1)

## martin-boundary (547041) | more than 6 years ago | (#24816103)

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24815597)

To quote a common phrase from the trenches of academia: Engineers feed poets. This sounds spiteful, a trait found in full display in our above argument. While it might be engaging to split hairs on the significance of others' fields, it'd do us well to commit to a modification of said quote: Engineers feed poets and mathematicians. Mathematicians gave way to engineering. Language gave way to mathematics.

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24819671)

Exactly. And this is coming from somebody who hates pure math.

For guys like me (and a lot of Slashdotters) they have BS and MS programs in "Applied Mathematics" or "Engineering Mathematics".

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24814327)

don't even write the name of the Theorem you refer to, a true mathematician knows them by volume and page number

That's really unfair, you know. Pagination can change from edition to edition: a True Mathematician uses volume.section.result-number(in order of appearance), unless disclaimer is made in an introduction, preface, or zeroth chapter relating which variant will be used.

## Re:You meant the wrong way (1)

## martin-boundary (547041) | more than 6 years ago | (#24816081)

The Bourbaki books are readable, however they are a bit dated, and they do _not_ aim to be textbooks for first year freshmen at all, which I strongly suspect the AC is.

-- It's incorrect to say that there are no examples. There are plenty, but if you haven't done a few years of university math already, you won't recognise _what_ they are about.

-- The applications certainly exist, but they are mostly mathematical themselves. That's on purpose, since the aim was to organize all of known mathematics.

A good way of understanding what Bourbaki is about is to imagine Euclid's Elements for _all_ of mathematics. It's beside the point to complain that Euclid's book doesn't have an application to, say, masonry. Pick up a book on masonry, and you'll get taught the geometry you need.

-- Drawings can sometimes help, and sometimes not. Bourbaki was begun in the 1930s, and the mathematical world had just discovered a whole lot of literally undrawable ("non-differentiable", "measurable") objects in calculus, for example.

--"The less explanations, the better: only idiots needs explanations." No, but only first years want their profs to spoon feed them. Mature students realize that they have to figure out most things on their own.

## Re:You meant the wrong way (2, Insightful)

## NaveNosnave (670012) | more than 6 years ago | (#24820345)

terriblefor students. Studentsneedto see examples of math as a process, not just as a finished product.## Re:You meant the wrong way (1)

## lekikui (1000144) | more than 6 years ago | (#24820777)

## Re:You meant the wrong way (0)

## Anonymous Coward | more than 6 years ago | (#24822805)

You are obviously confusing the Bourbaki books with the Unix/Linux manual.

(Wich actually worked quite well for me, so maybe if this is not an error, I think I'll by them :-))

## Metascore (2, Interesting)

## Anonymous Coward | more than 6 years ago | (#24812537)

From what I can tell, Metascore is an attempt by mathematicians to take over the government. In fact, every government.

http://www.metascore.org/ [metascore.org]

Difference is they do not seem to be very secretive.

## There is no Nobel prize for economics, wrestling, (0)

## Anonymous Coward | more than 6 years ago | (#24812543)

## Re:There is no Nobel prize for economics, wrestlin (0)

## Anonymous Coward | more than 6 years ago | (#24812643)

Wrong. http://nobelprize.org/nobel_prizes/economics/laureates/

Now about my spectacular flatulence...

## economics, wrestling, astrology, flatulence (1)

## SgtChaireBourne (457691) | more than 6 years ago | (#24812963)

## Re:economics, wrestling, astrology, flatulence (0)

## Anonymous Coward | more than 6 years ago | (#24813199)

wrong. Stopp spreading bullshit. that's the Sveriges Riksbank Prize in Economic Sciences, and unrelated to the Nobel prizes.

It's

technicallynot a Nobel, but it is indeed RELATED [wikipedia.org] .## They really are radicals! (4, Funny)

## CaptainPatent (1087643) | more than 6 years ago | (#24812579)

How does someone become a member of this finite group? Do they have to stand in the middle while the rest of them form a perfect square around them? I wonder if they have to hide their identity?

oh well, at least at the end there's pi!

## Re:They really are radicals! (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24813135)

The pi is a li

## Re:They really are radicals! (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24813459)

The cake is a lie group.

## Re:They really are radicals! (0)

## Anonymous Coward | more than 6 years ago | (#24813617)

The pi is a lie, too.

## Re:They really are radicals! (2, Funny)

## exp(pi*sqrt(163)) (613870) | more than 6 years ago | (#24814113)

You make sure you have an inverse and that you associate nicely with the other elements.

## Re:They really are radicals! (1)

## jonaskoelker (922170) | more than 6 years ago | (#24822989)

Just a quick comment from the left field (mama never taught me to be discrete): maybe they could stand in a ring instead (of a square) during their analysis of these complex issues, during their attempt to see what can be derived from the facts. That would seem more natural and rational; at least it's the norm.

## Not so secret... (3, Informative)

## mbone (558574) | more than 6 years ago | (#24812587)

This was common knowledge when I was taking advanced Math classes in mid 1970's.

## gna:a (-1, Offtopic)

## Anonymous Coward | more than 6 years ago | (#24812613)

## Re:gna:a (2, Funny)

## Anonymous Coward | more than 6 years ago | (#24812751)

"From steadily fucking," eh? Well, sir -- I wish I had YOUR problems.

## Re:gna:a (1)

## goose-incarnated (1145029) | more than 6 years ago | (#24813431)

didmarry a lawyer, so you probably mean something different when saying "fucking"## Why are we celebrating these books? (4, Insightful)

## dlenmn (145080) | more than 6 years ago | (#24812693)

From TFA:

The result was austere books with almost no examples, guide for intuition or pictures. Philip Davis of Brown University described them in an article in SIAM News as "mathematics with all its juices extracted; bare bones, skeletonic, anorexic stuff; Twiggy dressed in the tunic of Euclid." Michael Atiyah of the University of Edinburgh says: "They're not designed to be read. They're designed to set out a the is for how mathematics ought to be done."

Any they thought other books were dry? I guess books like this may have some use for hard core math types, but they sound like horrible books for almost anyone else. Examples, pictures, and the likes are very important for learning. Designing books not to be read seems like silly exercise.

## Re:Why are we celebrating these books? (4, Informative)

## Anonymous Coward | more than 6 years ago | (#24812807)

Bourbaki was writing for a graduate student or professional level mathematician, not a public audience. The writing is dry by today's standards - indeed, many texts today use more prose and include diagrams. However, Bourbaki was very good at getting the mathematics itself clearly defined.

## Re:Why are we celebrating these books? (2, Interesting)

## ObsessiveMathsFreak (773371) | more than 6 years ago | (#24816317)

It's just a pity they were never able to clearly get it

across.Bourbaki, and the Bourbaki style, makes great reference material. But that's all it makes. There is more to mathematics, and pictures and example are part of that "more". A big part. Bourbaki did not just forget these topics. They actively excluded them. Jean Dieudonne [wikipedia.org] stood up in the middle of a conference and shouted "Down with Euclid! Death to Triangles!". It was an irrational zealotry, but mathematicians are people too, and they followed the trend setters.

You cannot learn mathematics from a reference book, or from books and people that try to be like those reference books. This applies to graduate students and professionals studying mathematics just as much as it applies to preschoolers learning about shapes. Here's a link to another view of mathematics [uni-muenster.de] , and how it should be taught by V.I. Arnold, a famous Russian mathematician.

## You're funny (1)

## Nicolas MONNET (4727) | more than 6 years ago | (#24814087)

You're funny. You have no idea what mathematics actually are, do you? Or how hard core this stuff is *supposed* to be.

## Re:You're funny (1)

## dlenmn (145080) | more than 6 years ago | (#24815213)

All I know is that the books I've used for graduate math classes have had both diagrams and examples... I suppose that makes me outright hilarious.

## Re:Why are we celebrating these books? (2, Informative)

## L'homme de Fromage (838405) | more than 6 years ago | (#24815309)

Many people blame Bourbaki for the horrendous "new math" which infected mathematics teaching in the 1960's. And there is some validity to that accusation. A scathing indictment of Bourbaki was given by the renowned mathematician V.I. Arnold, author of famous books on classical mechanics and differential equations. Arnold tears apart the dry, lifeless and phony "rigor" and "purity" of Bourbaki and others who divorce mathematics from reality, which he describes as "sectarianism and isolationism which destroy the image of mathematics as a useful human activity in the eyes of all sensible people." Here's a link to his full comments:

http://pauli.uni-muenster.de/~munsteg/arnold.html [uni-muenster.de]

As a mathematician, I have to agree with the critics of Bourbaki. It put mathematics on the wrong path, in my opinion, and much of that influence continues on today. Mathematicians would do well to heed Arnold's advice on the direction mathematics needs to take. "Pure mathematicians" and other people who still think that Bourbaki was "doing mathematics the right way" are simply misguided.

## Re:Why are we celebrating these books? (0)

## Anonymous Coward | more than 6 years ago | (#24817413)

> "Pure mathematicians" and other people who still think that Bourbaki was "doing mathematics the right way" are simply misguided.

That is your opinion. And in my opinion like Arnold you are so blinded by your own use of mathematics that you do not see all of it by far.

Bourbakis is about laying an extremely solid, general foundation of mathematics and giving a detailed understanding of the core purely

mathematical problems (you could probably call it logic problems). Not recognizing its value is like saying that most numerical mathematics

proofs are useless because they essentially amount to beating the problem dead with formulas but without really understanding the "why".

Both positions are nonsense, they are different ways of approaching mathematics with different goal.

Now, Arnolds main criticism to me seems to be that some people try to apply the Bourbaki way to everything. That is something I can mostly

agree with, many if not most are going to work in applied mathematics, and while I think they should have seen and learned the style a bit,

it is not what they will be using day-to-day.

But calling names on "pure mathematicians" is like doing the same for the particle physicists building things like the LHC because there "obviously

is no use in what they are doing".

## Re:Why are we celebrating these books? (1, Interesting)

## Anonymous Coward | more than 6 years ago | (#24822847)

You might not be French. I am. And pure mathematicians here don't not care about applications. They actively deny their work has any purpose. For philosophical reasons, they see any application of mathematics as dirty. "Pure" mathematicians" and "applied" mathematicians actually don't talk to each other here. This is even more surprising once you learn that what is considered "applied mathematics" here is just considered "pure mathematics" elsewhere.

From pure to applied in France (making you either a CNU 25 or a CNU 26: jargon only undesrtandable if you work in a French University)

Logic/set theory

algebraic geometry

algebra

differential geometry

Functional analysis (which is used by many "applied" mathematicians)

PDE: pure way as study of the spectra of linear operators, Hille Yosida...

---Boundary between pure and applied---

PDE: nonlinear or on domains different from R^n

Numerical Analysis

Statistics

Scientific Calculus

For probability, it depends. Before you flame me, remember, it's not my classification, just the officious one (IIR it C).

## Re:Why are we celebrating these books? (0)

## Anonymous Coward | more than 6 years ago | (#24815461)

Examples are like quicksand.

## New Math of the 1960's - they invented it (4, Interesting)

## Cliff Stoll (242915) | more than 6 years ago | (#24812735)

Aargh! From these mathematicians grew the "New Math" of the early 1960's.

During the 1950's, high school math was mainly geometry, algebra, trig, and calculus.

Then came the New Math. Imported from France, it emphasized set theory, number bases, and abstract number theory. Students learned cardinality, commutative laws, associative laws, and "pure" math, with less applied math and problem-solving.

Many educators (and even more parents) saw the New Math as being too abstract for daily use and undercutting concrete skills such as computation. Physicists, especially objected, when college freshmen could calculate in multiple number bases, but couldn't solve algebraic equations.

Mathematician/singer Tom Lehrer wrote the song,"New Math", with the line, "It's so very simple that only a child can do it!"

One book, Why Johnny Can't Add - the Failure of the New Math, pointed out that in the mid 1970's teachers applauded the death of the New Math. By the late 70's, algebra was back in style, and even trigonometry was being taught. So ended the French invasion of high school math classes.

The latest, of course, is the new-new-math, also called rain-forest math. Don't get me started...

## New Math was Horrible! (4, Interesting)

## Anonymous Coward | more than 6 years ago | (#24813043)

I survived four years of New Math - it was so easy that you couldn't do anything wrong. Straight A's in math.

Then I got to college and met all those equations. Everyone else solved them but me. Two weeks into chem 101 and I was flailing.

It's true - the Bourbaki group *invented* the New Math, and pushed it into classrooms around the world. Millions of adults are now math-illerates because of these oh-so-pure mathematicians.

## Re:New Math was Horrible! (0)

## Anonymous Coward | more than 6 years ago | (#24813143)

This book review [adequacy.org] is for you.

## Re:New Math was Horrible! (0)

## hedwards (940851) | more than 6 years ago | (#24813409)

If it was so easy you couldn't do anything wrong then you were either a genius or it was completely without any value.

Clearly in your case if you weren't able to handle the chem 101 math that's an indication that you hadn't learned the math.

The mathematics involved with that level of chemistry is not that tough, and certainly not as much as is required for freshman level calculus.

Math is a pursuit where you're either right or wrong. In some cases being right may mean being within the margin for error but not usually in math class. Decimals should really always be considered wrong in math class unless they're the exact answer.

I'd suggest that actually the problems that most adults have are the direct result of new math and similar movements.

As much hated as story problems are, they are one of the best ways of making the math skills available for use. After all knowing calculus or more isn't particularly useful if you can't actually use it to solve problems.

## Re:New Math was Horrible! (1)

## Watson Ladd (955755) | more than 6 years ago | (#24815871)

## Re:New Math was Horrible! (2, Insightful)

## linzeal (197905) | more than 6 years ago | (#24817775)

## Re:New Math was Horrible! (1)

## pjt33 (739471) | more than 6 years ago | (#24819829)

...or it was completely without any value

I wouldn't be hasty to discount that possibility, given another of Lehrer's characterisations of "New Math":

[i]n the new approach, as you know, the important thing is to understand what you're doing rather than to get the right answer.

## Re:New Math was Horrible! (1)

## blahplusplus (757119) | more than 6 years ago | (#24814657)

"I survived four years of New Math - it was so easy that you couldn't do anything wrong. Straight A's in math. .... Millions of adults are now math-illerates because of these oh-so-pure mathematicians."

I agree but I think the whole problem is that we don' start with a geometric interpretation of math, the mayan's used shapes for numerals, and arabic symbols hide mathematical truths that are expressed better in images, visual geometric shapes.

We already do math unconsciously else we could not navigate, we could not determine is this distinct from that. (Boolean logic, yes it is there, no it is not)

## Re:New Math of the 1960's - they invented it (1)

## mbone (558574) | more than 6 years ago | (#24813419)

I took the new math, took lots of algebra along with the set theory, and actually thought it helped me as a physicist.

Lots depends on what you want to do. I can't imagine not knowing calculus, but plenty of people don't and they somehow don't seem to miss it.

## Re:New Math of the 1960's - they invented it (0)

## Anonymous Coward | more than 6 years ago | (#24814929)

This stuff was just starting to come around in the late 50's. I speak as one of it's victims. Urg the Horror of it all, and just when I was starting to get maths. Just starting to see the patterns and suddenly it's off to the fun house. Only now after many years can I face it.

Educationalists. Feh!

## The plus side of new math.. (1)

## tjstork (137384) | more than 6 years ago | (#24815389)

I had new math and as a result my equation solving ability was utterly horrible and honestly still is... but I did find that new math laid the groundwork for databases down the road... cardinality and set theory are sort of the gist of databases... and, well, commutative and associativity are useful for understanding operators in programming languages.

## Re:New Math of the 1960's - they invented it (1)

## WATist (902972) | more than 6 years ago | (#24816919)

## 'Anti-Globalism' exposed (-1, Offtopic)

## Anonymous Coward | more than 6 years ago | (#24812777)

From http://www.corrupt.org/act/interviews/alex_birch [corrupt.org] :

Cyberhit: Domination of Overpopulation DebateIe, blogspam popular websites to get hits to your shitty blog.

I don't reccomend reading that link; it's a handful of garbage arguments based on terrible analogies, utterly devoid of scholarly backing.

## The group's works (1)

## Bromskloss (750445) | more than 6 years ago | (#24812949)

Is the group's works [bourbaki.ens.fr] available online somewhere? I'd like to see their condensed style.

## Re:The group's works (1)

## Neil Strickland (1064886) | more than 6 years ago | (#24813255)

## Re:The group's works (1, Funny)

## Anonymous Coward | more than 6 years ago | (#24813563)

The guy just died, so they're copyrighted for only another 70 years. See how well it works?

## Secret Society (3, Funny)

## PPH (736903) | more than 6 years ago | (#24812989)

## Bourbaki (0)

## Anonymous Coward | more than 6 years ago | (#24813113)

Our math teacher said "If someone says 'It's very Bourbaki', they mean 'It's very bad'".

He was not a big fan of the Bourbaki-style math literature. And I understand why.

## Anti-Globalism on the Internet (0)

## Anonymous Coward | more than 6 years ago | (#24813319)

Anti-globalists use the Internet to fight globalism?

Isn't that like Al Gore flying around in his 727 to fight global warming?

## Re:Anti-Globalism on the Internet (0)

## Anonymous Coward | more than 6 years ago | (#24814747)

No, it is not.

Perhaps you want to think about what you just said and come back to us.

## These french... (1)

## sw155kn1f3 (600118) | more than 6 years ago | (#24813503)

They can make RTFA about mathematicians to sound like this is an article about some couturier. Well.. It's all geometry after all! .. AND applied to nude models ;) so this "secret society" should be into something, eh

## Re:These french... (1)

## ConceptJunkie (24823) | more than 6 years ago | (#24814229)

- Arwen, I'm your father, Agent Smith.- Well, you're just Smith, but my father is Aerosmith!

I think my brain just core-dumped. Count Dooku is wailing on Magneto with his light-sabre.

## Re:These french... (1)

## sw155kn1f3 (600118) | more than 6 years ago | (#24817545)

Yeah.. This is nice anecdote playing on The Matrix (Hugo Weaving playing agent Smith), Lord of the Rings (Hugo Weaving playing Elrond, father of Arwen played by Liv Tyler) and who Liv Tyler's father is :)

## French victories/defeats, anyone ? (0)

## Anonymous Coward | more than 6 years ago | (#24813877)

Wow...

It's been years since I came to read slashdot, and in a post about french mathematicians, I see no rabid flaming comments about cowardly defeats and other french-bashing pseudo-jokes.

I'm almost shocked.

Apparently, slashdot's evolution was not limited to its web page layout.

## Awesome victories (0, Flamebait)

## Nicolas MONNET (4727) | more than 6 years ago | (#24814135)

I wonder if this has something to do with the awesome victory achieve in Iraq by the super powerful US army? The meme was propped up when Chirac was telling you guys that Iraq would be a quagmire. Silly Jacques!

## from Straight Dope (5, Funny)

## mbius (890083) | more than 6 years ago | (#24814165)

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.

## About the Bourbaki crowd... (1, Informative)

## Anonymous Coward | more than 6 years ago | (#24818629)

1. Bourbaki was not a "secret society", although it didn't publish a membership list because membership wasn't particularly official. Even some non-French mathematicians participated occasionally.

2. They did not publish "text" books, they published carefully written reference books.

3. The reputation was they they met once a year or so in a nice French resort with a reputation for good wine, to enjoy themselves and argue about the best wording for proofs in the next volumes.

4. While in principle, you might read Bourbaki without a previous grounding -- indeed, substantial preparation -- in practice, it is not likely.

A handful of people who read slashdot may have read some Bourbaki, but it's hard to imagine cultures more different than the slapdash opinions here, and the carefully crafted logic and style which underlies the Bourbaki compendia.

(D. Erbach writing as AC)