Founder of the Secret Society of Mathematicians 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."
Metascore (Score:2, Interesting)
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.
New Math of the 1960's - they invented it (Score:5, Interesting)
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! (Score:4, Interesting)
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:You meant the wrong way (Score:5, Interesting)
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:Why are we celebrating these books? (Score:3, Interesting)
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.
Re:Why are we celebrating these books? (Score:1, Interesting)
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).