Nicolas Bourbaki spent much of the twentieth century publishing rigorous and revolutionary papers on mathematics. So why haven't you heard of him? Because he never existed. He was the name taken by a secret society of French mathematicians with some very odd rules.

In 1935, a group of French math students had two metaphorical bugs up their collective metaphorical ass. The first was the insistence on old-fashioned practices and teaching methods imposed by their teachers and mentors. The second was this hippified new-age schtick of head-in-the-clouds dreamers like Henri Poincaré, who insisted that the flow of ideas need not be hampered by things like completeness of theory or carefully refined presentation. They wanted a revolution! And they wanted the best kind of revolution: one that was strictly reasoned, gone over point-by-point, and that had to have the reasoned assent of every member of the revolutionary group before any public action was taken. 'Let's,' they said, 'get tedious.'

And damned if they didn't do exactly that. The Association des Collaborateurs de Nicolas Bourbaki began meeting to try to publish a rigorous book on set theory, and then march across the mathematical world until they devised a treatise on the great mathematical knowledge of their age.

It took a while. They met a few times per year, and at each meeting a mathematical topic was raised. Whoever wanted it would get the first crack at it, write it up, and bring it to the next meeting. There it would be read and criticized line by line. Anyone could interrupt with a question, comment, or heartless jibe at any time. One member described the process with typical French succinctness: "You are dismembered and screwed." Once the argument was ripped apart, the next person grabbed it and re-wrote it. It was then brought back to the next meeting to repeat the whole process. One of the main rules of the Bourbaki was unanimity. Unless everyone agreed that this was the best chapter it could be, it wasn't going anywhere. The average time for publication was eight to twelve years. These guys did not mess around.

Over the next twenty years, they came up with incredible texts, always publishing under the name of Nicolas Bourbaki. Rather than starting with quirks of mathematics, they focused on the most general arguments, trying to be complete. They also thought that, for every question, there was a way to answer it that was the most obvious, most concise, and most general solution, and didn't stop looking until they found it.

Although the Bourbaki still maintain an office today, the group's core was sacrificed to its first rule. Since young mathematicians were most likely to be up on what was new in mathematics, while older mathematicians clung to the familiar and were specialists in the hot topics of 30 years ago, there was mandatory retirement at age fifty. After twenty years of group sessions, at which it was not uncommon for four or five people to be shouting at the top of their voices all at the same time, perhaps the fifty-year-olds weren't that sad to go.

The other rule for the Bourbaki was that every member of the group had to be interested in every topic. When the group necessarily had to move to more specialist topics, having gone through the more general subjects, that rule became tougher to enforce. A lawsuit (what else?) against their publishing company over the specific rights of the previous books finished off the group, and the last volume was published in 1983.

Still, the society left behind a legacy of teaching style, notation, and rigor that remains in the mathematical community to this day.

They may also be in the next Dan Brown book. It's tough to say.

*Top Image: Prison Planet Forum*

Via Planet Math.