An Introduction to Nicolas Bourbaki, One of the Most Influential Mathematicians of All Time … Who Never Actually Lived

In 20th-cen­tu­ry math­e­mat­ics, the renowned name of Nico­las Bour­ba­ki stands alone in its class — the class, that is, of renowned math­e­mat­i­cal names that don’t actu­al­ly belong to real peo­ple. Bour­ba­ki refers not to a math­e­mati­cian, but to math­e­mati­cians; a whole secret soci­ety of them, in fact, who made their name by col­lec­tive­ly com­pos­ing Ele­ments of Math­e­mat­ic. Not, mind you, Ele­ments of Math­e­mat­ics: “Bourbaki’s Ele­ments of Math­e­mat­ic — a series of text­books and pro­gram­mat­ic writ­ings first appear­ing in 1939—pointedly omit­ted the ‘s’ from the end of ‘Math­e­mat­ics,’ ” writes JSTOR Dai­ly’s Michael Barany, “as a way of insist­ing on the fun­da­men­tal uni­ty and coher­ence of a dizzy­ing­ly var­ie­gat­ed field.”

That’s mere­ly the tip of Bour­bak­i’s ice­berg of eccen­tric­i­ties. Formed in 1934 “by alum­ni of the École nor­male supérieure, a sto­ried train­ing ground for French aca­d­e­m­ic and polit­i­cal elites,” this group of high-pow­ered math­e­mat­i­cal minds set about rec­ti­fy­ing their coun­try’s loss of near­ly an entire gen­er­a­tion of math­e­mati­cians in the First World War. (While Ger­many had kept its bright­est stu­dents and sci­en­tists out of bat­tle, the French com­mit­ment to égal­ité could per­mit no such favoritism.) It was the press­ing need for revised and updat­ed text­books that spurred the mem­bers of Bour­ba­ki to their col­lab­o­ra­tive­ly pseu­do­ny­mous, indi­vid­u­al­ly anony­mous work.

“Yet instead of writ­ing text­books,” explains Quan­ta’s Kevin Hart­nett, “they end­ed up cre­at­ing some­thing com­plete­ly nov­el: free-stand­ing books that explained advanced math­e­mat­ics with­out ref­er­ence to any out­side sources.” The most dis­tinc­tive fea­ture of this already unusu­al project “was the writ­ing style: rig­or­ous, for­mal and stripped to the log­i­cal studs. The books spelled out math­e­mat­i­cal the­o­rems from the ground up with­out skip­ping any steps — exhibit­ing an unusu­al degree of thor­ough­ness among math­e­mati­cians.”  Not that Bour­ba­ki lacked play­ful­ness: “In fan­ci­ful and pun-filled nar­ra­tives shared among one anoth­er and allud­ed to in out­ward-fac­ing writ­ing,” adds Barany, “Bourbaki’s col­lab­o­ra­tors embed­ded him in an elab­o­rate math­e­mat­i­cal-polit­i­cal uni­verse filled with the abstruse ter­mi­nol­o­gy and con­cepts of mod­ern the­o­ries.”

You can get an ani­mat­ed intro­duc­tion to Bour­ba­ki, which sur­vives even today as a still-pres­ti­gious and at least nom­i­nal­ly secret math­e­mat­i­cal soci­ety, in the TED-Ed les­son above. In the decades after the group’s found­ing, writes les­son author Pratik Aghor, “Bour­rbak­i’s pub­li­ca­tions became stan­dard ref­er­ences, and the group’s mem­bers took their prank as seri­ous­ly as their work.” Their com­mit­ment to the front was total: “they sent telegrams in Bour­bak­i’s name, announced his daugh­ter’s wed­ding, and pub­licly insult­ed any­one who doubt­ed his exis­tence. In 1968, when they could no longer main­tain the ruse, the group end­ed their joke the only way they could: they print­ed Bour­bak­i’s obit­u­ary, com­plete with math­e­mat­i­cal puns.” And if you laugh at the math­e­mat­i­cal pun with which Aghor ends the les­son, you may car­ry a bit of Bour­bak­i’s spir­it with­in your­self as well.

Relat­ed Con­tent:

Beau­ti­ful Equa­tions: Doc­u­men­tary Explores the Beau­ty of Ein­stein & Newton’s Great Equa­tions

The Math­e­mat­ics Behind Origa­mi, the Ancient Japan­ese Art of Paper Fold­ing

The Unex­pect­ed Math Behind Van Gogh’s Star­ry Night

Can You Solve These Ani­mat­ed Brain Teasers from TED-Ed?

The Map of Math­e­mat­ics: Ani­ma­tion Shows How All the Dif­fer­ent Fields in Math Fit Togeth­er

Why the World’s Best Math­e­mati­cians Are Hoard­ing Japan­ese Chalk

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities, the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les and the video series The City in Cin­e­ma. Fol­low him on Twit­ter at @colinmarshall or on Face­book.