THE MANY FACES OF THE BOURBAKI

 

Years ago, I caused to be posted on social media, a copy of a painting depicting a foustanella clad gentleman crossing the Sturt Desert. In the accompanying caption, I informed the viewer that the painting, by Antoine Dufresne, depicted the lost 1830 expedition of the hapless Ioannis Voidoulis of Imia, who perished during his ill-fated crossing after failing to heed John Oxley’s recommendation to jettison the stores of retsina he had brought with him. The revelation that our community could thus partake in Australia’s  colonial history was met with jubilation in some quarters and inundated as I was with requests for further information, I was able to furnish inquirers with facsimiles of his diaries, other paintings recording his time in the desert and also a brief chronology as to the circumstances of his arrival in Australia.

This of course was all nonsense, with the original painting recording a crossing of the Egyptian desert by the Albanian bodyguard of Mehmed Ali and only the divine Vrasidas Karalis was able to discern the artist I referenced was actually the main protagonist in the movie: The Shawshank Redemption.

Such pranks, apart from indicating that their authors possibly have too much spare time on their hands, sink under the weight of their internal contradictions and pretensions to farce. Sometimes however, they have unintended consequences. Take for example the Nicolas Bourbaki, the name of a collective of French mathematicians who under that name, published a series of works dealing with set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras and was also instrumental in the creation of what is known as the “New Math” which has plagued generations of schoolchildren ever since.

Like Voidoulis, whose name is an approximation of Oxley, Bourbaki is based loosely on a real person. Member of the Bourbaki Group André Weil remembered a student prank in which a senior student of the École Normale Supérieure posed as a professor and presented a bogus “theorem of Bourbaki.” It took a while for the ruse to be discovered and the mathematicians gleefully adopted the name.

Both the student and the mathematicians would have been conscious of the fact that they were appropriating the name of Franco-Greek general Charles-Denis Sauter Bourbaki, who fought with distinction in the Crimean War and the Franco- Prussian War, meeting a tragic end. He was the son of Greek Revolution freedom fighter Constantin Denis Bourbaki, who hailing from Cephallonia with Cretan ancestry, became aide-de-camp to Joseph Bonaparte, fought in the Battle of Waterloo and made various attempts to secure the Greek throne for Louis, Duke of Nemours, son of the Duke of Orléans. Having failed in this endeavour, he recruited a body of eighty men and placed himself under the command of Vasos Mavrovouniotis and Panagiotis Notaras. Captured at the battle of Kamatero, he was beheaded in 1827.

Back in in France, Charles-Denis, on the back of his father’s influence, after receiving a military education, rose to be aide-de-camp to King Louis Philippe. Noted for his valour during his service in Algeria, he became brigadier-general of the Zouaves and commanded the Algerian contingent of the French troops during the Crimean War, in Alma, Inkerman and Sevastopol.

The fall of the Bourbon dynasty in no way damaged his career prospects, succeeded as it was by Napoleon III, who esteemed the Bourbaki family highly. The following years would find Bourbaki in Italy, fighting for France to remove the Austrians from the peninsula and leading to Italian Unification. His successes were deemed significant enough for him to be touted, at least in France, as a candidate for the Greek throne which had become vacant after the removal of Otto I. It is no certain what the trajectory of Greek history would have been had Bourbaki not declined the proffered honour. According to one apocryphal story, when asked why he would not assume the Greek throne, he is said to have scoffed: “And meet the fate of Kapodistrias?”

The Franco-Prussian War of 1870 found Bourbaki commanding the French Imperial Guard and defending the city of Metz. While there, he fell victim to an elaborate ruse staged by the Prussians, whereby he was called to England, supposedly to seek instructions from the Empress Eugénie about an imminent peace treaty. He arrived only to find out that he had been hoodwinked and upon his return to Metz, was refused safe conduct into the city by the besieging Prussians, who went on to take it and raze its fortifications.

After the capture of Napoleon III at the battle of Sedan and the fall of the Second French Empire, Bourbaki offered his services to Léon Gambetta, founder of the Third French Republic. Provided with inexperienced and hastily recruited troops, he failed to raise the siege of Belfort, instead, being pursued towards the Swiss border. The parlous conditions and lack of provisions devastated his army. Of 150,000 who set out to cross the border, only 87,000 survived the crossing into Switzerland. The Swiss received the beleaguered soldiers, fed and clothed them but ultimately after six weeks, repatriated them, the scene being immortalised in the circular panoramic painting known as the Bourbaki Panorama, which purports to celebrate Swizz neutrality and hospitality, and still exists in Lucerne to the present day.

Rather than face the dishonourable prospect of having to surrender to the Prussians once back on French soil, Bourbaki attempted suicide, shooting himself in the head. However, as he later recounted, the bullet “flattened as if against a cast-iron plate” and he miraculously survived. His defiant gesture in preferring death to surrender profoundly moved the demoralised French who were experiencing the humiliation of Prussian occupation and it is in this context that “Bourbaki” became a household name, seized upon in later decades by the mischievous mathematicians in search of fractals and high farce.

Bourbaki went on to become military governor of Lyon. He attempted to run for the French Senate a few times but was unsuccessful and was retired owing to his outspokenness in 1881. Dying in 1897, he is commemorated in a number of Rue Bourbaki all around France, from Rouen, to Toulouse.

A proud man, Bourbaki was not to know that a number of textbooks would be attributed to a purported and non-existent member of his family, Nicolas. To further the ruse,  André Weil encouraged Indian mathematician and Marxist historian Damodar Kosambi to publish a scathing article against the theories of a certain Bourbaki, who Kosambi insisted was Russian, and had been killed during the Russian Revolution entitled: "On a Generalization of the Second Theorem of Bourbaki” in the Bulletin of the Academy of Sciences of the United Provinces of Agra and Oudh, Allahabad. The collective continued to publish articles in his name, even inventing a sister for him, the alter ego of Weil’s sister, Simone. So intent was the group of mathematicians upon maintaining the existence of Bourbaki, that when American mathematician Ralph Boas and editor of the journal Mathematical Reviews publicly questioned whether he  was real, he received via mail, a scathing letter, signed by Nicolas Bourbaki, stating: “Miserable worm, how dare you claim that I am not real….”

In 1950, an application made in the name of Nicolas Bourbaki to the American Mathematical Society was rejected on the basis that the Encyclopaedia Brittanica contained an entry according to which such a person did not exist. Soon after, the editor of the Encyclopaedia, Walter Yust, received a letter from an angry Nicolas Bourbaki, asking how it was possible for the Encyclopaedia to maintain he did not exist when he had published so many works and had entered into correspondence with him.

The Bourbaki still exist today, although their publishing activity has become sporadic over recent decades. Across the other side of the Atlantic, a real Nikolaos Bourbakis a Greek academic and computer scientist at Wright State University, is editor of the  International Journal on Artificial Intelligence Tools, at least that is, until proven otherwise….

DEAN KALIMNIOU

kalymnios@hotmail.com

First published in NKEE on Saturday 22 February 2025