"His name is Greek, his nationality is French and his history is curious. He is one of the most influential mathematicians of the 20th century. His works are read and cited
widely throughout the world. He has fervent supporters and staunch detractors in any group of mathematicians to meet. The strangest fact about him, however, is that he does not exist." From: P. R. Halmos, Nicolas Bourbaki. Scientific American, (1957), May, 88–99. https://www.scientificamerican.com/article/nicolas-bourbaki/
In mathematics, once you proof a theorem, it is valid forever and ever. This is crucial because the work of every new generation of mathematicians is based on legacy work
It was in Paris 1934 where the name Nicolas Bourbaki first appeared in a place rocked by turmoil at a volatile time in history. World War I had wiped out a generation of French intellectuals. As a result, the standard university-level calculus textbook, written more than two and half decades ago, was out of date.
Newly minted professors André Weil and Henri Cartan wanted a rigorous method to teach Stokes’ theorem, a key result of calculus. After realizing that others had similar concerns, Weil organized a meeting. This meeting took place on December 10, 1934 at a Parisian café called Capoulade. The nine mathematicians in attendance agreed to write a textbook ‘to define for 25 years the syllabus for the certificate in differential and integral calculus by writing, collectively, a treatise on analysis,’ which they hoped to complete in just six months. As a joke, they named themselves after an old French general who had been duped in the Franco-Prussian war.
widely throughout the world. He has fervent supporters and staunch detractors in any group of mathematicians to meet. The strangest fact about him, however, is that he does not exist." From: P. R. Halmos, Nicolas Bourbaki. Scientific American, (1957), May, 88–99. https://www.scientificamerican.com/article/nicolas-bourbaki/
In mathematics, once you proof a theorem, it is valid forever and ever. This is crucial because the work of every new generation of mathematicians is based on legacy work
It was in Paris 1934 where the name Nicolas Bourbaki first appeared in a place rocked by turmoil at a volatile time in history. World War I had wiped out a generation of French intellectuals. As a result, the standard university-level calculus textbook, written more than two and half decades ago, was out of date.
Newly minted professors André Weil and Henri Cartan wanted a rigorous method to teach Stokes’ theorem, a key result of calculus. After realizing that others had similar concerns, Weil organized a meeting. This meeting took place on December 10, 1934 at a Parisian café called Capoulade. The nine mathematicians in attendance agreed to write a textbook ‘to define for 25 years the syllabus for the certificate in differential and integral calculus by writing, collectively, a treatise on analysis,’ which they hoped to complete in just six months. As a joke, they named themselves after an old French general who had been duped in the Franco-Prussian war.
Bourbaki's mode of exposition, consisting of the arrangement of all the text under: Definition, Theorem, Preposition, Lemma, Proof, Example, Remark, etc., is without doubt welcome. Personally, I like his "tournant dangereux" (a "danger bend" sign), warning the reader not to make a wrong conclusion. Soon, Bourbaki realized that in addition to writing a text as mentioned above, it was also necessary to have discussions on contemporary topics that the text itself cannot cover in a reasonable time frame. To address this problem, Bourbaki met twice or thrice a year and arranged lectures on areas of the then current and topical interest. These “exposés” were also published in the widely popular series Bourbaki Seminar. Sometimes the meetings took place in the countryside to not get distracted from their main objective: rewrite the mathematics from top to bottom so to restructure the field on solid foundations.
Notations such as the symbol ∅ for the empty set, and terms like injective, surjective and bijective owe their widespread use to their adoption in the Éléments de mathématique. The group believed in the inherit unity of mathematics. They wanted to present the set of mathematics in its more pure and simple way. The results were abstracts and ambitious.
At that time, people started to think that the attempt of a new possible war about to begin. Weil escaped to Finland, hoping that he can keep Bourbaki alive from there, but ended up in jail as suspected of being a Soviet spy. According to his memories, he escaped from execution thanks to Rolf Nevanlinna (Finnish mathematician, who made significant contributions to complex analysis). Back in France, Weil was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen (France).
During his time in prison, Weil started to develop a completely new approach of mathematics, based on the Bourbaki's work. An approach that allows him to transform the algebra of equations to something more tangible...
Taking René Descartes as reference, who showed us how to convert shapes into numbers using coordinates: would it be possible to do something similar but in the opposite direction? Could it be possible to use intuitive ideas of geometry and shapes so to solve problems related to numbers and equations? Weil showed how to think in equations as shapes!, complicated even for the mathematicians of that time. And this was the beginning of a new concept: algebraic geometry.
And since then, that concept has allowed us to solve equations that for centuries seemed impossible. The most famous case was that it paved the way for the solution of Fermat's notoriously difficult Last Theorem, proved by British mathematician Andrew Wiles in 1995.
Weil was released from prison in May 1940 and, as many European mathematicians during that time, he moved to America. The Institute for Advanced Study at Princeton opened its doors in 1933 and at the end of the war there was a well-funded research center with countless emigrated scientists and many superstars, like Albert Einstein. With Europe ravaged by war and Göttingen destroyed by Hitler, Princeton quickly became the place to study mathematics.
The success of Bourbaki is linked to the scientific quality of his members. All of them have been extraordinary mathematicians. Five of them have obtained the Fields medal, most important international recognition of excellence in Mathematics, awarded at the International Congresses of Mathematicians that are held every four years: Laurent Schwartz (1950), Jean Pierre Serre (1954), Alexander Grothendieck (en 1966), Alain Connes (1982) and Jean-Christophe Yoccoz (1994).
Best,
Jesús
Notations such as the symbol ∅ for the empty set, and terms like injective, surjective and bijective owe their widespread use to their adoption in the Éléments de mathématique. The group believed in the inherit unity of mathematics. They wanted to present the set of mathematics in its more pure and simple way. The results were abstracts and ambitious.
At that time, people started to think that the attempt of a new possible war about to begin. Weil escaped to Finland, hoping that he can keep Bourbaki alive from there, but ended up in jail as suspected of being a Soviet spy. According to his memories, he escaped from execution thanks to Rolf Nevanlinna (Finnish mathematician, who made significant contributions to complex analysis). Back in France, Weil was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen (France).
During his time in prison, Weil started to develop a completely new approach of mathematics, based on the Bourbaki's work. An approach that allows him to transform the algebra of equations to something more tangible...
Taking René Descartes as reference, who showed us how to convert shapes into numbers using coordinates: would it be possible to do something similar but in the opposite direction? Could it be possible to use intuitive ideas of geometry and shapes so to solve problems related to numbers and equations? Weil showed how to think in equations as shapes!, complicated even for the mathematicians of that time. And this was the beginning of a new concept: algebraic geometry.
And since then, that concept has allowed us to solve equations that for centuries seemed impossible. The most famous case was that it paved the way for the solution of Fermat's notoriously difficult Last Theorem, proved by British mathematician Andrew Wiles in 1995.
Weil was released from prison in May 1940 and, as many European mathematicians during that time, he moved to America. The Institute for Advanced Study at Princeton opened its doors in 1933 and at the end of the war there was a well-funded research center with countless emigrated scientists and many superstars, like Albert Einstein. With Europe ravaged by war and Göttingen destroyed by Hitler, Princeton quickly became the place to study mathematics.
The success of Bourbaki is linked to the scientific quality of his members. All of them have been extraordinary mathematicians. Five of them have obtained the Fields medal, most important international recognition of excellence in Mathematics, awarded at the International Congresses of Mathematicians that are held every four years: Laurent Schwartz (1950), Jean Pierre Serre (1954), Alexander Grothendieck (en 1966), Alain Connes (1982) and Jean-Christophe Yoccoz (1994).
Best,
Jesús