This is a question for Mathematicians and Mathematics lovers and the others!
This video may help every body to start.. https://www.youtube.com/watch?v=QYyuZ3_PQ4M
Bourbaki was not an experiment, it was a PROGRAM. Program, on one hand, to unify mathematics and, on the other hand, to put it at the highest level of generality (or abstraction). None of these directions worked precisely as Bourbaki's members intended, as the development of mathematics in the recent 30, or so, years shows. Nevertheless, it was the most serious attempt in those directions since G. Cantor's revolution.
Definitely, "bourbakism" reflected on teaching mathematics in France. I have a book by G. Choquet on plane geometry intended as a high-school textbook. A very good idea, high level of abstraction, but only for good and very good students. On the other hand, as an undergraduate at Warsaw University in Poland, I was taught mathematical analysis based on the Dieudonne's book. Similarly, I was studying Bourbaki's book on real functions. The beauty of Boubaki's presentation is still stunning.
Speaking of logic, one should realize that the concept of mathematical logic, when Bourbaki started its activities before WWII, was is the making.
Except for Alfred Tarski, there was the largest group of other logicians in one place in the world (13 people, including two professors). BTW, it was Boleslaw Sobocinski (after WWII professor at the University of Notre Dame) who introduced the so-called "inverse Polish notation" to the world of computer science. This notation was earlier used by J. Lukasiewicz in his work on logic. Sobocinski was named the "father of computer logic" in the US. It goes away from Bourbaki, but is relevant.
These are my two cents on Bourbaki.
Hi, personnely when I was young and was studiying mathamatics in France the Bourbaki school was very strong. Thus, our professors tried to increase as much as possible the abstractness of any notion. When you are young it is not always easy to undertand the real meaning of each abstract notion and you see it as a kind of "theorretical game" you play especially when trying to demonstrate theorems. Later, when you are at the University, you understand that all this mathematical formalism is beneficial and that it helps you a lot.
@Richard .. D’accord ! C’est évidement très different pour un étudiant étranger en premiere année venant a l'université française d'une tradition educative a l'américaine très approximative et sans maths dites moderne du tout. On a commencé par les polynômes.. définition “ En algèbre, une fonction polynôme ou fonction polynomiale est une application associée à un polynôme à coefficients dans un anneau commutatif (souvent un corps commutatif K) de ..” Évidemment, résultante nulle, Rien compris ! Il faut un an pour déchiffrer ! Je suis allé voir le Professeur! Il m’a conseillé de voir l’assistant et lui demander qu’ es ce que c’est qu’une bijection .. je l’a vu reponse : c’est une injection et surjection a la foi ! Bonne Journée.
In light of the possible incoherence of mapping the actual infinite onto reality, it seems questionable whether all mathematics can be grounded on set theory as the Bourbaki group imagined.
Bourbaki was not an experiment, it was a PROGRAM. Program, on one hand, to unify mathematics and, on the other hand, to put it at the highest level of generality (or abstraction). None of these directions worked precisely as Bourbaki's members intended, as the development of mathematics in the recent 30, or so, years shows. Nevertheless, it was the most serious attempt in those directions since G. Cantor's revolution.
Definitely, "bourbakism" reflected on teaching mathematics in France. I have a book by G. Choquet on plane geometry intended as a high-school textbook. A very good idea, high level of abstraction, but only for good and very good students. On the other hand, as an undergraduate at Warsaw University in Poland, I was taught mathematical analysis based on the Dieudonne's book. Similarly, I was studying Bourbaki's book on real functions. The beauty of Boubaki's presentation is still stunning.
Speaking of logic, one should realize that the concept of mathematical logic, when Bourbaki started its activities before WWII, was is the making.
Except for Alfred Tarski, there was the largest group of other logicians in one place in the world (13 people, including two professors). BTW, it was Boleslaw Sobocinski (after WWII professor at the University of Notre Dame) who introduced the so-called "inverse Polish notation" to the world of computer science. This notation was earlier used by J. Lukasiewicz in his work on logic. Sobocinski was named the "father of computer logic" in the US. It goes away from Bourbaki, but is relevant.
These are my two cents on Bourbaki.
@Roman, Thank you, I have no problem with the word « program ». I think in France, education people are thinking about the very high degree of abstraction in a way that will lead to less abstraction in Education. Which is an implicit criticism of that “ experimental program ”!
In France of the 1980s, students in schools of law, had “Topology” in their programs, first year students in schools of medicine had notions about Fourier transforms in their syllabus.
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