Henri Cartan is no longer with us

ScienceNews reported the great mathematician Henri Cartan died at the age of 104.

He was no doubt one of the giants of mathematicians of the 20th century.
ScienceNews says: "In addition to his work in Bourbaki, Cartan made groundbreaking contributions to a wide array of mathematical fields, including complex analysis, algebraic topology and homological algebra. He received the Wolf Prize in 1980, one of the highest honors in mathematics, for his work on the theory of analytic functions. Two of his students won the Fields medal, sometimes considered equivalent to the Nobel Prize in mathematics, one won the Nobel Prize in physics and another won the economics Nobel."

I first encountered his name when I was a Math student, reading Homological Algebra by Henri Cartan & Samuel Eilenberg.
The book was considered some kind of a bible of algebraic topology, but very hard to read. I usually read books very fast, but this must have been the slowest book I ever read, and I must admit that I have only read about 70% of the book.

Only later did I discover that Henri Cartan was actually one of Nicolas Bourbaki authors. Nicolas Bourbaki is the pseudonym of a group of mainly French mathematicians who wrote the Bourbaki series of mathematics. The group included, at one time or other, Henri Cartan, Claude Chevalley, Jean Coulomb, Jean Delsarte, Jean Dieudonné, Charles Ehresmann, René de Possel, Szolem Mandelbrojt, André Weil, Laurent Schwartz, Jean-Pierre Serre, Alexander Grothendieck, Samuel Eilenberg, Serge Lang and Roger Godement.
See the Wikipedia entry on Bourbaki.
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I would not have read Bourbaki, if it was not my class assignment to make a presentation on one of the chapters of Bourbaki's Algèbre. I don't read French, and there were no English or German translations available. Luckily, the Bourbaki style of writing does not employ a rich vocabulary, and I managed to make the presentation without too many embarrassments.

The Bourbaki style of mathematics is very rigorous, abstract, general, axiomatic, formal with little examples and no diagrams. It seems to be in the spirit of Hilbert's formalism. The approach makes it easy to apply one abstract formalism to a very wide areas of applications, hence its generality.

Not everybody likes the approach, Bourbaki has come under criticisms, mainly for being unintuitive and because some mathematical fields were omitted.

Personally, I think intuition is of utmost importance in mathematics, if it is not obtained from books like Bourbaki, perhaps it can be obtained from other sources such as personal contacts with teachers and colleagues. In addition, these days, people talk about mathematics informally on the net, see e.g. A Neighborhood of Infinity , The n-Category Café, as well as Terrence Tao's blog

Related post: The Unreasonable Effectiveness of Mathematics