By Conforto F.
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The aim of this ebook is to illustrate that complicated numbers and geometry could be combined jointly superbly. This ends up in effortless proofs and common generalizations of many theorems in airplane geometry, corresponding to the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem.
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GBK Did you ever join Bourbaki? 43 C Well I did for one year but I got quickly discouraged. They had already done the point somehow. I found out that they had about 500 manuscripts each of around 200 pages which were sitting in the cupboard somewhere, some already for twenty years. So writing one more of these looked like such a loss of energy. When they had someone like Dieudonne who wrote during his mathematical life something like 80000 pages of mathematics in a relentless way, the machine would function.
So you are given a polynomial and you want to know where the roots are in the complex plane. That was my first problem. I had found a notion, some kind of weak ordering in the complex numbers, which was simplifying all the proofs of the theorems in the books I was looking at and one could go a bit further. I worked on that for some time. MK Then you moved to Von Neumann algebras quickly. 42 C It took me a lot of time to find what I really wanted to do. When I moved to von Neumann algebras I had the impression that it was a part of mathematics that was widely accepted.
C Yes 68 was a turbulent time. We had already built the right kind of mood for 68. GBK So your were in Paris in the best place and in the best time. C Yes it was a good time. I think it was ideal that we were a small group of people and our only motivation was pure thought and no talking about careers. We couldn’t care the less and our main occupation was just discussing mathematics and challenging each other with problems. I don’t mean ”puzzles” but problems which required a lot of thought, time or speed was not a factor, we just had all the time we needed.