Mauricio Peixoto (April 15, 1921-April 28, 2019)

Sometime after my Ph.D in 2001, I met Mauricio Peixoto in the corridors of IMPA and he took me to his office and gave me a bunch of his articles on focal decomposition. At that time I was mainly reading many texts in Picard-Lefschetz theory as I needed this in my Ph.D. thesis. Soon I landed on K. Lamotke's article "The topology of complex projective varieties after S. Lefschetz" (1981) and this article took me to read "A page of mathematical autobiography" (1968) by S. Lefschetz. I put Mauricio's paper in my desk and did not read them deeply as I found them too far from my narrow point of view to mathematics, or maybe I was an arrogant fresh Ph.D man who did not care other mathematics rather than his own. Sometimes I was having a glance at the articles and then back to my own staff again. Few days later, I went to the library of IMPA to find Lefschetz' article. I remember my own puzzle and amazement after reading the first lines of this paper. "As my natural taste has always been to look forward rather than backward this is a task which I did not care to undertake. Now, however, I feel most grateful to my friend Mauricio Peixoto for having coaxed me into accepting it. For it has provided me with my first opportunity to cast an objective glance at my early mathematical work, my algebro-geometric phase[...] The time which I mean to cover runs from 1911 to 1924, from my doctorate to my research on fixed points", Lefschetz writes. I was totally confused, "Is this the same Mauricio with whom I talked few days ago?", I asked myself in astonishment. I was lookinig Mauricio's name on papers on focal decomposition abandoned in a corner of my desk and his name in Lefschetz's article in front of me, and still was not believing that these are the same names. Later, Mauricio himself explained me that he was a Post-Doc at Princeton under the supervison of S. Lefschetz and during this period they became good friends. I realized that one of the good friends of Lefschetz was next door to me, and in my small and limited world, Lefschetz' mathematics was part of a far away history. Mauricio told me many of his conversations with Lefschetz. He told me that the young Lefschetz when wrote his famous 1924 book and went to Paris to talk with E. Picard about his work, Picard had a very cold reaction to his work. It must be noted that this work eventually took Lefschetz from Nebraska to Princeton. This might have been similar to the reaction of Cauchy when Abel went to Paris to talk with him about what is now called "Abelian integrals". I understood that all of us, mathematicians, are part of a chain, in which science is passed from one generation to another. We sometimes promote each other and sometimes do not care about work of each other, but at the end what is important is our heritage to the next generation of mathematicians.



Hossein Movasati
April 31, 2019.