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.