I was
asked to say a few words as a toast to Professor Graciano de Oliveira.
Graciano
de
Oliveira of course does not need an introduction. Practically
everyone here knows him. Many of us, even if some don’t know it, do our
research work under his influence. It may be a distant influence, but
it is certainly there: on eigenvalues and singular values, on
completion problems and inverse problems, on invariant polynomials and
control theory, on multilinear algebra and preserver problems. Many
lines of research that we now see very active in Portugal, in Spain and
in other countries have their roots in papers Graciano de Oliveira
wrote in the 60s, 70s and 80s.
I was
a witness to Graciano de Oliveira’s second wave of student inspiration
(the first, in the early 70s, led to the beginning of the research
career of José Perdigão Dias da Silva and Eduardo Marques de Sá). This
was in Coimbra in the late 70s and early 80s. I still remember very
well the constant seminars, the regular visiting by famous people, the
lists of open problems circulating. And I remember even better Graciano
de Oliveira’s style of questions: Why don’t you try normal instead of
Hermitian?… Permanent instead of determinant?… F instead of C?…
And
the worst of all: What are you doing here? When will you write your
first paper? Why don’t you write more papers?
Sometimes
we
had our doubts, and asked silly questions, such as: What is this
good for? Is there any application for this? And the answer was
immediate: Of course it is applied mathematics, you can apply it to
writing a thesis. It seems a joke, but there was a lesson in this: if
you worked hard, if you thought about mathematical problems, you would
be training your mind. Afterwards – after writing your thesis – you
could apply this training to whatever you wanted, pure or applied.
And I
should point out that, even if the suggestions seemed quite arbitrary,
there was, most of the time, very good mathematical taste in the
subjects studied in the seminars and in the problems suggested. For
example, the Horn and Mirsky papers of the 50s and 60s on eigenvalues,
singular values and diagonal elements. Or Horn’s famous paper on
eigenvalues of sums of Hermitian matrices. These are papers that have
had a great influence and have been studied and generalized by many
people in deep settings.
The
constant questioning also illustrates another feature of Graciano de
Oliveira, which is his love for conversation, for argument, even for
provocation. I am sure many of you have had first-hand experience of
this. Graciano de Oliveira loves to provoke you, to argue with you, to
find fault in your logic. If you are not very sure of yourself, he will
easily win over you in a logical argument. And he likes logical jokes.
As an example, I recall the visit of a famous mathematician, who had
something peculiar about his eyes. Someone said: “Did you notice? The
whites of his eyes are blue.” Graciano de Oliveira immediately replied:
“That’s nothing. I know lots of people for whom the blues of the eyes
are white.”
Anyway, the good thing is that we all, who lost
so many arguments with him, will have many years to try and think of
new, better answers to Graciano de Oliveira’s questions, and to think
about the mathematical problems for which, directly or indirectly, he
was the inspiration.