[Music]
It makes you feel like your brain is
able to do something big, and it's also
a very very happy moment, and it's just
like... the reason why I keep doing the job
that I have, and the reason why I accept
the defeats that often happen in this
kind of work, and I think over the years
what I notice is that the feeling of
finally being able to finish the proof,
it is as intense as the first time when
I started my research. My goal was not to
be employed in one of the best
universities in the world or proving the
most important theorem, but I had been
very lucky. I happened to be somehow in
the right place at the right moment. So I
grew up in a small town in Italy, in a
very rural part of Italy, and all my
family, they were all farmers - so there
was no math people at all. In fact, I had
no idea that you could have a career as
a mathematician. And unfortunately, my
father died when I was 10, and it was a
very chaotic moment. Working on math
problems was somehow a way of bringing
into my life some kind of logic order,
which I always felt like I needed. I need
things to be pretty organized so that
was just a way of coping: a coping
mechanism with the situation. In Italy at
that time, high school was not mandatory,
but my brother, luckily for me he's 10
years older, and being a boy he was the
one who was supposed to improve the
the situation. So he was already assigned
as the first that will go to college and
convinced my mother that I need to go to
high school. And this high school I went
to, it was a very rigorous science school
with a lot of emphasis on math and
physics. And so that worked out well for
me because I really liked math,
and at the end of the high school was
again the question what I will do.
There was not much money at home, but I
had a great math teacher in high school,
and he convinced my mom to send me to
college and study math, so then I would
become a high school teacher like
himself, and it would be a great job for
a woman. And I picked University of
Bologna as a college without really
telling anybody, because I had friends
that went there, but in particular
because there was a boy who really
liked me [laughing]. So I was very lucky because
University of Bologna is actually an
excellent place to study mathematics, but
when I started learning more sophisticated
mathematics, I just decided: This
is what I like to do, I would like to do this
for as long as I can. And I realized that
there is a way of doing it beyond
college which is doing a PhD which I
didn't know what it was, or why
people would do that. I just wanted to
keep doing research, so I started my
research on my PhD thesis in a field
that at that time was just at the
beginning. So, by default, I became an
expert in the field. So if I had started
my PhD two years before or three years
later, maybe this would not have happened.
I work on the pure side of partial
differential equations, which is a branch
of analysis. And within this field I
study something called dispersive
partial differential equations. So, these
equations come from physics and they had
a long history very often. I do not make
up the equations, but since they cannot
be solved directly, with abstract tools
we try to figure out what are the
properties and qualities of the solutions
without really being able to write
them down, by inventing or discovering
certain elements in abstract mathematics
that will give us answers to questions
that originally might come from physics
and in practice are solved in this more
abstract setting. So what I like about
that is not really giving the physical
answer, but actually discovering the
invention of the tools that will bring
us to those answers.
[Music]
So there has been a
defining moment in a sense in my research, and this sort of started in a
negative way.
I was at Institute for Advanced Study and I
was supposed to give a talk, and the
night before I reviewed my talk and was
ready to give that talk the day after, but at
the same time I got an email from a
Japanese mathematician who said that he
actually wasn't sure about a step in a
certain paper which was the same paper I
was presenting the day after. And so it
turned out that I wasn't sure about that
step either at that point, so I couldn't
really give that talk. It was a very
negative moment, let's put it that way,
but what happened is that from
investigating further this particular
step in the proof of that particular
theorem, I started a collaboration with
this Japanese mathematician and at the
same time a collaboration with two other
Americans. All of our names are Colliander,
Keel, myself,
Takaoka and Tao, and now we are called as the
"I team", so we worked a lot together. We have
a lot of very good papers together, we
are now known as a team somehow, and that
was a very important moment for the
evolution of my research. So I started
from a negative thing, but it ended up to be
probably the most fruitful path to my
career so far.
[Music]
So, to explain it in a simple way, it basically says the following: Since the
equations that I studied come from
physics and in physics if a system is
closed and there is no interaction from
outside, you expect there are certain
things that remain the same, constant in
time. For example, the energy, the total
energy of the system. But in order to be
able to write mathematically what
energy is... Usually the energy is
composed of the kinetic part and the
potential part, so you have to write a
certain integral. To make sense of them,
the function that you are integrating
has to be a sort of certain regularity,
or else you cannot write it down. In our
invention of this "almost conservation
law" what we did was, well, the solution of
the equation that we are looking at didn't
have enough regularity to be able to
write those integrals, and hence you
cannot even talk about the conserved
quantity. But what we did was: We modified
the function a certain way to give it a
little bit more regularity, and then
being able to write the same formula for
the conserved law. But since what you
have doesn't have the right regularity
it's not quite conserved - but it's
almost conserved, and that
still gives you a lot of information. And
then, we're trying to make the object
which is not as nice nicer to be able to
use something which is physical, but of
course because you made an approximation
to start with, what you have is not
something that remains constant in time
but almost does, and that helps.
[Music]
I actually feel like I have been very
lucky to grow up in Italy, because in
high school, girls were supposed to be
better than boys and that's the message
I got, so I didn't really worry about
being good in math and I didn't feel
like it was something that will make me
less attractive in high school. So in
college I guess it was even better somehow,
maybe because you already start with
a cohort of people that just like math,
and you spend most of the time with
that cohort. But a big difference came
when I moved to the United States and
that was something that I was not
expecting, you know. I wasn't aware or I haven't
had any idea that there was an issue. And
again, when I was doing my PhD
I had a lot of issues at the beginning: I
didn't speak any English, there was a
very different way of learning math,
there was a lot of homework that I was not
used to. So at the beginning, I didn't pay
attention to anything, it was just kind of
survival mode. It was more towards the
end of my PhD that when there was the
process of looking for a job for the
next step like a postdoc, that I started
realizing how mean somehow the
environment was for women, and in
particular the first time of
understanding of this issue
unfortunately came from my colleague
grad students. In fact, when I
received my offer to spend a year at the Institute
for Advanced Study and two years at
Stanford University, well, a couple of my
male colleagues said: "Oh yeah, that's
because these are women jobs, that's why
you've got these positions" and I was
completely taken aback by that
observation. And then I have started looking
more into this issue, and it's true - there
are positions that are
specifically set up for women in order
to increase the diversity of the various
departments, and although I had no proof
that these positions that I obtained
were for women, there was none of that
written, then I start doubting and this
somehow stayed with me and stays with me
until now unfortunately, so...
[Music]
Maybe it's a good idea to ignore what usually the voice tells you,
like: "Women
cannot do math, women are not good at science
and women don't have the same kind of
brain". It worked for me to try to know
them, and if you are witty or you
find some kind of cute and good way of
responding, say that that's not the
truth. But it never worked for me:
engaging in a very stubborn manner
to fight this kind of biases.
I always did it in practice, like: I proved
theorems, I showed that I could do it,
more than just talk and trying to dissuade
these people from thinking in this way,
so I would say just go ahead. If you like
it, you will always find along the way
people that will appreciate you. Maybe
not everybody, obviously, but you don't need
everybody. You just need somebody who really
takes you under his or her wing and
believes in you, and you will be going. So
just look for that person and do what
you like.
[Music]
