IEEE Circuits and Systems Magazine - Q4 2022 - 5

a fantastic famous painting) is much more fun than
standard images. You have an opportunity to work with
people from completely different domains, try to understand
what their problem is, then abstract the problem
and start thinking mathematically about the solution.
Question 5: What do you think is an exciting trend in
signal processing, especially in the age of artificial intelligence?
Can you share your vision on the possible innovations
in your field?
Prof. Daubechies: I think we'll have a better understanding
of how neural networks work and how they can do
better. I do believe that mathematics and mathematical
analysis, not necessarily mathematicians - there are a
lot of people who do great mathematical analysis and
who aren't mathematicians - will play a big role there
and that will make these tools better, more targeted,
more energy-efficient, and requires less data to learn
from. I think there is still a lot to do. There will be people
who say, " well, I don't want to wait for all the theory in
order to work on applications " and that's absolutely fine
and completely understandable and it would be terrible
if that were not the case. So we should use them for
applications, but we should at the same time, work on
building the theories so that applications can become
much better.
Question 6: Can you share the approach you take to advising
your students in your research group? What do
you think is the most important characteristics when
recruiting PhD students?
Prof. Daubechies: I do want to see my students at least
once a week, regardless of whether they have made progress
or not. I ask my students to not avoid me if they have
not made progress. All my graduate students have access
into my calendar. I have an open door and I encourage
them to come in and talk to me if they can find time on
my schedule. I direct the reading and my students would
also come to me with articles that they were interested
in. We would discuss research papers, and I would also
invite them to meetings I had with senior students and
postdocs. I typically do not give my graduate students
a dissertation problem. I tell my PhD students that what
they really would be doing in the first couple of years
is building an intellectual landscape where they would
start seeing how different things that people are working
on fit together and how they are all implicitly part of this
landscape. And then, I tell them " You will start seeing
that there are paths that are not completely dense and
problems that have not been explored. If some of these
problems interests you, then you will have found a thesis
problem. " This approach may not work well with some
FOURTH QUARTER 2022
of my students, so I had to steer a bit more, but in most
cases my students would indeed find research problems
that they have a passion for and become independent researchers
through this training process.
I think two things that are important, one is you really
want to build understanding. For example, if you
see a derivation, you may think can I do it better or in
a simpler way rather than just try to learn it all. I mean
you fight with it and in fighting with it, you learn it. This
process gives you a much better understanding than
just reading books and absorbing material cover to
cover but haven't done much with it. The other thing
is you are also willing to learn a lot. I encourage my students
to take every pure mathematics course they have
an appetite for even though we are working on applied
mathematics.
Question 7: You are a legendary female researcher, just
to name a few, you were the first woman to become a
full professor of mathematics at Princeton University,
the first woman to receive the National Academy of
Sciences Award in Mathematics, and the first women
to won the William Benter Prize in Applied Mathematics
from City University of Hong Kong. Throughout your
career, have you ever faced any specific challenges as a
female researcher?
Prof. Daubechies: When I am asked how I feel about
being the first female to win an award in mathematics, I
said it wasn't my problem, it was theirs. I feel that there
are perceptions about women that are not accurate,
and I do make special efforts to encourage women and
our young girls to stick with mathematics because they
can do it just as well. I don't have big theories about it,
and I think it's a cultural thing. Looking at the number
of women in academia in mathematics in Europe, the
percentage changes drastically from one country to the
other. There may be a few genetic differences, but not
that as much as in those wide variations in the presence
of women in mathematics. It's a sad thing for everybody
when you have a profession that could be done as well
by women but there are very few women and underrepresentation
in it. Encouraging the next generation,
it's something even for the men in the profession today.
That's why I work at these issues, and I can sometimes
get angry when people tell me mathematics is not blind.
Mathematics itself is blind and you cannot tell the difference
between an article written by a woman or a man
unless the style is so particular that you recognize that
person, but it's not that you recognize it as a woman
versus a man. But our profession is far from blind.
(continued on page 61)
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IEEE Circuits and Systems Magazine - Q4 2022

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