As a senior at Blair in 1995, Samit Dasgupta won fourth place in the 1995 Westinghouse Science Talent Search with a project on the Schinzel Hypothesis. He has been studying Number Theory ever since, as an undergraduate at Harvard, a graduate student at UC-Berkeley, and as a professor at UC-Santa Cruz. He spoke with Ted Jou '99 about his research and his memories of Blair:Can you talk generally about your research?I study Number Theory, which is a branch of pure mathematics. Within number theory I study Algebraic Number Theory. Broadly speaking, Number Theory has to do with two types of problems: One is finding the solution to equations in the rational numbers, and the other is studying the distribution of prime numbers. How long have you been working in Algebraic Number Theory?My focus in Algebraic Number Theory began as an undergraduate. I have been interested in Number Theory for a long time. In high school I went to math summer camps, and there was one at Ohio State where I learned the basics of Number Theory. When I was in high school, I was more interested in Analytic Number Theory, and I did my Senior Research Project in Analytic Number Theory. When I got to college I focused more on the Algebraic side, which I guess was a fine-tuning of my interests. So I have known for a while not only that I wanted to be a mathematician but that I wanted to be a number theorist. How would you describe Analytic Number Theory vs. Algebraic Number Theory?Analytic Number Theory uses methods of Calculus, more specifically Complex Analysis, to answer number theoretic questions such the distribution of the prime numbers. When you’re actually trying to prove a theorem, you’re doing a lot of Analysis, which is higher level Calculus. In contrast, in Algebraic Number Theory you’re not usually doing Calculus, where you’re taking derivatives and integrals, but you’re using more algebraic-type structures. The algebra involved is just a higher level of the Algebra that we have all learned in high school. So the difference between analytic and algebraic number theory has to do with what type of foundational mathematics is applied to solve number theoretic questions. What does Number Theory look like on a day-to-day or week-to-week basis for you?It depends on what stage
of the process you are in on a project. On any given day, you might be
working on several different projects at different stages. Usually at
the beginning of a project, what happens is you are reading a paper or
you go to a talk or somehow you get exposed to a problem, and you
realize that some expertise that you have might shed light on a problem,
either with a solution or just some partial progress – you might not
know until you carry out the research. The
research part of it then becomes just thinking. Once you realize that
there is a problem that you might be able to say something about, you
apply the methods that you’ve learned to see if they can be used to
attack that problem, and some of that might involve doing literature
searches and reading papers that are either about that topic or about
some method that you think might apply to that topic. Eventually you
just work on the problem, and you sit with a pad and a pen and go to
work. You get stuck sometimes and you go talk to people for ideas, but
that is basically what it comes down to. I don’t want to glamorize it, but usually there is an “aha” moment when you get the key insight that will enable you to prove the result.
It happens in jumps and steps. In math research, you don’t necessarily
make clear progress in each day of work – it's very difficult to have
the patience for it. On the one hand you have to continually work and
work and keep at it with a lot of determination, but you can go months
and months with basically no progress or no visible signs of progress.
Obviously you’re making progress – you’re thinking and you’re increasing
your understanding of the difficulties of a problem – but you might not
actually come up with a solution after months and months of thinking
about it. And then finally, in one moment it comes, and it kind of feels
like if I just had that moment months earlier then I would have saved
all that time. But really it’s all the months and months of putting the
time into it that enables you to have that “aha” moment. For most papers
there’s probably one or two moments you can look back at and say that’s
the breakthrough that I had that enabled me to write this paper.I noticed on your website you had a list of some conferences that you helped to organize. Can you tell me about that?What advice would you have for undergraduates or even high school students with an interest in math and are thinking about pursuing academic math?There are a lot of things
to say ... My first advice these days is to get a very solid foundation
in the basics of Mathematics. Students these days seem to know at least
the words for really advanced topics at a young age that before we only
thought of as graduate or even postgraduate material. Now, even
undergrads are talking about them. Obviously, there’s only so much
anyone can process and understand at a young age, and if they’re
learning these advanced topics at least superficially, that means there
is something more fundamental and basic lower down that they are
skipping or glossing over or not giving adequate time to. So
my advice for younger people is actually to make sure you understand
the basics well before you move on to more advanced topics. It’s not a race. It’s more important to understand something really well,
the basics, so that when you get to more advanced topics you’re very
comfortable, than it is to think about advanced topics from a really
young age and not be able to make progress because you don’t understand
the background or the history behind why people are thinking about these
advanced topics. If you want to be successful, it’s important to have a
solid foundation.The
other thing, very generally, is the kind of mindset you need to do
academic research. You have to be very determined and you have to be
willing to stick to something for a really long time. As I alluded to
earlier, you have to think about research problems for a really long
time. One
reason I mention this is that people get into mathematics often because
of contests, and that’s true for me too – I took part in a lot of high
school and college math competitions. These are the types of
competitions where you’re given a problem that you have to solve within
20 or 30 minutes at most, if not 5 or 10 minutes. If you don’t solve it
in that time, you just move on to the next problem, and whoever can
solve the most of those problems 10 to 15 minutes at a time wins. Math
research is not like that at all. You’re usually thinking about things
for months and months at a time. It’s not necessarily the quickest mathematicians who are most successful by any means.
The most successful mathematicians are those who are able to have keen
insights into deep problems, and those come about by ruminating on
things for really long periods of time and becoming an expert on
something.I wanted to ask you a few questions about your memories of Blair and the Magnet. Is there anything you learned or did in the Magnet that you still carry with you today?I can say one thing, which
is that the Magnet Program was an incredible training ground for me. I
can tell you that I went to Harvard for undergraduate after Blair, and I thought Blair was harder than Harvard. It really prepared me for college and afterwards, so that’s one thing.The
other thing is that I really took for granted the diversity that you
had at a school like Blair, both racially and culturally and equally
importantly, intellectually – just the different ideas that people have
and different interests that they have. The person next to you might be
interested in computer science and the person on the other side might be
interested in poetry. And there were so many ideas just from your
friends, not to mention all the amazing teachers that we had. I was kind
of used to that, and I took it for granted. Unfortunately, once you’re
older, you’re often in situations where you’re not surrounded by such
diversity. Are there any particular teachers that stand out in your memory?Since I was really focused
in math, of course Eric Walstein had a big influence on me, even more
through working with him on the County Math Team than through the
courses that I took. However, I remember that the biggest influence on
me was really my Computer Science courses. Even though I didn’t follow
in it in college, I really loved computer science courses in high
school. I learned the most from them, and they influenced the way that I
thought about problems in a way that has been very valuable to me. The
two teachers I really remember are Ms. [Mary Ellen] Verona and Ms.
[Susan] Ragan. They were really great teachers, and I remember I learned
things in high school that computer science majors in Harvard didn’t
learn until their second or third year. So that was the level of
advanced teaching we had in the Magnet program. Sometimes
you don’t appreciate these kinds of things, but for me I’ve been very
cognizant of the extent to which that training has helped me in my
career and in my life in general, even though I didn’t go into Computer
Science ... It helped me understand how to think about problems from a
problem-solving point of view and how to create algorithms and
structures to attack the problem. That’s something that can help you not
only in mathematics but in your life in general: How to break down a problem into pieces, and compartmentalize and how to do things efficiently –those are all important things that serve one well both in one’s career and in life. |