Can you explain the basics of pi and why it is relevant in math?
Kilikan: As a mathematician you see pi everywhere. It is in
number theory, waves, anything circular of course. So I see pi all the
time. What is so special about it? Its just a symbol to us, but it is
not actually that symbol. So, I thought of my first encounter with pi,
which of course was back when I was a little girl in school, but it took
a while to appreciate the vastness in it. The reality hit me when I was
in college. No matter how many digits of pi you find there will always
be more. So I ended up realizing that means we cannot actually define
it. We will never ever be able to fully know what pi is.
Rossi: There is a result that allows you to calculate any
digit of pi in binary. If you say, Just tell me the one billionth
decimal of pi, no one knows how to do that. You have to calculate a
billion digits, but in binary thats a decimal. When I was a kid I
remember there would be an announcement almost every year that someone
did another calculation of pi. What the use of that was, I dont know.
Kilikian: I think this sort of quest, the holy grail of
finding one more digit of pi is far beyond its practical use. So its
just curiosity. What will the next one be and how will we find it? I
dont know how far we will ever get.
Rossi: It is amazing when you think about it. If you take the
ratio between the diameter of a circle that is a pure number and its
pi. It is the fundamental non-integer ratio out there. It just turns up
in everything.
Most people solely see pi as a math concept, but are there practical uses for it outside of standard math?
Rossi: Ill give you an example. While I was a graduate
student I also ran a pizza restaurant. My parents and I were setting up
the menu, and one of the things we noticed about the data from other
restaurants is medium pizzas never sell very well. My father asked me,
Is it price? It never occurred to him to calculate the area of each
one. Now theres a little more to it than that, but we sat down and did
all this really quick using pi.
So whats the conclusion?
Rossi: Its overpriced. Did people calculate and make a
decision? No, but I think they just experienced it. You experience it
enough times that youre like, Oh Ill just get the large and get a lot
more pizza. Even though people dont reason explicitly in math,
cognitively people reason statistically.
Given pis relevance and fundamental place in society, why do you
think its important that Pi Day is a (sort of, unofficial) holiday?
Kilikian: I have to confess that I didnt know this was a
holiday until I moved to the U.S. I think the good part of having a
holiday like this is just having a recognition of how important this
number is in mathematics. It might be a good starting point for new
people who want to be interested in science, even study why
mathematicians like this number so much. It is important to get kids
interested in mathematics or STEM in general. And that will open a door
to finding the importance of this and finding a segway to actually
opening other doors after.
Rossi: Pi Day is more than celebrating a number. Pi Day is a
celebration of mathematics. It's the fundamental abstraction of reality
when you think about it and thats really important. Like Eirini said,
its about contemplating the infinite.
Do you come across pi in your own research or teaching?
Kilikian: Well, teaching of course. It comes up in calculus
classes a lot. I havent taught too many classes, but in the range of
classes I have taught, pi was always there. In my research it is related
to some probability and distributions.
Are there problems you are not currently looking at, but would like to eventually research?
Kilikian: I like baking and I was wondering how I could
combine this with my math interests. I know there is this thing called
cooking mathematics where people study the fusion of heat in foods. I
havent got into this ever, but it is something I would like to at least
be informed about.
Rossi: Well, its a little bit complicated. You know
snowflakes all look different, theres a very good mathematical reason
for that. I think theres a simple way to express the mathematics and
explain the structures we see. I would just like to understand that a
lot more deeply. I think there is something universal in there, and Id
like to get a grip on that in my free time.
Do you have advice for high school students on how they can prepare for college-level math?
Rossi: I would just say that any decision you make is more
powerful if it has mathematics behind it. Curriculum kind of tends to
lead you down certain roots, but I like to think mathematics is broad.
We went really deep in the 60s because of the space race all calculus and
differential equations. Theres all kinds of wonderful things. So, Id
say it's exciting. Theres a lot of mathematics to pick and choose from
and it gives you insight and power over making these critical decisions.
Kilikian: What I would add is, people coming into college
shouldnt be afraid to challenge themselves. Whenever you go to learn
something new it will be challenging, it will be hard for you. So give
it a chance and mathematics can be very rewarding.
Do either of you get strange questions from family members about what exactly you do as a mathematician?
Kilikian: I can go in tangents and talk a lot so at some point
family members will stop me and say, Oh okay, what other news? They
dont care about the deep math of what Im doing. What happens even more
is I explain math to my husband even if he doesnt ask. The poor guy
has to hear about ideas. It is very interesting and funny because he
understands maybe less than half, but he looks excited because Im
excited.
Rossi: Well, Ill tell you a
story. I have an uncle who worked for the railroads. Hes very
skeptical of people with college degrees. So after I finished my math
degrees I visited. So he walked up to me and he said, Youre a
mathematician huh? Tell me which numbers to pick for the Pick Six
lottery. I said, Well, Uncle Stach, its random. He says, Yeah well,
but certainly some might turn out more than others? I said, Yeah,
well if I were you I wouldnt bet on the lottery, but if I were to bet
on the lottery, I would pick a sequence like 6-5-4-3-2-1 because no one
else will do that. They pick birthdays and other stuff. So then if you
win, you have the same chance, but no one else will pick it so you wont
have to split the winning.
Kilikian: Please tell me that he won the lottery.
Rossi: No, he didnt win, and he thought my idea was stupid because 6-5-4-3-2-1 would never come up in the lottery.
It could!
Rossi: Absolutely, exactly the same chance as any other combination. So we had a long conversation about that.
Kilikian: Did you convince him by the end?
Rossi: Yeah, I think I had him. But Im sure he didnt win anyway, so hes like, Ah, that idiot nephew.
So playing off the idea of pies on Pi Day, what are your favorites?
Kilikian: I like all pies. It is very hard for me to choose. I
would definitely pick a savory pie, not a sweet pie. Either spinach pie
or leek pie or cheese pie.
Rossi: Id say either lemon meringue or apple. Half and half would be good.
Article by Carlett Spike; photo by Wenbo Fan; graphic by Jeffrey Chase
