To close out the semester, here is a conversation I had with fellow math PhD student Michael Catli. Michael and I both started our PhDs in Fall 2023. I knew him slightly before that, via a mutual friend at Seton Hall University, where Michael completed his undergraduate studies. Michael now works in the group of Professor Alexei Miasnikov and is a teaching assistant for the first-year calculus sequence. I found this conversation, edited for conciseness and clarity, to be particularly fascinating, so a more complete account of it can be found on The Stute’s website. Happy last day of classes, and good luck on finals!
Charlie: What was your experience with mathematics growing up? What about the subject excited you, or made you want to pursue it at the university level?
Michael: I really liked math along with science, and as a kid, I actually wanted to be an astronaut because I just loved space and was so excited to think about things that existed outside of the planet. In elementary and middle school, I used my parents’ laptop to look up math stuff beyond what I was learning in school, and got a lot more into mathematics after courses in algebra and geometry in high school. I got to teaching myself calculus from the internet in junior year, and senior year, I bought Cornel Ioan Valean’s “Almost Impossible Integrals, Sums, and Series,” and would work on problems from it all day. This prompted a study into other areas of mathematics used to evaluate integrals, and I came to see mathematics as the number one way to improve the ability to think. That’s a loaded statement, but I feel like it’s really true, and improving my ability to think made math the most stimulating subject for me, and that can be attractive for anyone as well.
C: That perspective on math you give at the end is really interesting! I know a lot of people lump mathematics into the sciences thanks to STEM being such a popular acronym, while others (typically mathematicians) believe that the subject is more of an art, or at least has more artistic elements, due to its abstractness, compared to the other sciences. It seems like you’re saying mathematics to you is a kind of philosophy — could you comment a bit more on that?
M: You could view math as a big circle, and then the sciences and engineering fields can make up a part of that circle, in the sense that they depend a lot of times on being able to make conclusions utilizing mathematics. I’m not saying that math is any better than these fields, because you can be very stimulated by these other fields too, but I think all of them require the ability to think mathematically. This mathematical ability really strengthens overall cognitive ability and reasoning skills. Ultimately, it’s hard to describe this mathematical ability in words—like somebody once said, “Mathematics is what mathematicians do”—and that’s all you can really say about it. But this ability to think or desire to strengthen your ability to think is what drives your ability to study the subject.
C: That’s a really great explanation of the connection between mathematics and logic and reasoning skills! Now I want to ask about the work you’re currently doing for your PhD. What is your current research focus?
M: It’s still in the very beginning stages, but I’m currently trying to prove results about what we call the decidability of certain problems, specifically problems within group theory. I’m trying to show that in certain groups, there’s no easy algorithm for finding a solution to any given system of equations. For those not familiar with group theory, the idea of a group is that you have a set of elements, and then you can perform what’s called a binary operation on any two elements to get a different element in the set. You can also “divide” by any element, and there’s some element that acts like a “1,” both with respect to this operation. An example of this is the multiplication of two nonzero numbers: each number has a reciprocal, and you can multiply by the reciprocal to obtain the “division” I just mentioned; 1 acts as the identity, since any number times 1 is again that number.
Interested in hearing more? Visit The Stute’s website for the full conversation!
