Not Your Mothers’ Math
Mathematics is all about numbers and memorization and absolutes. This is the concept held by most: math is a necessary skill you must acquire in order to do your taxes, balance your checkbook, or pay your restaurant tab. At the next level—on the way to becoming an architect, engineer, scientist, or statistician—victory on the field of trigonometry and calculus is mandated. Mathematics is exacting and precise, and there is always a correct answer.
MSCS grad students left to right: Ellie Dannenberg, Janet Page, Jessica Dyer, Yen Duong, Cara Mullen.
Enter the world of pure mathematics however, and the reality of what math is, and can be, gets flipped on its head.
“We are not subject to empiricism or data,” said Yen Duong, a PhD candidate in the Department of Mathematics, Statistics, and Computer Science. “I’ve read articles about epistemic privilege which pretty much describe the approach of pure mathematicians: ‘we know we are right and everyone else knows we are right.’ It’s awesome,” said Duong, who earned a dual degree in mathematics and philosophy as an undergraduate at Yale.
“Pure math is more similar to something like philosophy than it is a science,” explained PhD candidate Jessica Dyer, who came to UIC from the University of California Santa Barbara after earning her BS in mathematics. “We do not have a lab, we aren’t running experiments. There is no testing of hypotheses through scientific method. We think through problems logically, work out the details, and write it up.”
As scholars, pure mathematicians study the intrinsic nature of abstract concepts. For their graduate degree, they develop an original thesis and work on its proof throughout graduate school. Later, a mathematician may prove any number of theorems during his or her career, and those theorems may be related to the graduate school work, but that is not always the case. Certainly, they must build on arithmetical skills to do their work, but at this level they rarely, if ever, actually deal with numbers.
Grad students discuss a pure math problem.
“Abstract math classes are challenging and I love the idea of proving things, rather than just plugging numbers into formulas,” said Cara Mullen, who worked as a consultant after earning her BA in math from Pomona College in Claremont, CA. “I have always enjoyed working with numbers, but as a consultant I was using formulas and arithmetic, not ‘real math’—theorems and proofs—and it was not as interesting to me.” Mullen is now a fourth-year PhD student, working in the fields of number theory and arithmetic dynamics.
The universe of pure math does have a connection with the world of applied mathematics—which develops data and models critical to science and technology—but that is not why pure mathematicians do what they do. They “do” math for the same reason that dancers dance, sculptors sculpt, and musicians play—because it is their passion.
“I didn't actually like math until my junior or senior year in high school,” explained PhD candidate Janet Page, who earned her BS in math from UCLA and is working in algebraic geometry at UIC. “I finally had a teacher who really cared and answered my ‘why!’ questions—which had never been answered before. During my second or third year in college I took my first pure math class and realized that I wanted to do math as my career.”
“I have always liked math, even in elementary school, but I did not know that math could be a career,” said Ellie Dannenberg, a PhD candidate working in geometric topology. “My first semester at University of Georgia I took calculus just for fun and had a really awesome woman math professor who kept encouraging me to take more math courses. Her encouragement led me to become a math major.”
Dannenberg is quick to point out that the stereotype of mathematicians as exceptional is untrue. “It is not always the easiest thing and I’m not always amazing at it, but I can learn it and I have a good time working hard. It does take some level of ability, but we are not all ‘math geniuses.’”
Dyer, who completed an undergraduate minor in linguistics, credits her parents with encouraging her mathematical abilities and aspirations. “When I first took abstract algebra, however, it was a completely different way of looking at things because there are no numbers,” she explained. “I was struggling and was going to drop, but my professor said my questions indicated that I really should stay.” Dyer is now doing her graduate work in dynamical systems.
Recruited to LAS from her master’s program at UCSB, Duong is working in geometric group theory as a University Fellow. She began her journey to pure mathematics as a youngster in the University of Minnesota Talented Youth Mathematics Program. “We moved to California and I was the first freshman at my high school to ever take calculus. They thought I was a genius, but I wasn’t—I just had the advantage of this amazing program. I sat down for my first day of calculus homework and burst into tears. It has been hard work ever since.
“Generally, math is really hard,” Duong continued, noting the collegial, supportive atmosphere in the MSCS department. “We are all trying to climb a mountain and no one here is going to pull you off the mountain.”
“When I came here for visiting day, everyone was very welcoming,” said Dyer. “So when we have our visiting days, I make a point of going and talking to the prospects because that was really important for me.”
Also important in a historically male-dominated field is the mentorship and tradition of women mathematicians at UIC. Among the noted women professors paving the way in MSCS have been Louise Hay—who came to UIC in 1968 and served as department head from 1980 until her death in 1989—and Professors Emerita Susan Friedlander, Bhama Srinivasan, and Vera Pless. Current female professors and mentors include Alina Cojocaru, Mara Martinez, Irina Nenciu, Brooke Shipley, Dima Sinapova, Alison Superfine, and Jing Wang.
Audience members at AWM program share a math laugh. Photo by Jessica Dyer
Srinivasan served as the fifth President of the Association for Women in Mathematics and was a participant at the November 15, 2013 UIC AWM Student Chapter panel, Women in Mathematics: Reflections and History from Female Mathematicians.
“The department has been very supportive of AWM activities,” said Dyer. “The organization has a long and strong history at UIC, and over the past few years we’ve been doing quite a few events.”
Last year, Duong and Dannenberg planned and presented the first Midwest Women in Math Symposium. The second conference, held at the University of Notre Dame in April, was attended by Dannenberg, Dyer, and Duong.
Left to right: Professor Aime Wilkinson of University of Chicago, Jessica Dyer, Professor Emerita Alexandra Bellow of Northwestern, Yen Duong, and Bhama Srinivasan at the AWM panel. Photo courtesy of Dyer
While Dannenberg, Duong, Dyer, Mullen, and Page have found their calling in the high reaches of pure math, they also are concerned about the generalized aversion to math so prevalent in the United States.
“We do have a math-phobic culture in which a lot of parents pass their fear of math on to their children,” said Duong. “Sadly, it is often the mothers. A child will ask for help with math homework and mom reacts by telegraphing fear.”
“Primary teachers, who are predominantly women, are responsible for teaching all subjects and many of them suffer from math phobia themselves,” said Mullen. “I was lucky in that I had a number of strong female role models in my early math classes. For a while I considered teaching elementary school math myself so that I could be one of those role models for future students. I was going to save the world by teaching young kids to love math.”
Dyer agreed that kids are set up to fear math: “I’ve read studies that elementary teachers will often begin a lesson with a statement such as, ‘Now we are going to learn fractions. Don’t be scared, I know this is really hard.’”
To help change that paradigm, Dannenberg and Page both volunteer with UIC’s Math Circle, an after-school program run by MSCS Assistant Professor Ben Klaff, that exposes young people grades 5-8 to math they would never normally see in school.
“A few weeks ago we did a unit with them on code breaking and some basic cryptography,” said Dannenberg. “This program is open to any interested student. It is not just for ‘gifted’ math students.”
“We work with interesting exercises such as logic puzzles,” added Page. “It gets them used to the idea that math does not have to be the same type of problem over and over again on the blackboard. It can be creative.”
Left to right: Ellie Dannenberg, Janet Page, Jessica Dyer, Yen Duong, Cara Mullen.
“What if we taught music the way we teach math, if students had to learn to read notes without ever being exposed to music?” asked Dyer. “There is a great article by Paul Lockhart, ‘A Mathematician’s Lament,’ that really explores this idea. It is a question of how you approach the subject. The standard school curriculum does not express the beauty of what we do.”
“I think one answer to math fear is to learn about math. Read Steven Strogatz’s The Joy of X (Mariner, 2012). Look up Jordan Ellenberg,” said Duong, who teaches in MSCS’s Emerging Scholars Program. “I taught fifth graders with The Number Devil (Macmillan, 2000). “If you just read that to your kids they will be less scared—and you will be less scared.”
Photos by Joshua Clark unless otherwise indicated.