How can one create a meaningful career in mathematics research? Dr. Catherine Sulem, a professor at U of T’s Department of Mathematics who has been has recently been recognized for her achievements, wrote to The Varsity about her experiences in mathematics research and her advice to students.

The Centre de recherches mathématiques (CRM), the Fields Institute, and the Pacific Institute for the Mathematical Sciences (PIMS) jointly awarded Sulem the CRM-Fields-PIMS prize for outstanding Canadian research achievements in mathematics.

Sulem’s work includes influential findings in the “study of non-linear partial differential equations,” the resolution of “multiple questions [about the non-linear Schrödinger equation] that had resisted analysis for years,” and her groundbreaking analysis of water waves, as the Fields Institute reported.

Road to mathematics

When Sulem was a graduate student, she “attended many talks about turbulence in fluids,” as at the time, new ideas combined “mathematical analysis, computer simulations and graphic visualizations to bring new insights and increase our understanding of nonlinear dynamical processes,” she wrote.

This inspired Sulem and “helped [her] form the directions of [her] research interests.”

Sulem’s high school teacher also played an important role in her interest in mathematics by teaching her proofs, notably “what it means to [prove] something in mathematics.” She was also taught the important lesson that “if you claim something, you have to prove it.”

Research in mathematics

As Sulem explained, her research is in the area of “nonlinear partial differential equations which are used to model phenomena in the natural world.”

The Oak Ridge National Laboratory (ORNL) defines a partial differential equation (PDE) as “any equation involving a function of more than one independent variable and at least one partial derivative of that function.”

“The distinction between linear and nonlinear PDEs is extremely important in computational science… Generally, nonlinear PDEs do not yield to analytical solution approaches,” the ORNL explains.

In particular, Sulem studies the “evolution equations that describe wave phenomena occurring in fluid dynamics, optics and plasma physics.”

Teamwork is a key component of her work. “[Throughout] my career, I have maintained solid and durable collaborations,” she noted. “These collaborations play a vital role in my research.”

As she has progressed in her field, she expressed that she has “learned that among the most important elements of the process of discovery and knowledge building are patience and humility, together with the ability to appreciate and connect different points of view.”

Navigating motherhood

Sulem discussed how she achieved a healthy work-life balance by having a strong support system.

“When my children were small,” wrote Sulem, “my husband Edward Bierstone, who is also a mathematician, and I fully shared the responsibility of the home and the upbringing of the children. This was instrumental to me having a fulfilling career.”

She went on, “As a mother, I found it was important to rely on the help of others, at the same time not trying to control everything and seek perfection.”

“Have confidence in yourself”

“To young girls, I would say what my mother used to tell me and my siblings: Enjoy your studies and your learning. Because, when you understand or know something, it is yours. Nobody can take it from you, and it makes you strong and independent.”

Her advice to women pursuing STEM degrees or careers is that “it is very important not [to] be isolated, not being shy of asking advice and listening to advice.”

“A career in STEM is a long journey. It is not easy but it can bring a lot of joy if you are passionate about it. Have confidence in yourself, follow your passion and be true to yourself.”