DS25 Panel Addresses Essential Facets of Interdisciplinary Research

Research in the mathematical sciences—and particularly in dynamical systems—provides opportunities to foster rich relationships with other fields and delve into a diverse array of applications. Scientists who pursue interdisciplinary projects encounter an exciting range of possibilities in their work but must also contend with questions about funding, publication, and career advancement.

“The most interesting thing about interdisciplinary [work] is thinking about a problem from lots of different angles and tackling it with different tools,” Dorit Hammerling of the Colorado School of Mines said during the 2025 SIAM Conference on Applications of Dynamical Systems, which was held in Denver, Colo., this past May. Hammerling took part in an interdisciplinary research panel that also featured Daniel Abrams of Northwestern University, Chris Budd of the University of Bath, Mari Kawakatsu of the University of Pennsylvania, and Jonathan Rubin of the University of Pittsburgh. Cecilia Diniz Behn of the Colorado School of Mines and Igor Belykh of Georgia State University chaired the session, which addressed the intricacies of working at the interface of multiple scientific fields.

The panelists’ own career histories exemplified the varied pathways that can lead to interdisciplinary research. Their individual backgrounds span fields such as mathematics, engineering, and physics, and they currently work in areas that include geoscience, mathematical biology, and industrial mathematics. For instance, Kawakatsu began college as a physics major, but classes in the social sciences inspired an interest in collective behavior that—combined with an inclination towards mathematical modeling—has shaped her graduate and postdoctoral studies. “Applied math programs tend to be a bit more flexible about the kinds of projects you can explore,” she said. “It looks a little like I’m meandering, but there’s a core interest in collective behavior.”

When diving into a novel domain, it is important to identify collaborators who possess expertise on the problem of interest, either within or outside of the mathematical sciences. “People see problems in a completely different way when they come from different backgrounds,” Abrams said. “You don’t need a collaborator to get started, but you do need to find someone to talk to eventually so you know how people with different backgrounds view your ideas.”

Opportunities for new professional partnerships can emerge in unexpected places, but one surefire way to make connections and learn the priorities of various research disciplines is through conferences. “Go to conferences of all different types, immerse yourself in different fields, and see what people in those fields care about,” Rubin said. Some scientific gatherings even schedule structured sessions for attendees to build relationships and work together. “In my experience as a graduate student and postdoc, I found smaller-scale workshops with dedicated time for project work to be helpful,” Kawakatsu said.

Partaking in a variety of activities close to home—such as seminars at one’s own university—can be similarly beneficial. “Having local collaborators can’t be beat, especially when you’re getting started in a field,” Rubin said. “There can be a steep learning curve, so thinking globally but acting locally is a good strategy.” The panelists agreed that even casual social interactions may lead to interesting and unexpected collaborations. “The key is talking to people you don’t know,” Abrams said. “Lots of people can find common, interdisciplinary interests.”

Certain openings are particularly advantageous for students who wish to explore several research pathways and make connections early in their careers. “During my graduate training, I was fortunate to have the opportunity to go to different kinds of conferences and be exposed to interdisciplinary research,” Kawakatsu said. “You need to know the cultures of different disciplines to do cool work.” Budd extolled the benefits of online and in-person brainstorming sessions—such as the European Study Groups with Industry—that encourage Ph.D. students from diverse disciplines to drive the development of new ideas. SIAM also offers several programs that allow students to engage with mathematical modeling in a team-driven, application-based setting, including the Graduate Student Mathematical Modeling Camp and Mathematical Problems in Industry Workshop.

While academics who are beginning to explore interdisciplinary research may initially be unsure of the funding process, these types of projects are often appealing to funders. In addition to federal grants, monetary support can stem from private foundations, discipline-agnostic fellowships at universities, and directly from industry. “If you’re doing interdisciplinary work, there’s a much broader funding landscape out there,” Budd said. “Be aware of it and use it to your advantage.” Collaborators must also recognize that principal investigators in different fields will have unique grant needs and strategies; for instance, biology laboratories typically have higher overhead costs than most applied mathematics groups.

Once a project is underway, researchers must determine the most suitable platform for publication — should they target a journal that focuses on mathematics, the application domain, or interdisciplinary science? A complicating factor is that many interdisciplinary journals are high impact and thus quite competitive; there are not very many smaller, more specialized interdisciplinary journals that can serve as a middle ground. A number of other questions are also at play, such as what venues will best advance junior researchers’ careers, which journals are most relevant to collaborators, and how one can effectively reach the intended readership. “Trying to understand your audience and communicate with them is really important,” Budd said.

Multiple SIAM journals offer cross-cutting platforms between applied mathematics and other disciplines, and another option has just been made available: the newly minted SIAM Journal on Life Sciences, of which Rubin is editor-in-chief. “Hopefully there will now be a perfect place to publish anything on math and the life sciences,” he said. “The idea is to have a journal that puts mathematics in the center of each paper—not hides it away in the supplements—but nevertheless has accessibility to everyone in the life sciences.”

Interdisciplinary researchers must often make special considerations when navigating the hiring and tenure processes, as their publication records may deviate from the industry standard and journal impact factors can vary by field. When working towards academic tenure, faculty must pay close attention to departmental expectations and maintain a broader understanding of the discipline. Ultimately, however, the panelists concurred that it is most important to pursue intriguing problems and publish in relevant places, even though this approach may involve a philosophical choice between an optimal career strategy versus more personal interests and goals. “We should trust our intuition on what matters and do good stuff, and it will work out,” Hammerling said.

Difficulties and failures are an inevitable part of the interdisciplinary process, and things do not always go as planned. To get a sense of a specific research direction’s promise while keeping the stakes low, faculty can potentially assign the prospective problem to a class or undergraduate assistant. This initial investigative step can provide intel as to whether a project is too simple and hence easily solvable with existing tools, or too difficult to be worth the time and effort. “There’s a decision of whether you’re willing to put in all that work, and if it’s in that sweet spot of what you’re working on,” Hammerling said.

Though potential collaborators may share the same general interests, it is essential to clearly communicate goals and intentions when developing a project to ensure that everyone is willing and able to approach the problem in the same way. As a study progresses, one of the biggest issues can be maintaining clear communication between disparate teams and researchers who may use clashing terminology and have different levels of familiarity with certain techniques. Frequent updates on research progress, questions, and roadblocks throughout a project’s entire lifecycle can help keep everything on track. “You have to face the fact that interdisciplinary research is hard and accept when it doesn’t work,” Budd said. “Don’t be discouraged, and learn from your mistakes.”

Yet despite the challenges, interdisciplinarity can be incredibly rewarding. This unique avenue of research allows scientists to explore pressing problems that interface with multiple fields in exciting ways — as long as they are prepared to address any dilemmas that might arise. “Some things will not work out or go as fast as you hope they do,” Abrams said. “If everything works out exactly as you expect, you probably aren’t trying things that are difficult.”