The field of mathematical oncology has undergone a transformative journey over the past few decades, evolving into an interdisciplinary domain of research. What began as a niche area in the late 1990s now encompasses a global community of researchers working together to understand the complexities of cancer. The 2024 Fields Thematic Program on Mathematical Oncology (FieMO) at the Fields Institute in Toronto (July-December 2024) was a testament to this growth, bringing together mathematicians, medical scientists, and biologists for six months of exploration, collaboration, and discovery.

The key objectives of FieMO were to reflect on the achievements of mathematical oncology over the past quarter-century, to explore the state of the art of the field, and to develop methods and data for future research. The recent advancements have been remarkable. For example in the modelling of cancer metastasis, cancer-induced angiogenesis, cancer immune responses and all kind of treatments such as chemotherapy, radiation, CAR T-cell therapies, adaptive therapies, oncolytic virotherapies, and many more. Mathematical models have significantly improved the precision and effectiveness of these treatments.

Mathematical oncology has also left a significant mark on mathematics itself. FieMO highlighted this reciprocal relationship, showcasing examples where biological challenges stimulated mathematical innovations. For example the modeling of angiogenesis inspired new directions in biased reinforced random walks and the study of coupled PDEs; cancer treatment optimization fostered breakthroughs in optimal control theory; and observing cancer cell migration led to advancements in kinetic transport equations and their scaling limits.

During the Thematic Program, Fields Institute hosted six workshops, two Fields postdocs (Sumaira Rehman and Seemadri Subhadarshini), three Distinguished Visitors (Natalia Komarova, Helen Byrne, Thomas Hillen), a seminar series, a graduate course and many long-term and short-term visitors. The workshops tackled pressing topics, including the hallmarks of cancer, cancer ecology and evolution, cancer treatment resistance, and cancer immune dynamics. The graduate course on Mathematical Oncology was led by Thomas Hillen with guest lectures by Natalia Komarova, Anna Marciniak-Czochra, Mark Chaplain, Thomas Yankeelov, and Luigi Preziosi. The recording of these lectures are still available on the Fields website http://www.fields.utoronto.ca/activities/24-25/oncology. This website also contains recordings of the main lectures of the workshops and the seminars.

The intimate setting of the Fields Institute fostered deep interactions in small groups and one-on-one, creating opportunities for mentorship and collaboration that are rare in larger conferences. In addition, Thomas used the opportunity to interview visitors at the Fields Institute and start a youtube channel on Math Onco Interviews. See the blog post and the youtube channel: Math Oncology Interviews YouTube Playlist.

We (Sumaira and Thomas) have been fortunate to attend all six workshops and we were curious to classify the lectures into the following categories. Please understand that we chose these categories ourselves, and they do not reflect any official categorization:

1. One protein, one cell type: Often in biological or medical research, scientists find their favorite protein, or cell type, and analyse the heck out of it. The purpose is to understand every aspect of this protein (or cell type) and investigate its usefulness for treatment. Examples are NOTCH, or Wint, or Vegf, or aspirin, or colon stem cells, or glioma microtubes, etc.
2. One cancer: Then there are many studies that focus on a specific cancer such as breast, brain, colon, leukemia, etc.
3. Processes: Under processes we summarize conceptual studies that focus on a process, for example homeostasis, metastasis, angiogenesis, cancer stem cells, drug resistance, in some cases without specifying the cancer type.
4. Methods: Here we include work that is focussed on methodological questions such as theoretical work on differential equations, individual based modelling, statistical methodology, etc.
5. Methods AI: We took out all AI approaches from the Methods category to see if and how AI was used.

The graphic below shows the percentages of each category among the 70 talks that we heard.

It is quite interesting to see that the Processes and Methods sections cover ⅔ of the talks, where One Protein, One Cell Type has only 17%. Also of note is that the AI methods, although discussed by everybody, is the clear minority among the talks. We expect that this is about to change in the future.

The Fields Thematic Program in Mathematical Oncology placed a strong emphasis on supporting women in the field, fostering an inclusive environment where female researchers were encouraged to participate, collaborate, and excel. We actively involved female participants in the organization of events, in group discussions, talks, and seminars to provide platforms for their ideas to be heard and valued. Sumaira mentioned that this support created a sense of empowerment and belonging that motivated her to contribute and interact confidently. All participants benefited immensely from this experience, fostering creativity in a collaborative environment.

Thematic programs like FieMO are more than academic events; they are transformative journeys that shape the field and initiate careers of junior researchers. We witnessed first hand how mathematics can drive progress in cancer research, and we felt the excitement of contributing to a larger mission.

We extend our heartfelt thanks to the Fields Institute, the organizing committee, and the many speakers and participants who made this program a success. As we look to the future, we hope the legacy of FieMO will inspire the next generation of mathematical oncologists to push the boundaries of what is possible.

Links

• The Fields Math Onco page can be found here. http://www.fields.utoronto.ca/activities/24-25/oncology
• For a visual recap of the program’s highlights, watch the pictorial video of the Thematic Program.
• For more insights, including interviews with program participants, please visit the Math Oncology Interviews YouTube Playlist.

All photos were taken by Thomas Hillen and Sumaira Rehman. Reprinted with permission of all those who are recognizable on these pictures, thank you!