6

Roles for Stakeholders

The workshop’s final session was a panel discussion on the perspectives of mathematical organizations. Moderated by Heather Macbeth, Fordham University, the panel included Gunnar Carlsson, American Mathematical Society (AMS); Brendan Hassett, Institute for Computational and Experimental Research in Mathematics (ICERM); Dimitri Shlyakhtenko, Institute for Pure and Applied Mathematics; and Suzanne Weekes, Society for Industrial and Applied Mathematics (SIAM). Each panelist’s organization is unique, but they share the goal of supporting mathematical research and the exchange of mathematical knowledge.

Noting that each organization has an existing framework for interdisciplinary work, Macbeth asked about specific examples of interdisciplinary collaboration. Weekes remarked that SIAM is affiliated with various organizations like the Computing Research Association, the American Automatic Control Council, the Association for Computing Machinery, the American Statistical Association, the Mathematical Association of America, and AMS. She noted that SIAM often runs sessions at conferences of other societies or organizations, and vice versa, and the applied nature of SIAM lends to natural collaboration. Carlsson added that AMS often supports workshops of an interdisciplinary nature held by other institutes and encourages mathematicians to attend such workshops. In response to a question on the challenges to building interdisciplinary connections, Hassett observed that people with different backgrounds engage differently in interdisciplinary programs. Oftentimes, mathematicians can spend weeks away from their home institution immersing themselves in

another community, but many people working in application spaces like biology or computer science, for example, can only be involved for a short time. With this in mind, ICERM develops interdisciplinary programs that include both short, concentrated periods for targeted application areas and longer periods for mathematicians. He summarized that it is important to design programs intentionally by considering these cultural differences and ensuring that everyone can engage meaningfully, even if engagement differs between people. Shlyakhtenko added that in interdisciplinary work, different groups of people often have not only different opinions on a problem but also different conceptions of the problem itself. Translation is a key issue. He advocated for highlighting the benefits of interdisciplinary work to encourage collaboration: There is great convergence between disciplines, but a lack of interdisciplinary work leads to a duplication of efforts.

Macbeth asked the panelists to reflect on the workshop by commenting on what artificial intelligence (AI) might be able to do for mathematics. Shlyakhtenko noted that language models have been used for translation for several years and wondered whether they could be used for the similar “translation” problem that researchers encounter in interdisciplinary work—working with unfamiliar terminology. He also mentioned that mathematics has invested centuries of notation and education into ensuring readability to scientists and others not fully trained in mathematics, and he advocated for prioritizing this accessibility as mathematics progresses and perhaps becomes formalized. Carlsson remarked that mathematical reasoning includes several aspects beyond theorems and proofs, such as experimentation or the notion of idealized models, which may not be quantitatively exact but can reveal insights qualitatively. He encouraged mathematicians to take the initiative to be more involved with AI and indicated that their involvement could improve understanding and explainability of AI. Building on the idea of experimentation in mathematics, Weekes expressed excitement toward AI’s ability to find patterns in massive data, reveal new insights, and inform mathematics. Hassett commented that theorem proving and machine learning projects require more complex collaboration than traditional mathematics. Collaboration is growing, and he suggested that mathematical institutes could support this collaboration by connecting mathematicians and researchers from different backgrounds. Weekes added that the community will need to evolve to appreciate work in these new paradigms. Shlyakhtenko observed that large-scale collaboration is already common and growing in other areas, such as gravitational wave physics. He urged the mathematics community to move away from traditional reward metrics toward more holistic recognition and suggested that professional societies could advocate for this shift.

Macbeth remarked that professional societies provide resources for mathematicians and mathematics departments and inquired about what new shared resources and frameworks might be necessary. Referencing MathSciNet, a specialized database for mathematics publications, Carlsson wondered whether an “AISciNet” might be possible. He also suggested that mathematics may need faster, updated publication models. Current mathematical publication processes are slow compared to many other sciences, and they create a barrier to mathematicians engaging with AI. Hassett described how ICERM is hosting a conference¹ in July that invites researchers to submit manuscripts, allowing for quick dissemination to a wide audience. He indicated that some areas of mathematics, especially those driven by data and algorithms, could move to new publication models by learning from computer science. Macbeth suggested that computerized proofs may also aid in accelerating the review process.

Macbeth transmitted an audience question, asking for the panelists’ thoughts on how the younger generation can learn to interact with AI technologies and how these technologies can be integrated into mathematics education. Shlyakhtenko observed that, in general, younger people are naturally engaging more with AI. For mathematics specifically, he cautioned that any new technologies that become common in research (e.g., proof assistants) should also be integrated into educational curricula early—at the undergraduate or even high school level—to ensure that mathematics stays relatively accessible. Hassett remarked that some areas in pure mathematics can rely on the same traditional curricula that have not changed for decades. Many people can therefore teach those courses, but curricula involving new technology will require greater pedological engagement and training for teachers. He urged mathematicians to reflect on how flexibility can be added to curricula so that students can be exposed to technologies such as proof assistants. Macbeth concluded that overall, mathematicians need new approaches in addition to—not in replacement of—traditional approaches to accommodate these developing technologies.

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¹ Information about the conference can be found at https://icerm.brown.edu/events/sc-23-lucant, accessed August 2, 2023.