Undergraduate mathematics education (UME) is developing rapidly; yet, its future research agendas depend on how the UME community broadens its methods, strengthens dialogue across theoretical perspectives, and addresses neglected areas of inquiry. Building on the work of Dreyfus et al. (2025), who reflect on the first decade of IJRUME, we focus on current debates and forward-looking priorities shaped by recent publications and contributions to international conferences. As three early-to-mid-career researchers with varied trajectories and engagement within the broader UME community, we join voices to reflect collectively on the field. We organise our discussion around three dimensions: methods, theories, and topics. Methodologically, while small-scale qualitative studies have enriched the field, future progress requires extending this work through quantitative and mixed-methods approaches, alongside critical engagement with computational and AI-based methods. Theoretically, UME’s rich diversity of frameworks is a strength; however, it calls for deeper, open dialogue across different perspectives. Regarding topics, equity, digital technologies, and interdisciplinary connections are growing areas of inquiry. At the same time, gaps remain in the teaching and learning of advanced mathematical content and the experiences of postgraduate students. Looking ahead, we emphasise the need for collective reflection on community building, dialogue, and critique. Strengthening UME research relies on collaboration across contexts, active support for newcomers, and a culture of thoughtful critique to foster an inclusive, reflective, and responsive community.
