Toward Abstraction, Causality, and Common Sense
Thinking Machines investigates what it would take for AI systems to move beyond pattern recognition toward genuine reasoning, exploring the mathematical, structural, and conceptual foundations that enable abstraction, generalization, and understanding. It spans research that uses generative models to probe social and psychological processes as well as work that examines the deep interplay between AI and mathematics, from hypothesis generation to the testing and evaluation of scientific claims. Across these directions, the series asks how uncertainty, causality, and narrative shape scientific inquiry, and how we can rigorously assess the reliability and reproducibility of knowledge produced with AI.
Leads: Andrew Blumberg, Herbert and Florence Irving Professor of Cancer Data Research, Mathematics, and Computer Science; Kriste Krstovski, Data Science Institute; Ivan Corwin, Mathematics; and Daniel Hsu, Computer Science
Awarded: Fall 2025Events & Activities: Spring 2026
This program examines the deep, two-way relationship between artificial intelligence and mathematics, highlighting how each field informs and strengthens the other. The first phase focuses on the foundational uses of AI in mathematics, beginning with a research-oriented symposium that includes a hands-on training workshop on large language models, followed by a dedicated symposium on pedagogy. The second phase turns to the mathematical foundations of AI, featuring symposia that surface core theoretical challenges and emerging research questions arising from modern AI applications. Together, these sessions create a structured pathway for scholars to engage with both sides of this rapidly evolving intersection, which spans disciplines ranging from engineering and business to the social sciences and the biomedical and physical sciences.
Program Overview: The workshop series will include symposium sessions across both themes: (Fun)damental Uses of AI in Math and (Fun)damental Uses of Math in AI. Sessions for faculty will provide an overview of research opportunities and help align researchers around potential collaboration, culminating in an event focused on forming potential research teams. Other seminars with invited guest speakers will be planned throughout the series.
Lead: Yamil Velez, Political Science
Social scientists are increasingly leveraging Generative AI models to learn about political and psychological processes. In political science, economics, and psychology, large language models are being used to classify content, generate experimental stimuli such as persuasive messages, simulate responses to surveys and incentivized experiments, and devise adaptive surveys that respond to participant input. While excitement about these tools is increasing, there is less guidance on how to rigorously incorporate them into research. This program addresses this gap by bringing together scholars developing both novel applications and methodological approaches needed to advance the field.
Program Overview: In an upcoming workshop, Columbia faculty and guest speakers from other leading institutions will explore research that leverages Generative AI to study politics and psychology, share methodological best practices, and collaboratively develop approaches that strengthen the field.
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