Making Written Theorems Explorable by Grounding Them in Formal Representations

LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding explanations in a formalized representation enables interactive affordances beyond what static text supports. We instantiate this idea for mathematical proof comprehension with explorable theorems, a system that uses LLMs to translate a theorem and its written proof into Lean, a programming language for machine-checked proofs, and links the written proof with the Lean code. Readers can work through the proof at a step-level granularity, test custom examples or counterexamples, and trace the logical dependencies bridging each step. Each worked-out step is produced by executing the Lean proof on that example and extracting its intermediate state. A user study ($n = 16$) shows potential advantages of this approach: in a proof-reading task, participants who had access to the provided explorability features gave better, more correct, and more detailed answers to comprehension questions, demonstrating a stronger overall understanding of the underlying mathematics.

LitPivot: Developing Well-Situated Research Ideas Through Dynamic Contextualization and Critique within the Literature Landscape

Developing a novel research idea is hard. It must be distinct enough from prior work to claim a contribution while also building on it. This requires iteratively reviewing literature and refining an idea based on what a researcher reads; yet when an idea changes, the literature that matters often changes with it. Most tools offer limited support for this interplay: literature tools help researchers understand a fixed body of work, while ideation tools evaluate ideas against a static, pre-curated set of papers. We introduce literature-initiated pivots, a mechanism where engagement with literature prompts revision to a developing idea, and where that revision changes which literature is relevant. We operationalize this in LitPivot, where researchers concurrently draft and vet an idea. LitPivot dynamically retrieves clusters of papers relevant to a selected part of the idea and proposes literature-informed critiques for how to revise it. A lab study ($n{=}17$) shows researchers produced higher-rated ideas with stronger self-reported understanding of the literature space; an open-ended study ($n{=}5$) reveals how researchers use LitPivot to iteratively evolve their own ideas.