Intentmaking and Sensemaking: Human Interaction with AI-Guided Mathematical Discovery

TL;DR

This paper explores how expert mathematicians interact with AI tools like AlphaEvolve, highlighting the iterative processes of intentmaking and sensemaking in scientific discovery.

Contribution

It introduces the concepts of intentmaking and sensemaking as key workflows in human-AI collaborative mathematical research, based on a user study.

Findings

Identified intentmaking as a distinct workflow in AI-assisted discovery.

Described a cycle of defining goals and interpreting results during investigation.

Proposed design principles for AI tools that support scientific sensemaking.

Abstract

Artificial intelligence offers powerful new tools for scientific discovery, but the interaction paradigms required to effectively harness these systems remain underexplored. In this paper, we present findings from a formative user study with 11 expert mathematicians who used AlphaEvolve, an evolutionary coding agent, to tackle advanced problems in their fields of expertise. We identify and characterize a distinct workflow we term intentmaking, the iterative process of discovering, defining, and refining one's experimental goals through active system interaction. We frame this as a natural extension to sensemaking, the cognitive process of building an understanding of complex or novel data. We suggest that users enter a cycle of intentmaking (defining and updating their experiment) and sensemaking (interpreting the results) which repeats many times during the course of an investigation. Our documentation of these themes suggests an approach to designing AI tools for scientific discovery that goes beyond the existing question/answer model of many current systems, treating them as collaborative instruments rather than opaque black-box assistants.