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

We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative reality of mathematical workflows, including ideation, literature search, computational exploration, theorem proving and theory building. By providing an asynchronous, stateful workspace that manages uncertainty, refines user intent, tracks failed hypotheses, and outputs native mathematical artifacts, the system mirrors human collaborative workflows. In early tests, the AI co-mathematician helped researchers solve open problems, identify new research directions, and uncover overlooked literature references. Besides demonstrating a highly interactive paradigm for AI-assisted mathematical discovery, the AI co-mathematician also achieves state of the art results on hard problem-solving benchmarks, including scoring 48% on FrontierMath Tier 4, a new high score among all AI systems evaluated.

Agentic artificial intelligence (AI) systems are beginning to assist, accelerate, and partially automate scientific discovery, performing tasks that span literature synthesis, code generation, data analysis, hypothesis proposal, and model criticism. We argue that this transition is qualitative rather than incremental, and that suitably designed multi-agent systems may evolve from passive computational tools into ``AI scientists'' that can expand the hypothesis-generating and verification capacity of science. Such systems must be developed and deployed within a scientific ecosystem fit for purpose: institutions must be redesigned for verification, accountability, interpretability, and dual-use safety. We sketch how multi-agent architectures, illustrated by the prototype framework \textit{Denario}, accelerate the discovery cycle and traverse model spaces beyond human reach; examine what this implies for authorship, peer review, and the enduring role of human scientists; and close with recommendations for governing AI as an epistemic actor rather than a mere instrument.

Scientific discovery is an extended process of ideation--surveying prior work, forming hypotheses, and refining reasoning--yet existing approaches treat this phase as a brief preamble despite its central role in research. We introduce SCISENSE, a sensemaking-grounded framework that operationalizes ideation as a structured sequence of eight cognitive stages (Pirolli & Card, 2005). We construct SCISENSE-Traj, a 100K-scale dataset of citation-conditioned research trajectories in two modes: Target, where an LLM reconstructs the ideation path leading to a known paper from its cited works, and Infer, where the LLM proposes novel directions from the same citations. We distill these into SCISENSE-LM, a family of sensemaking LLMs spanning 3B to 70B parameters. Contrary to the assumption that looser supervision promotes greater exploration, Target-trained models achieve a 2.0% improvement in trajectory quality over Infer-trained models while also producing more novel and diverse outputs. This advantage propagates downstream: coding agents conditioned on Target trajectories produce research artifacts with higher executability and quality than those conditioned on Infer trajectories. This suggests that targeted ideation reduces cognitive burden on downstream agents, freeing them to explore more creatively. SCISENSE offers both a practical tool for augmenting LLM-driven research workflows and a principled testbed for studying how planning shapes scientific discovery.