prompt

Free

Interactive AI research partner for open-ended mathematical discovery

FreeFree tier

Type

Open Source

Visit Website GitHub (40 stars)

About prompt

The AI Co-Mathematician is an interactive, stateful research partner designed for mathematicians working on open-ended problems. It provides holistic support across the full lifecycle of mathematical discovery, including ideation refinement, literature knowledge retrieval, computational exploration, conjecture formation, theorem proving, and theory building. The system tracks user intent over multiple turns, maintains a dead ends log to avoid revisiting failed hypotheses, and aims to mirror human mathematical workflows that are exploratory and iterative. Based on Google DeepMind's research (arXiv 2605.06651, May 2026), it scored 48% on FrontierMath Tier 4, a new high among AI systems.

Key Features

Ideation Refinement – sharpens half-formed intuitions into well-defined problems and tracks intent across turns

Literature Knowledge Retrieval – surfaces relevant theorems, techniques, and prior work, flagging solved or equivalent problems

Computational Exploration – proposes symbolic computations, numerical experiments, and visualizations to build intuition

Conjecture & Theory Building – formulates testable conjectures, builds intermediate lemmas, and tracks failed hypotheses in a dead ends log

Theorem Proving & Verification – sketches proof strategies using formal reasoning patterns and flags gaps or circular arguments

Pros & Cons

Pros

Comprehensive support across the entire mathematical research workflow
Stateful memory tracks evolving user intent and avoids redundant failures
Based on cutting-edge AI research with a record score on FrontierMath
Available as a free, open-source prompt for integration with LLMs

Cons

Requires a capable LLM to execute; effectiveness depends on the underlying model
Not a standalone tool – must be used within a chat interface or LLM platform
No graphical interface or integrated computing environment out of the box

Best For

Assisting mathematicians in open-ended research problemsExploring conjectures and building new mathematical theoriesPerforming computational experiments to gain insight into mathematical structuresSynthesizing literature from adjacent mathematical fieldsVerifying proof strategies and identifying logical gaps