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conjecture-exploration

Explore mathematical conjectures by gathering evidence and identifying counterexamples.

3|Updated Feb 9, 2026
Search Tags:#evidence#proof#symbolic-computation#conjecture#counterexample#sequence-lookup
One-click install
npx skills add https://github.com/0bserver07/bourbaki --skill conjecture-exploration
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: conjecture-exploration
Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/conjecture-exploration
Command: npx skills add https://github.com/0bserver07/bourbaki --skill conjecture-exploration

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Systematically explore mathematical conjectures by gathering evidence, identifying counterexamples, and guiding toward a proof strategy.

Core Features & Use Cases

  • Structured exploration: parse a conjecture, formalize it, and map the domain and quantifiers; generate evidence templates and potential counterexamples.
  • Evidence-driven decision: run small-case testing and pattern discovery using symbolic_compute and sequence_lookup tools to build toward a conclusion.

Quick Start

Provide an initial exploration plan for a specified conjecture and outline the next steps.

Frequently Asked Questions about conjecture-exploration

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I explore a mathematical conjecture to find proof strategies?▼

Mathematical conjecture exploration works by parsing the statement, formalizing the domain and quantifiers, running small-case testing, and discovering patterns to build evidence that either supports or refutes the claim.

How do I find counterexamples to a conjecture about integers or real numbers?▼

Finding counterexamples involves generating potential edge cases, testing small-case scenarios, and using sequence lookups to systematically search for instances that violate the proposed mathematical rule.

Can I use symbolic computation to test conjectures across different mathematical domains?▼

Yes, symbolic computation can test conjectures across domains such as integers, real numbers, sets, and sequences by running calculations to verify patterns and discover potential counterexamples.

What is the best way to start investigating a new mathematical conjecture?▼

The best way to start investigating a conjecture is to parse the statement, formalize it by mapping the domain and quantifiers, generate an initial exploration plan, and outline evidence templates for systematic testing.

Does conjecture exploration require access to web search and sequence lookup tools?▼

Yes, conjecture exploration requires access to symbolic computation, sequence lookups, and web search tools to gather evidence, discover patterns, and generate structured reports for subsequent proof steps.

When should I not rely on automated evidence gathering for mathematical proofs?▼

Automated evidence gathering does not replace formal proofs; it only provides guidance toward proof strategies. You should not rely on it when a rigorous, complete mathematical proof is required for publication or formal verification.

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