Workflow for attempting to solve Erdős problems. Use when the user wants to work on a specific Erdős problem, analyze open problems, or find tractable problems to attempt.
name erdos-solver description Workflow for attempting to solve Erdős problems. Use when the user wants to work on a specific Erdős problem, analyze open problems, or find tractable problems to attempt. Erdős Problem Solver Workflow A structured approach to working on Erdős problems, informed by lessons from AI research efforts (Gemini/Aletheia, GPT-5). Quick Start Commands
./erdos get {number} --json
./erdos open --tag primes --formalized
./erdos find "keyword" Phase 1: Problem Selection Finding Good Candidates from tools.query_db import ErdosDB with ErdosDB() as db:
tractable = db.get_tractable_problems()
formalized = db.get_formalized_problems()
primes = db.search_by_tag( "primes" , status= "open" )
active = db.get_problems_being_worked_on() Selection Criteria Factor Why It Matters Has Lean formalization Clearer statement, verifiable Tagged "formalisable" Community thinks it's well-defined Recent comments Active discussion, partial progress No prize Less likely to be extremely hard Status = "open" Actually unsolved Phase 2: Deep Understanding 2.1 Read Everything p = db.get_problem(number) print (p.statement)
print (p.references)
print (p.comments)
print (p.lean_url)
2.2 Understand the Intent Common issues (from Gemini paper): Notational conventions differ (additive vs Dirichlet convolution) "Strong" vs "weak" completeness Implicit assumptions in Erdős's original formulation Errors in transcription from original papers Check : Does erdosproblems.com note any issues with the statement? 2.3 Literature Review
Warning : ~40% of "novel" AI solutions were already in literature (Gemini study). Phase 3: Technique Selection Based on problem domain, consult: NUMBER_THEORY.md COMBINATORICS.md GRAPH_THEORY.md GEOMETRY.md Quick Technique Selector Problem Pattern Try First "Is there infinitely many..." Construction, Pell equations "Does there exist..." Probabilistic method "For all n, is it true..." Induction, counterexample search "What is the maximum..." Extremal arguments "Can we color..." Ramsey theory "How many distinct..." Incidence geometry Phase 4: Solution Attempt 4.1 Start Simple Check small cases (n = 1, 2, 3, ...) Look for counterexamples if conjecture seems false Try direct approach before clever tricks 4.2 Work Incrementally Informal sketch → Detailed proof → Formal verification (if Lean available) 4.3 Document Everything Keep track of: Approaches tried Why they failed Partial progress Related problems that might help Phase 5: Post-Solution Pipeline After generating a solution, follow POST_SOLUTION.md : SOLUTION → Self-Audit → Novelty Check → Formalize → Peer Review → Submit 5.1 Self-Audit Use VERIFICATION.md checklist. Rate each component A-F. 5.2 Novelty Check (LOCAL DATA FIRST!) Priority order:
./erdos get {number} --json
grep -i "{number}" .claude/skills/math-techniques/LITERATURE.md
ls .claude/examples/solution_attempt_*.md
5.3 Formalization (if Lean available)
./erdos get {number} --json | jq .lean_url 5.4 Peer Review → Submission See POST_SOLUTION.md for full pipeline. Phase 6: Documentation Cite Everything (Including Ourselves)
This solution
:
.claude/examples/solution_attempt_N.md
Document Outcomes
Outcome
Action
Solved
Submit PR to erdosproblems.com
Partial
Document progress, remaining gaps
Literature
Report reference to update database
Example Workflow
p = db.get_problem( "1051" )
assert p.status == "open"
if p.lean_url: print ( f"Lean at: {p.lean_url} " )
Pitfalls to Avoid Assuming "open" means unsolved