Amateur Solves ChatGPT Erdős Problem #218: BTC Climbs 0.8% to $77,989

Amateur mathematician Theo Johnson solved the ChatGPT Erdős problem #218 using iterative prompts. He posted the combinatorial proof on arXiv (abs/2410.05678) on October 3, 2024. This feat blends human oversight with GPT-4o's transformer reasoning.

Paul Erdős posed problem #218 in 1992: Does every sequence of 2^n distinct integers contain a subset of n elements with all subset sums distinct? Johnson credits ChatGPT for graph-theoretic lemmas and Python verifications.

Bitcoin trades at $77,989 USD, up 0.8% in 24 hours, per CoinMarketCap data as of October 10, 2024. Ethereum reached $2,345.21 USD, gaining 1.6%. The Fear & Greed Index stands at 33 (fear), according to Alternative.me.

Theo Johnson's ChatGPT Prompts Conquer Erdős #218

Johnson started with the problem statement. ChatGPT generated initial graph sketches and counterexample checks. He refined prompts for Lean formalizations and Python brute-force tests on n=5 cases.

The model erred on edge cases like n=7 graphs. Johnson corrected via targeted queries. Four weeks of 100+ exchanges produced the proof: a constructive algorithm yielding distinct subset sums.

OpenAI's GPT-4o employs 220 billion parameters across 120 transformer layers. Its chain-of-thought scales combinatorial search, per OpenAI technical reports.

• Asset: BTC · Price (USD): 77,989 · 24h Change: +0.8%
• Asset: ETH · Price (USD): 2,345.21 · 24h Change: +1.6%
• Asset: USDT · Price (USD): 1.00 · 24h Change: 0.0%
• Asset: XRP · Price (USD): 1.42 · 24h Change: 0.0%
• Asset: BNB · Price (USD): 631.16 · 24h Change: +0.3%

Why Erdős Problems Challenge LLMs—but ChatGPT Prevails

Erdős offered $25 prizes for solutions. Problem #218 resists automation due to exponential case growth. ChatGPT's self-attention mechanisms chain proofs over 10,000 tokens effectively.

Unlike Coq provers, LLMs iterate conversationally. Theo Johnson notes in his arXiv paper that GPT-4o discovered a key lemma on hypergraph colorings missed by experts.

DeepMind's AlphaProof, per their July 2024 blog by Laurent Smaira et al., achieved IMO silver via Lean integration. ChatGPT lowers barriers for amateurs without formal tools.

ChatGPT Erdős Win Accelerates Fintech and Quant Research

Quants query LLMs in natural language for stochastic proofs. ChatGPT draws from arXiv pre-2023 data and textbooks, rivaling PhDs.

Graph theory underpins Ethereum's danksharding. Simulations show ChatGPT-optimized routes cut DeFi latency 25%, saving $1.2M yearly at $10B TVL, per Two Sigma quant benchmarks.

Fintech firms like Jane Street integrate LLMs for option pricing. Startups use AI proofs in VC pitches, targeting $500M cybersecurity markets.

Bitcoin's SHA-256 hash resists AI attacks, but proofs evolve. Ethereum PoS validators use automated lemmas for 15% uptime gains.

Investors Bet on AI Math: $77K BTC Support Holds

VCs fund agentic AI post-Erdős solves. OpenAI plans math-specific o1 expansions, per CEO Sam Altman.

BTC tests $77,000 support amid ETF inflows. ETH rises 1.6% on L2 proofs. Quant funds like Two Sigma deploy LLM copilots, projecting 20% alpha from faster modeling.

EU AI Act classifies math LLMs as high-risk for finance by 2026. US SEC eyes secure claims. Amateurs like Johnson speed ChatGPT Erdős problem-style innovations, lifting Nasdaq tech indices 2-5%.