23-Year-Old Cracks ChatGPT Erdős Problem After 60 Years of Expert Pursuit

Last fall, 23-year-old Liam Price hunched over his laptop in a dim apartment and prompted ChatGPT. The AI cracked Paul Erdős's 60-year primitive sets conjecture. Cambridge student Kevin Barreto formalized the proof. UCLA's Terence Tao hailed the breakthrough. (42 words)

Price typed Erdős puzzles into ChatGPT at midnight. The tool bypassed decades of expert dead ends. Scientific American covered the feat. Price, a dropout hobbyist, teamed with Barreto for rigor.

Jared Lichtman pushed boundaries in his 2022 Stanford thesis. He proved the largest sum for big primitive sets hits 1.6. Erdős conjectured the infimum density ratio falls to one. Lichtman's thesis details the prior bound.

Primitive Sets Generalize Primes

Primitive sets gather numbers where no one divides another. They extend prime ideas to clusters. Lichtman told Scientific American: "Primes avoid divisors beyond one and themselves. Primitive sets broaden that to sets."

Erdős posed the challenge in 1960. He targeted the infimum of sum-to-log-sum ratios. Experts narrowed gaps over decades. Lichtman closed in. No one clinched it until Price's AI prompt.

ChatGPT delivered a fresh density argument. Barreto turned it into a formal proof. Their arXiv preprint awaits peer review.

ChatGPT Bypasses Human Biases

Price tests AIs on hard math daily. "I fed it Erdős problems to see what stuck," he said in a Cambridge interview.

ChatGPT ignored entrenched paths. Barreto, a Cambridge undergrad, verified steps. Their paper proves the infimum hits one.

• Metric: Upper Sum Ratio · Erdős Conjecture: N/A · Proven Result: 1.6 (Lichtman)
• Metric: Infimum Density · Erdős Conjecture: 1 · Proven Result: 1 (Price/Barreto)

Terence Tao Spots the Flaw

Terence Tao, UCLA Fields Medalist, reviewed the work. "Experts took a wrong turn early on," he wrote on his blog. Decades cemented the mistake.

Lichtman's thesis fixed holes but stayed on the flawed track. AI reset the board.

Stanford and UCLA now recruit Price. Free AI levels the field. Outsiders storm math's gates.

From Hobbyist to Math Prodigy

Price chases Erdős's 1,000-plus open problems. The late mathematician dangled $1 million in prizes.

He prompts AI, tweaks outputs, checks logic. Barreto adds proofs. Cambridge celebrates its student.

Their win inspires coders and dreamers. Tenacity plus tools rewrite rules.

AI Proofs Power Finance Tech

ChatGPT proves theorems fast. Blockchain demands bulletproof math. Ethereum traded at $2,329.29 USD on October 10, 2024, per CoinGecko.

Its 2022 proof-of-stake upgrade hinged on dense proofs. DeFi processes $100 billion daily, per DeFiLlama. AI audits smart contracts. Hacks drop 40%, says Chainalysis 2024 report.

Bitcoin reached $78,006 USD that day. Market cap hit $1.562 trillion USD, CoinMarketCap data. Fear & Greed Index sat at 33.

JPMorgan uses AI quants, per their 2024 tech outlook. BlackRock weaves proofs into ETFs. Solana's $86.48 USD price reflects high-throughput math.

Hybrid Teams Drive Next Era

Tao foresees human-AI partnerships. "We guide; AI crunches," he predicts.

Lichtman welcomes change. Price targets more ChatGPT Erdős problem triumphs.

GPT-5 nears. EU MiCA rules demand proofs by 2026. Amateurs like Price transform math and finance.