Even experts are surprised by AI's latest 'vibe-mathing' advance

Abstraction: Amateur uses GPT-5.4 Pro to solve 60-year-old Erdős primitive sets problem

Key points:

• Liam Price (23, no advanced math training) solved a 60-year-old Erdős problem via a single prompt to GPT-5.4 Pro; the problem concerns the maximum score of primitive sets as numbers approach infinity
• The LLM used a formula from related mathematical areas that humans had never thought to apply here, bypassing the "wrong turn at move one" that stumped prior experts including Lichtman
• Raw ChatGPT output was poor quality; Lichtman and Terence Tao (UCLA) had to distill the key insight and shorten the proof
• Jared Duker Lichtman (Stanford) sees the solution as validating his intuition that similar problems share a "unifying feel," confirmed by the new method
• Tao: "We have discovered a new way to think about large numbers and their anatomy" — method may generalize to other problems
• Case study in "vibe mathing": AI finds a novel approach where collective human expertise had a systematic blind spot

Connections: Chatgpt · Openai · Terence Tao · Large Language Models · AI For Mathematics

Source: https://www.scientificamerican.com/article/amateur-armed-with-chatgpt-vibe-maths-a-60-year-old-problem/