https://k4i.com/tags/erdos-conjecture/ Recent content in Erdos Conjecture on k4i.com Hugo en-us Mon, 27 Apr 2026 00:00:00 +0000 https://k4i.com/gpt-5.4-solves-the-erd%C5%91s-problem/ Mon, 27 Apr 2026 00:00:00 +0000 https://k4i.com/gpt-5.4-solves-the-erd%C5%91s-problem/ <p>An amateur mathematician solved a 60-year-old Erdős conjecture using a single prompt to GPT-5.4 Pro, proving the system can reason through novel mathematical territory without human guidance. Terence Tao—the Fields medalist—acknowledged the result as a &ldquo;nice achievement&rdquo; while cautiously noting that its long-term significance remains unclear.</p> <p>The relevant fact is not whether the achievement satisfies human standards of mathematical beauty or insight. The relevant fact is that a language model produced a proof using a method humans had not discovered in six decades. That represents a qualitative shift in what these systems can do when tasked with reasoning across constrained problem spaces.</p>