# AI solved the Erdos Problem... Source: https://www.youtube.com/watch?v=N8I2wYXt4m8 Recap page: https://rapidrecap.app/video/N8I2wYXt4m8 Generated: 2026-01-12T04:33:54.824+00:00 --- ## Quick Overview The exponential growth of AI capability, illustrated by a graph where AI intelligence rapidly surpasses average and even high human intelligence thresholds over time, is leading to AI models autonomously solving complex mathematical problems like those in the Erdos collection, resulting in new proofs and counterexamples that are being validated by leading mathematicians like Terence Tao. **Key Points:** - Terence Tao confirmed that AI tools passed a milestone by solving Erdos Problem #728 more or less autonomously after initial human feedback, with the result not replicated in existing literature. - The proof for Erdos Problem #728 was generated by ChatGPT 5.2 Pro and formalized with Harmonic. - Neel Somani reported a weekend win where his proof for Erdos Problem #397, generated by GPT 5.2 Pro and formalized with Harmonic, was accepted by Terence Tao. - The video contrasts human progress (slow, linear improvement across industries like Finance, Logistics, and Advertising) with AI progress (exponential curve), suggesting AI will soon surpass even the highest human intelligence. - The AI's capability is demonstrated by its ability to read every paper written, write proofs/code, and perform experiments 10x faster than humans, leading to new discoveries. - The speaker highlights that AI-generated solutions are already achieving full solutions (Green dots) or partial solutions (Yellow dots) for previously open Erdos problems, and GPT-5.2 was involved in solving #728 and #397. ![Screenshot at 0:03: The central graphic illustrating the core argument: an exponential red curve labeled "AI Intelligence" rapidly rising past horizontal lines representing "ANT," "BIRD," "CHIMP," "DUMB HUMAN," and "EINSTEIN," with a yellow dot marking "YOU ARE HERE" just above the human level, signifying the imminent transition to superintelligence.](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-00-03.jpg) **Context:** The video discusses the accelerating capabilities of Artificial Intelligence, particularly in complex, abstract reasoning fields like mathematics, using the context of the Erdos problems—a collection of difficult, often unsolved mathematical challenges. The speaker references recent social media announcements, including posts by mathematician Terence Tao and researcher Neel Somani, detailing AI's role in solving problems previously considered out of reach for automation. The presentation relies heavily on a visual metaphor: an exponential curve representing AI progress rapidly overtaking human intelligence levels. ## Detailed Analysis The speaker explains the concept of accelerating AI capability using a graph that plots Intelligence (Y-axis) against Time (X-axis). The red curve, representing AI Intelligence, shows exponential growth, quickly surpassing the levels of average human intelligence (green line) and highly intelligent humans (blue line), suggesting an impending intelligence explosion. This accelerating capability is evidenced by recent successes in solving Erdos problems. Terence Tao confirmed AI's role in solving Erdos Problem #728 more or less autonomously, utilizing feedback from an initial attempt. The proof involved ChatGPT 5.2 Pro and Harmonic. Neel Somani also reported that GPT 5.2 Pro generated and formalized a proof for Erdos Problem #397, which Terence Tao accepted. The speaker contrasts this rapid AI progress with the slow, linear improvements seen in industries like finance (Black-Scholes model), logistics (Traveling Salesperson Problem), and advertising (Real-Time Bidding), all of which were disrupted by mathematical modeling. The AI's advantage stems from its ability to read all known literature, write proofs/code, and run millions of experiments 24/7 at speeds 10x or more than humans. The tables shown categorize AI contributions: fully generated solutions (Green), partial solutions (Yellow), and negative results (Red), indicating that AI is already providing novel, fully solved proofs for problems previously thought open, like Erdos #397 and #728, often using tools like Aristotle, ChatGPT 5.2 Pro, and AlphaEvolve. ### AI Progress Curve - Red curve (AI Intelligence) shows exponential growth surpassing human levels (Avg Int, High Int) over time - This rapid ascent contrasts sharply with the slower, linear progress seen in human-dominated fields. ### Recent Erdos Problem Successes - Terence Tao confirmed AI autonomously solved Erdos Problem #728; Neel Somani reported GPT 5.2 Pro solved #397, accepted by Tao. ### Category 1 - AI-generated solutions, partial solutions, or negative results: Shows examples where AI produced full solutions (Green), partial results (Yellow), or incorrect/negative results (Red) for previously open problems. ### Category 2 - Fully AI-generated solutions to problems with prior human work: Lists problems where AI achieved full solutions, such as #333, #397, and #897, even when earlier human solutions were known or later confirmed. ### Industry Disruptions via Math - Finance (Black-Scholes), Logistics (Traveling Salesperson), and Advertising (RTB) were all transformed by applying mathematical modeling, setting the stage for AI disruption. ### AI's Advantage - AI can read all written math literature, write proofs/code, and run experiments 10x faster than humans, 24/7, leading to rapid, non-linear advancements. ![Screenshot at 0:03: The central graphic illustrating the core argument: an exponential red curve labeled "AI Intelligence" rapidly rising past horizontal lines representing "ANT," "BIRD," "CHIMP," "DUMB HUMAN," and "EINSTEIN," with a yellow dot marking "YOU ARE HERE" just above the human level, signifying the imminent transition to superintelligence.](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-00-03.jpg) ![Screenshot at 0:24: A Twitter thread showing recent announcements where AI tools \(like ChatGPT 5.2 Pro\) solved Erdos problems \(#728 and #729\), directly contradicting past declarations that AI "would NEVER do this."](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-00-24.jpg) ![Screenshot at 0:52: A screenshot of the Erdos Problems website showing 1135 problems in the database, with 457 \(40%\) solved, highlighting the scope of the challenge.](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-00-52.jpg) ![Screenshot at 1:23: Terence Tao's post confirming the application of AI tools to Erdos problems passed a milestone, solving #728 more or less autonomously by AI.](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-01-23.jpg) ![Screenshot at 7:33: A GitHub page titled "AI contributions to Erdős problems" showing a legend for outcomes \(Green=full solution, Yellow=partial, Red=failure\) used to categorize AI progress on these mathematical challenges.](https://ss.rapidrecap.app/screens/N8I2wYXt4m8/00-07-33.jpg)