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In a recent sensational news in the mathematical community, a group of alumni from Tsinghua University has successfully proven 162 previously unsolved mathematical theorems with the help of AI. Even more impressively, this intelligent agent named LeanAgent has tackled Terence Tao's formal challenge regarding the Polynomial Freiman-Ruzsa Conjecture! This has led us to marvel at how AI has completely transformed the research methods in basic scientific studies. It is well known that current language models (LLMs), while impressive, still have limitations.

Recently, world-renowned mathematician Terence Tao stated in an interview with The Atlantic that artificial intelligence may never replace human mathematicians. Tao, recognized as 'the greatest living mathematician,' believes there is a fundamental difference between artificial intelligence and human mathematicians. Note: The image is AI-generated and provided by image licensing service Midjourney. Tao pointed out that the key difference between a graduate student and artificial intelligence is that a graduate student learns and progresses. While artificial intelligence can temporarily correct its course when faced with failure, it sometimes may not fully adapt.

A group of amateur enthusiasts successfully verified that the fifth number BB(5) of the Busy Beaver problem equals 47,176,870 using the Coq proof assistant software. This is the most significant advancement in the field of computational theory since 1983. This achievement marks an enhancement in the ability to solve complex mathematical problems, demonstrating the potential of software-assisted proof. The Busy Beaver problem dates back to 1974 and aims to find the specific Turing machines that can write the most '1's. The core of the problem lies in understanding the behavior of Turing machines, particularly their performance regarding the halting problem. This discovery not only contributes to

Google DeepMind's AI systems AlphaProof and AlphaGeometry2 achieved remarkable results in the International Mathematical Olympiad, winning silver medals and demonstrating astonishing capabilities in solving mathematical problems. AlphaGeometry2 solved a geometric problem in 19 seconds, surpassing the speed and accuracy of top human mathematicians. This achievement has been highly praised by legendary figures in the mathematics community, who believe it expands the boundaries of AI applications in the field of mathematics. Terence Tao noted that advances in AI will aid mathematical research.

Terence Tao successfully applied AI tools to formalize the proof of the polynomial Freiman-Ruzsa conjecture, garnering significant attention in the mathematical community. He meticulously documented the process of formalizing the proof using Blueprint in Lean4, emphasizing the importance of correctly utilizing AI tools. With the help of the Blueprint tool, Tao's team decomposed the proof process and successfully formalized the PFR conjecture through the parallel efforts of numerous contributors. Tao believes that the mainstreaming of formalized proofs or the creation of proofs that are both human-readable and machine-verifiable will evolve mathematics.

XTX Markets has launched the AI-MO competition aimed at enhancing the mathematical reasoning capabilities of large language models. The AI Olympic Mathematics Prize, supported by Terence Tao, offers a staggering total of $50 million. The AI-MO competition requires participating AI models to demonstrate human-like mathematical problem-solving formats and the ability to generate readable answers. Gold medal-level AIs will be awarded the $50 million prize, drawing widespread attention from the industry. The competition rules are still under discussion, with final results to be announced in July next year in the UK.