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The Day AI Seized the Gold Medal ─ Gemini Deep Think and the Future of Mathematics

The Day AI Seized the Gold Medal ─ Gemini Deep Think and the Future of Mathematics

2025年07月24日 01:21

1. Background: The Stage of "AI vs. Mathematics Olympiad"

The International Mathematical Olympiad (IMO), established in 1959, is known as the pinnacle of intellectual competition. It is a grueling contest where participants solve six problems in 4.5 hours, with only the top 8% earning a gold medal. DeepMind's large language model "Gemini Deep Think (GDT)" took on the challenge, scoring 35 points (out of a possible 42) and officially receiving a gold medal recognition.36Kr


2. What Makes It "Official"?

Until last year, AlphaProof/AlphaGeometry translated proofs into formal languages like "Lean" for scoring. However, GDT read the problem statements directly in English and generated proofs in natural language. The fact that judges scored it using the same rubric as for humans is the basis for its "official recognition."36Kr


3. Deep Think Mode and Parallel Reasoning

GDT is equipped with an extended reasoning mode called "Deep Think," which balances accuracy and speed by parallelly developing and integrating multiple thought paths.

  • Parallel Reasoning: Simultaneously generates diverse hypotheses and uses a convergence judgment algorithm to select among them

  • Reinforcement Learning: Self-improvement using past IMO answer corpora

  • Time Management: Dynamically allocates computational resources within the 4.5-hour constraint

As a result, it fully solved 5 problems and achieved 35 points.36Kr


4. Problem-Specific Highlights

Problem DomainTypical Human Top SolutionGDT's Distinctive Approach
Analytic Geometry (P1)Partitioning Point Sets & ProjectionVisualized the point covering problem and classified it at once using the concept of **"sunlight rays"**
Geometry (P2)Contour Auxiliary Points and Angle TrackingGradually reduced using incenter→tangent→orthocenter
Functional Inequality (P3)Asymptotic Analysis of Maximum ValueNamed it the Bonza function, divided cases, and proved upper bound 4 = lower bound 4
Integer Sequence (P4)Invariant + Proof by ContradictionFixed invariance at "even and multiple of 3" as a fixed point
Combinatorial Game (P5)Symmetric Strategy & Critical ValueConstructed a winning strategy with λ<√2/1 and λ>√2/1 as the watershed

(※P6 was not attempted)


5. Enthusiasm and Skepticism on Social Media

 


  • Sundar Pichai (Google CEO)

    “From silver to gold in just a year – astonishing progress!”X (formerly Twitter)

  • Google DeepMind Official

    “First AI to reach IMO gold‑medal standard, solving 5 / 6 problems.”X (formerly Twitter)

  • Hacker News / Reddit saw heated discussions on "complete proofs in natural language are shocking" and "P3 might have been easier than usual."techmeme.com

  • Elon Musk briefly replied "Congrats" while also sarcastically noting, "The timetable for AI taking over human jobs has been moved up again."The Times of India

Meanwhile, OpenAI claims its GPT-Grok series models are also unofficially gold-medal level, sparking ongoing debates over the transparency of scoring methods.


6. Why It Matters

  1. Generalization of Reasoning
    Mathematics is the ultimate form of natural language reasoning, and breakthroughs here can extend to high-precision reasoning fields like law, scientific research, and engineering design.

  2. AI as a Tool
    This achievement suggests the potential for AI to serve as an "auxiliary line" for human mathematicians, with applications in generating proof ideas, error detection, and creating training problems.

  3. Reducing Educational Disparities
    If free/low-cost tools supporting IMO-level problem understanding are realized, they could correct regional disparities in mathematics education.


7. Remaining Challenges

  • Verification Costs: Proofs in natural language are difficult to correct. A bridge with formalization (like Lean) is essential.

  • Data Leak Suspicion: How to avoid overfitting on past problems and solution examples.

  • "Cheat Sheet" Controversy: Criticism that large-scale context input undermines fairness.


8. Future Roadmap

DeepMind announced it would provide GDT to researchers and integrate the reasoning module into the next Gemini Ultra. OpenAI, Anthropic, and others are preparing similar challenges, with expectations that the "AI Mathematics Olympiad" will become a permanent competition.



Reference Article

Google's Gemini Deep Think AI Wins Officially Recognized Mathematics Olympiad Gold Medal - OSCHINA
Source: https://www.oschina.net/news/361739

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