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51 min
2 min

The last IMO problem AI could not solve

Offers deep insights into problem-solving and AI limitations in math.

FOR WHOMath enthusiasts
DenseAnalysisExpert

Channel: 3Blue1Brown

Context

The video, presented by 3Blue1Brown, explores a challenging problem from the 2025 International Math Olympiad that AI struggled to solve, focusing on the creativity and intuition required to tackle it.

Key points

  • The 2025 International Math Olympiad featured a problem that less than 1% of participants solved, marking it as a significant challenge for both humans and AI. 0:09
  • AI models, like Google's AlphaProof, have made strides in solving IMO problems but struggled with problem number six due to its demand for patience and understanding. 1:43
  • The problem involves tiling a 2025 by 2025 grid with specific constraints, requiring a minimum number of tiles while leaving one uncovered square per row and column. 4:09
  • A key insight involves understanding how tiles can efficiently cover the grid, with the most efficient tiling having tiles touch four different gaps. 12:09
  • The solution involves using square tiles in a windmill pattern, with the optimal arrangement using 45 by 45 tiles for the 2025 grid. 14:30
  • The proof of optimality involves complex reasoning, including the use of longest increasing and decreasing subsequences to define tile placement. 31:12
  • The video emphasizes the importance of motivated explanations in mathematics, suggesting they should be valued alongside proofs for their role in advancing understanding. 49:01

Quotes

This question doesn't contribute to a deep understanding of mathematics nor is it particularly difficult when compared with mathematical research.
The value of this question lies in the fact that it warmed my heart when I solved it.
Like a good book or a touching song, the value here is human.
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