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Synthetic Olympiad-level Theorems
Here are some synthetic theorems discovered by AIPS, showcasing the symmetrical beauty and concise style of IMO inequalities. These theorems have been evaluated by professional contestants, including two national Mathematical Olympiad gold medalists and one silver medalist. Some of these theorems are recognized to meet the IMO-level standards, such as Problem 3 and Problem 5 depicted in the following figure.
Synthetic Theorem Selected for Mathematical Olympiad
Among the synthetic theorems discovered by AIPS, one problem was selected as a competition problem in a major city's 2024 Mathematical Olympiad, as depicted below. It received favorable feedback for its appropriate difficulty, concise formulation, and range of solutions. This problem was published online, and 75 contestants provided evaluations on its difficulty and elegance. The average difficulty score was 3.3 out of 7, and the elegance score was 2.2 out of 5. We present four solutions below, one provided by AIPS and three by humans.
Selected Theorem for a Major City's Mathematical Olympiad
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