Wang Yixiao, a student from the second grade of Shenzhen Middle School. (Picture / flip from Weibo)
Recently, a math problem posed by Wei Dongyi, a gold medalist of the 49th and 50th International Mathematical Olympiad and a researcher at the School of Mathematical Sciences of Peking University, has attracted extensive attention from math enthusiasts. Nearly a hundred students from universities and middle schools at home and abroad Readers submitted answers. Unexpectedly, a problem that even the artificial intelligence GPT-4 might not solve was successfully solved by a second-year middle school student, which aroused heated discussions outside.
“Southern Metropolis Daily” reported that this topic mainly examines the skills of power series and taking logarithms. By taking logarithms of inequalities and then using Taylor series of logarithmic functions, it can be written in the form of complete square summation. Note that this inequality cannot It is derived directly from the case of n=2. According to Wei Dongyi, there is only one clue to the answer to this question, so he selected 3 “better answer examples” with high similarity of answers among nearly a hundred answers, all of which can be used as standard answers.
The report pointed out that Wang Yixiao, a sophomore in Shenzhen Middle School, was selected for his answer and was highly recognized by Wei Dongyi. It is delightful!” It is reported that among the 2 excellent answers selected by Wei Dongyi, 2 are from a domestic university and an overseas university, and Wang Yixiao’s answer is the only answer from a middle school student.
Wang Yixiao said, “I can’t believe that Teacher Wei Dongyi can choose my answer. Thanks to “Wei Shen” for his affirmation and encouragement; thanks to the school for cultivating students’ independent thinking ability and giving us a good learning environment; thanks to all the teachers There is still a long way to go, I still have a lot of shortcomings, I will continue to work hard and climb to the top!”
According to Wang Yixiao, last week, Ruan Zhongnan, the coach of the Shenzhen-China competition, reposted a tweet regarding an inequality topic from Peking University and encouraged them to actively contribute. Wang Yixiao, who usually has a strong interest in competition problems, especially the algebra part, first saw that “Wei Shen” was posing the problem, and thought that the problem would be super difficult, and he must have no clue, but following a simple identity transformation, a more obvious problem was formed. in conclusion.
When returning home at noon, Wang Yixiao wrote down the process in detail, “I am very excited that I can solve Teacher Wei Dongyi’s problem.” Teacher Ruan Zhongnan commented that Wang Yixiao observed that following taking the logarithm of the multiplication formula of the problem, he used the Taylor scale Number expansion can eliminate the even-order terms of the series, and combine the odd-order terms into a complete sum of squares by exchanging the order of summation, thus proving its non-negativeness. Finally, the discussion on the conditions for the establishment of the equal sign is concise and rigorous, showing his keen algebraic intuition and proficient algebraic skills.
