Solving a Mathematical Conjecture
Today, while reading the Guangzhou Daily, I accidentally discovered a name I had never heard before—Wang Xiaowei.
He, like me, belongs to the post-90s generation and is a senior student at Shaoguan University. Now, he has earned a new title: the solver of the difficult problem known as the “Prime Conjecture in the Problem of Representing Numbers Using Only Ones.”
The “Prime Conjecture in the Problem of Representing Numbers Using Only Ones” appears in the book Unsolved Problems in Number Theory by the Canadian mathematician Richard K. Guy. It is a number theory conjecture proposed by Guy in the 1950s: for a given prime p, does the equation f(p) = f(p-1) + 1 always hold? Here, “representing numbers using only ones” refers to expressing natural numbers using only the digit 1 through addition, multiplication, and parentheses. For a given natural number n, the minimum number of 1s required to represent it is denoted as f(n). It is said that many mathematicians had previously verified that this conjecture holds for all primes up to 300 million.
However, Wang Xiaowei disproved this proposition by providing a counterexample. He pointed out that when p = 353,942,783, this formula does not hold. After four months of intensive research, Wang Xiaowei successfully discovered this counterexample by applying operations, analysis, and optimization from set theory. After finding the counterexample, Wang was filled with excitement and sent his report to several domestic journals, but the results were disappointing; none of the journals were interested in his paper. “I also doubted whether my efforts were worth it, but my strong interest in mathematics kept me going,” Wang said. He translated his paper into English, titled A counterexample to the prime conjecture of expressing numbers using just ones, and submitted it to the world’s most authoritative number theory journal—Journal of Number Theory, published by Elsevier. The appreciation of foreign experts finally brought him the joy of success; the paper was published in the 133rd volume of the journal (February of next year). The mathematical master Shing-Tung Yau also communicated with Wang Xiaowei via email and expressed his affirmation.
The Future Path of Mathematics
However, this article is not intended to promote how great his achievements are, but rather to discuss the persistent pursuit of one’s own interests.
In the current young generation, few people can settle down like him and immerse themselves in learning something they love. Wang Xiaowei, who just turned 22 this year, is a senior in the Mathematics Department of Shaoguan University. Shaoguan University is just a very ordinary Tier 2A university, but even in such an environment, he can still focus on what he loves, pursue it persistently, and have no regrets. I sincerely admire him.
In his first year of junior high school, he met his mathematics teacher, Li Chongying. It was because of Teacher Li that he fell in love with mathematics. “Only after truly entering it did I realize how wonderful the world of mathematics is.” Teacher Li is nearly sixty years old and has taught junior high school mathematics for over 30 years. Mentioning Wang Xiaowei, Li Chongying still has a deep impression. “He was a very hardworking student and very interested in mathematics; such students are rare nowadays.”
Reading this passage, I suddenly felt very familiar and moved. At the risk of sounding presumptuous, I am truly very similar to him. I met my mathematics teacher, Wu Yaofeng, in the fifth grade, and then I fell completely in love with mathematics and have persisted until now. I long to maintain my interest in mathematics and strive for it all my life. However, do I have his courage?
In addition to focusing on his professional knowledge in mathematics, Wang Xiaowei has also dabbled in physics, astronomy, psychology, and even self-taught foreign languages. At the same time, he enjoys reading a wide range of foreign classics. In high school, he showed a clear lack of adaptation to exam-oriented education. He felt that exams could not truly reflect a person’s learning level, and he hated everything being for the sake of the Gaokao (National College Entrance Examination), so his Gaokao results were not ideal. This continued after entering university; because he spent most of his time on subjects he was interested in, Wang Xiaowei was indifferent to his grades in other courses. Although he can easily read original English mathematical works and even write professional papers entirely in English, he has not yet passed the College English Test Band 4 (CET-4).
In this, I see no trace of willfulness or regret; I see only immense courage and profound love.
In 2010, Liu Lu, a 22-year-old student at Central South University, solved the world-class mathematical problem known as the “Seetapun Conjecture” and was exceptionally appointed as a full professor and researcher by the university, becoming the youngest professor in China. This event deeply touched Wang Xiaowei, who was then a sophomore and equally passionate about mathematics. Consequently, he began attempting to solve mathematical conjectures. In the first semester of his junior year, Wang Xiaowei developed a strong interest in the “Prime Conjecture in the Problem of Representing Numbers Using Only Ones” from the book Unsolved Problems in Number Theory and worked hard on it until it was resolved.
His father, Wang Guanyuan, did not fully support his son burying his head in pure mathematical theory research at home. His father worried that his son was becoming increasingly incompatible with the realistic education system, which might affect his future career development.
“I am not dumber than others; it’s just that I am unwilling to waste my energy on exams I have no interest in,” Wang Xiaowei said.
Li Zhen is one of Wang Xiaowei’s few friends. Li Zhen recalled that in junior high school, the Chinese teacher once said to the whole class, “Wang Xiaowei is the first to awaken; he knows what he wants.”
I Am Willing to Learn from Him
“In our generation, few people can settle down like him and immerse themselves in learning something they love,” Li Zhen lamented.
“I originally thought I could obtain a recommendation for graduate school by solving a difficult problem, but Shaoguan University is just an ordinary Tier 2 university and does not have the qualification for such recommendations.” Wang Xiaowei said that he also wants to continue his studies but has to face the awkwardness of having nowhere to go. As a senior, he missed the opportunity for online graduate school registration, and with no hope for recommendation, he can only seek other paths.
Wang Xiaowei said the ideal situation would be for a good university to provide him with an opportunity. If not, it doesn’t matter; he will find a job first, working during the day and studying at night to continue his mathematical research. “If there is a good research environment, I am willing to spend my whole life studying mathematics,” he said.
In short, he is a great role model for me! I want to learn from him, not to solve some great conjecture, but for the sake of persistent pursuit and persistent love.
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