Goldbach's conjecture

Author: Xu Chi
Publisher:
Publish Date: 2005-05-01
Features: "In contemporary language, the Goldbach Conjecture has two parts: the first part is called the odd number conjecture, and the second part is called the even number conjecture. The odd number conjecture states that any odd number greater than or equal to 7 can be expressed as the sum of three prime numbers. The even number conjecture says that any even number greater than or equal to 4 can be expressed as the sum of two prime numbers." As for the difficulty of the Goldbach Conjecture, I won't say much about it. I want to discuss why modern mathematics has little interest in the Goldbach Conjecture and why many so-called amateur mathematicians in China have a strong interest in it. In fact, in 1900, the great mathematician Hilbert delivered a report at the International Congress of Mathematicians, proposing 23 challenging problems. The Goldbach Conjecture is a subproblem of the eighth problem, which also includes the Riemann Hypothesis and the Twin Prime Conjecture. The modern mathematical community generally believes that the most valuable is the Generalized Riemann Hypothesis. If the Riemann Hypothesis is proven true, many problems would find their answers, while the Goldbach Conjecture and the Twin Prime Conjecture are relatively isolated. Solving these two problems alone would not significantly contribute to solving other problems. Therefore, mathematicians tend to focus on solving more valuable problems while discovering new theories or tools, "incidentally" solving the Goldbach Conjecture. "In contemporary language, the Goldbach Conjecture has two parts: the first part is called the odd number conjecture, and the second part is called the even number conjecture. The odd number conjecture states that any odd number greater than or equal to 7 can be expressed as the sum of three prime numbers. The even number conjecture says that any even number greater than or equal to 4 can be expressed as the sum of two prime numbers." As for the difficulty of the Goldbach Conjecture, I won't say much about it. I want to discuss why modern mathematics has little interest in the Goldbach Conjecture and why many so-called amateur mathematicians in China have a strong interest in it. In fact, in 1900, the great mathematician Hilbert delivered a report at the International Congress of Mathematicians, proposing 23 challenging problems. The Goldbach Conjecture is a subproblem of the eighth problem, which also includes the Riemann Hypothesis and the Twin Prime Conjecture. The modern mathematical community generally believes that the most valuable is the Generalized Riemann Hypothesis. If the Riemann Hypothesis is proven true, many problems would find their answers, while the Goldbach Conjecture and the Twin Prime Conjecture are relatively isolated. Solving these two problems alone would not significantly contribute to solving other problems. Therefore, mathematicians tend to focus on solving more valuable problems while discovering new theories or tools, "incidentally" solving the Goldbach Conjecture.