In 1978, writer Xu Chi published the reportage "Goldbach's Conjecture" in People's Literature, which described the outstanding contributions of Chinese mathematician Chen Jingrun to the study of Goldbach's Conjecture. As a result, many people came to know about Goldbach's Conjecture and believed that it aimed to prove "1+1=2". But was Goldbach's Conjecture really about proving "1+1=2"? As early as 1742, German mathematician Goldbach wrote to the great mathematician Euler and proposed two conjectures: (1) Any even number greater than 2 is the sum of two prime numbers; (2) Any odd number greater than 5 is the sum of three prime numbers. Euler said he believed Goldbach's conjectures were correct, but he couldn't prove them. It's easy to prove that (2) is a corollary of (1). Therefore, the first conjecture is the most fundamental. Since prime numbers only have one factor, the conjecture (1) is usually expressed as (1+1). (1+1) is actually a representation of Goldbach's Conjecture, not to prove "1+1=2", which doesn't need to be proven.
Goldbach's Conjecture has attracted the interest of many famous mathematicians around the world and achieved great progress in proof. In 1922, British mathematicians Hardy and Littlewood proposed the "circle method". In 1937, Soviet mathematician Ivan Matveevich Vinogradov used the circle method combined with his own method to prove that every sufficiently large odd number is the sum of three prime numbers, essentially proving the second problem of Goldbach's Conjecture. Thus, Goldbach's Conjecture mainly refers to the first problem. Mathematicians around the world have put a lot of effort into this difficult problem. In 1920, Norwegian mathematician Braun improved the ancient "sieve method" and proved that every sufficiently large even number is the sum of two integers with no more than 9 prime factors, namely (9+9). German mathematician Ladermann proved (7+7) in 1924. British mathematician Esterman proved (6+6) in 1932. Soviet mathematician Buchstab proved (5+5) and (4+4) in 1938 and 1940 respectively. It's like athletes constantly breaking world records. In 1956, Chinese mathematician Wang Yuan proved (3+4), and in the same year, Soviet mathematician A. Vinogradov proved (3+3). In 1957, Wang Yuan proved (2+3). The drawback of these results is that none of the two numbers added together can be guaranteed to be prime numbers. By 1962, Chinese mathematician Pan Chengdong and Soviet mathematician Barban independently proved (1+5). In 1963, Pan Chengdong, Wang Yuan, and Barban all proved (1+4). In 1965, A. Vinogradov, Buchstab, and Italian mathematician Bomberi proved (1+3). After making new important improvements to the sieve method, Chinese mathematician Chen Jingrun proved (1+2) in 1966, achieving the best result so far in the world on the difficult problem of Goldbach's Conjecture (1). He proved that: any sufficiently large even number can be expressed as the sum of two numbers, one of which is a prime number, and the other is either a prime number or the product of two prime numbers. The world calls this theorem the "Chen's Theorem". This theorem has received great attention from the world's mathematical community, and many mathematicians are committed to simplifying the proof of this theorem. At present, there are five simplified proofs in the world, and the simplest simplified proof was made by Chinese mathematicians Wang Yuan, Ding Xiaqi, and Pan Chengdong together.
The proof of Goldbach's Conjecture is not over yet, and we still need to make a final push. After decades of research by mathematicians around the world, we can see that Goldbach's Conjecture, like other classic problems, has achieved all its achievements on the basis of the achievements of predecessors and through circuitous paths. For example,If one doesn't even understand the basics of number theory and hasn't studied the achievements of predecessors, attempting to prove (1 + 1) out of sheer enthusiasm would only be a waste of time and lead to erroneous results. Mathematics is a very rigorous discipline that cannot be approached carelessly. It requires not only the spirit of innovation but also a rigorous scientific attitude, which is the key to success for many mathematicians.