Orion Crest, Series_1

Chapter 100: Tools, better to use your own

　　"None of them?"

　　Molina froze, she looked at Orion, and said in a sceptical tone, "I know you're a genius ...... although Goldbach's Conjecture is not my field of study, but if I've heard you correctly, you're really planning to overturn and redo a century's worth of work, aren't you? "

　　Orion smiled faintly and said in a relaxed tone.

　　"The problem of a+b boils down to a complicated formulation of Goldbach's Conjecture, whereby every large even number N can be represented as A+B, where the number of prime factors of A and B does not exceed a and b, respectively. and when a=b=1, the problem ultimately comes back to its original formulation, whereby any even number greater than 2 can be written as the sum of two prime numbers. "

　　A prime number is naturally a prime number when the number of prime factors is 1.

　　So, the form 1+1 is, ultimately, Goldbach's Conjecture itself.

　　In a teasing tone, Molina said, "Do you mean that all the people who have been studying Goldbach's Conjecture for a century have been doing nothing?"

　　"Of course not," Orion shook his head and suddenly threw out a question that she hadn't expected, "Do you know anything about sports?"

　　Molina froze slightly and frowned, "Sports?"

　　Orion: "Long jump, you know it?"

　　Molina skimmed her mouth and said breathlessly, "Of course."

　　Orion smiled faintly and said, "The a+b proof method that Brown opens is equivalent to the run assist before the long jump. Although the time of the run up itself is not counted in the results, is the run up useless? By the same token, a+b is the equivalent of the run-up to Goldbach's Conjecture. If it were not for it, there would not have been a later large sieve method - a tool for analytic number theory research full of inspiration and potential. One might even say that the value of the Large Sieve Method goes beyond the Goldbach Conjecture itself."

　　Whether or not the Large Sieve Method actually makes it past the final 1+1, it has fulfilled its historical mission and plays an important role in analytic number theory. Including Orion, all benefited greatly from it.

　　Ruffling the long hair around her ears, Molina looked at Orion: "So, how do you plan to prove it?"

　　The corner of Orion's mouth curled up into a confident smile.

　　"Of course, proving it in my own way."

　　For some reason, seeing the confident smile on his face, Molina's heartbeat inexplicably speeds up for two seconds.

　　Of course, for a woman who had already decided to marry Maths, that so-called heartbeat acceleration was just a moment ......

　　......

　　The solution of a mathematical conjecture requires the accumulation of workloads, and a creative genius.

　　Neither can be achieved without the other.

　　It's like Fermat's last theorem.

　　When the Taniyama Shimura conjecture was proved, even though one could not yet see a concrete prospect, all hearts were in the right place because a tool to solve the problem had appeared. Sure enough, Andrew Wiles, eventually completed this historic work.

　　But for Goldbach's Conjecture, both the large sieve method and the circle method fell short of this feeling.

　　The previous work has done a lot of groundwork, but whether it is from "9 + 9" to "1 + 2" Chen's theorem, or Helfgott's proof of Goldbach's weak conjecture under odd conditions, are just one step short of the final step. Even the significance of Chen's theorem was more to let other mathematicians understand that the path of the large sieve method had been taken to the extreme by Chen Jingrun, and this path was no longer feasible.