Orion Crest, Series_1

Chapter 106: Surprising comments

　　If the root idea of the least-quadratic non-residue estimate for modulo primes in the group construction method came from the large sieve method, then the part of Helfgott's paper on Fourier analysis of functions on the circumference of a circle has given his theory a richness of branches and leaves.

　　This "99 %" part of his work began before he went to California last year to hear the lecture, and it has now been completed. The remaining 1% is the inspiration that keeps most people away from the truth.

　　And that piece of the puzzle, now, is in Orion's hands.

　　Without waiting for Charles Feferman to finish the class, Orion quietly packed up his things, just as he had quietly come and gone.

　　The old professor standing on the podium just looked at the direction he left, the corner of his mouth hooked up a smile, and then as if nothing had happened, he continued to use that slow and methodical voice to talk about his number theory class.

　　Back at the flat, Orion picked up a pen and scribbled on a piece of paper.

　　Thoughts flowed like a spring!

　　He spilled out the fifth page, then the sixth, then the seventh. ......

　　Time passed by.

　　The wall clock went past noon and turned to dusk, until the sky outside the window grew darker.

　　When Orion reached the end of the sixteenth page of the paper, he finally stopped the tip of the pencil, which was trembling slightly in his hand, and looked at the results of the research in front of him.

　　"...... Then Bombieri's Theorem is introduced here, and the dozens of lines further down are obvious ...... Great job!"

　　Taking a deep breath, Orion leaned back in his chair and exhaled the long pent-up air in his chest, his tightly furrowed brow finally stretching into a smile.

　　The next step was to solve Goldbach's Conjecture.

　　From now on, his boat was truly sailing into an uncharted sea.

　　However, he believed he could do it.

　　This causeless but unshakeable belief was probably the same feeling Andrew Wiles had when he looked at Fermat's Last Theorem after completing the proof of Taniyama Shimura's theorem.

　　When an tool is accomplished, fulfilling the mission of that tool is nothing more than a matter of going along for the ride.

　　The Goldbach's Conjecture, which had combined the strengths of many studies, had been precipitated for nearly two hundred years, and had been drilled by several generations of mathematicians, had finally come to this point.

　　Orion had no pride in his heart, but only honour.

　　He was honoured that he would be the one to put the roof on this building.

　　After half a minute of reminiscing about this unspeakable emotion, Orion took out his mobile phone and sent a text message to his mentor Deligne and his friends in Princeton, telling them that his project had entered a critical stage, and that he intended to retreat for a period of time, so that they would not have to worry.

　　Then, he turned off his mobile phone and completely closed himself in this small room of about ten square metres ......

　　It has come to this point, if it goes well, it shouldn't take too long.

　　If it doesn't go well ......

　　Then he won't come out!

　　......