Announcement: This ID Has Made a Major Breakthrough on the Goldbach Conjecture

2007/8/11 16:59:11

On August 11, 2007 AD, at 4:47 PM, after multiple rounds of re-verification, this ID is confident that this ID has made a major breakthrough on the Goldbach Conjecture. This ID's interest lies in studying a new domain, for which a new set of methods was developed. It was discovered inadvertently that this set of methods offers fresh perspectives on certain problems in integer theory, and sporadic but uninterrupted research has been conducted on this. This method is effective not only for the Goldbach Conjecture but also for problems like the 3x+1 problem.

Since the problem has not been completely solved, it would be inappropriate to disclose the specific method. For now, only a rough description of the specific results is announced.

According to this method, even numbers are divided into two classes. For the first class, the required object does not exist, which directly corresponds to the validity of the Goldbach Conjecture. For the second class, the required object exists, but the quantity of such objects specifically corresponds, for each number, to the solutions of two Diophantine equations. It can be proven that: (the cube of the number of second-class numbers less than M) / (the number of first-class numbers less than M) approaches 0 as M approaches positive infinity.

The remaining problem is this: for the second class of numbers, both corresponding Diophantine equations have only finitely many solutions. Once this problem is resolved, the Goldbach Conjecture will also hold for the second class of numbers.

This ID's method is completely different from all previous approaches by others. It has one most powerful feature: should there exist an even number that does not satisfy the Goldbach Conjecture, this ID's method can directly construct it.

Now, the problem has been transformed into a question about the number of solutions to two Diophantine equations.

Of course, we are still very far from ultimate success, because the problem of the number of solutions to Diophantine equations is itself not easy to study. For the first equation, a rough estimate suggests the difficulty is relatively low, and it should be solvable soon. For the second equation, the difficulty is much greater, and it can only be left to luck—let us hope it does not turn out to be as troublesome as the one encountered in Fermat's conjecture.

After some rough deliberation, using tools from the arithmetic of elliptic curves and modular forms, I still have not found an approach to the second equation. Wiles proved the semi-stable case of the Taniyama-Shimura-Weil conjecture to settle Fermat's conjecture—a detour so breathtaking it moved heaven and earth, driving ghosts to tears. Unfortunately, he did not pave the way for this ID's equation. It seems the road must be walked alone.

This ID is utterly exhausted now—I have not slept at all. Time to rest.

Signing off for now. Goodbye.