Abstract:
In less than ten days, the world of mathematics has experienced the ultimate roller coaster ride! On October 6, OpenAI claimed that AI had proved the quasi-Riemannian hypothesis. Mathematician Alex Kontororvin bluntly said: If someone finds this result, he will definitely win the Fields Medal immediately, no suspense!
He later added that zero points without Siegel might count as "two Fields Medals."
Other scholars also commented positively.
This is simply a dimension-reducing blow from silicon-based life to humans!
But some people did not surrender or withdraw.
Now, with the help of AI, mathematicians have proven some form of the generalized Riemann Hypothesis!
Just a few days later, good news came one after another.
The result of this quasi-Riemann hypothesis brings an important computational complexity result:
Burgisser proved Valiant's conjecture: on the complex field, VP! = VNP
After that, three human mathematicians completed the ultimate victory and completely solved a classic problem that had been pending for 19 years.
And they also left a statement:
No artificial intelligence tools were used in this work.
No artificial intelligence tools were used in this work.
Attack overnight! Humanity takes back the initiative
On October 6, OpenAI had no flash of inspiration or epiphany. Their AI was like a super bulldozer, violently proving the quasi-Riemann Hypothesis.
Number theorist Hector Pasten expressed his unequivocal amazement at OpenAI's results in excluding Landau–Siegel zeros, emphasizing that this was a "solved problem" rather than just progress.
Some netizens asked Claude Fable 5.5 to explain the proof of OpenAI’s 199-page quasi-Riemann hypothesis, and the evaluation was very high:
This is the first ever fixed interval without a zero point.
Although this is not the Riemann Hypothesis itself, if this statement is true, it is currently the closest conclusion to the Riemann Hypothesis.
But if AI can even see through this level of underlying structure, what value does human mathematicians have?
Panic spreads in mathematics circles.
But a true master will not lament. Now that the road is clear, step on the accelerator and move forward!
Only 6 days later, on October 12, a new paper suddenly appeared on the preprint platform Hexagon.
The authors are human mathematicians Cureton and Thorner.
Link: https://hexagonmath.org/2610.00200v1
They had no time to mourn the spring and autumn. Instead, they made a bold move with extremely vicious eyes:
Pan.
They directly applied the tools polished by AI to a broader and more complex mathematical object -
Finite order Hecke L function
.What is the L function? It is the "ultimate evolved version" of the Riemann Zeta function.
In modern number theory, great proofs such as Fermat's Last Theorem are almost inseparable from it.
Cureton and Thorner used the quasi-Riemannian breakthrough provided by AI to achieve an astonishing result:
All finite-order Hecke L functions have absolutely no zeros on the right side of "1-1/6000".
Link: https://hexagonmath.org/pdf/2610.00200v1
It doesn’t matter if you don’t understand. To use an analogy.
Zero point is like a reef in the sea.
In the past, this sea area was filled with fog, making it difficult for ships to move. Now, two mathematicians have used AI radar to forcibly draw a "safe zone."
There are absolutely no reefs in this area.
The safe zone is established. The first piece of territory was snatched away by humans.
But the fun has just begun.
Extreme Fury: Extreme Strangulation from 1/6000 to 1/32
The moment 1/6000 appeared, the DNA of math geeks around the world moved.
This is too small. Too conservative.
Since the door frame is already loose, why not demolish the wall as well?
An open source hackathon swept the world and exploded in an instant.
The smartest brains in the world are connected through the Internet and begin to squeeze this constant to the limit.
This is the most passionate scene in modern mathematics, starting a group strangulation.
The logic is ruthlessly streamlined. Errors are deboned and fleshed out. The boundaries are pushed outward again and again.
1/1000. 1/500. 1/100.
The constant shrinks sharply like a free fall!
In the end, the entire community pinned the security boundary of this "Zero Point Free Zone" on an extremely exaggerated number:
1/32
.
The safe zone has been enlarged hundreds of times!
Afraid of making mistakes? Worried that human intuition is unreliable? It doesn’t matter, go directly to the machine to verify!
The open source community has used the most ruthless referee——
Lean Theorem Prover
.This is a formal verification language that only accepts dead logic. Any tiny logical gap will cause the program to crash.
The relevant proof is a formal Lean proof generated by the mathematical agent AxiomProver, which is on the open source Github.
https://github.com/AxiomMath/DedekindZetaZeroFree
The boundary of 1/32 is not only deduced by humans, but also established by machine logic.
This isn't the only byproduct.
Seal the throat with one sword! 19 years of unsolved problems were wiped out
All the preparations, all the carnival, are waiting for this moment today.
On the arXiv preprint platform, a blockbuster paper co-signed by Frei, Somos and Widmer turned out.
https://arxiv.org/abs/2610.18491
The academic tsunami triggered by OpenAI finally shattered the hardest rock.
Target:
Ellenberg–Venkatesh boundary in 2007.
This is a thorn in the side of algebraic number theory.
In 2007, two math giants gave an extremely perfect limit for the number field group ℓ-torsion.
But it comes with a fatal flaw:
It is conditional.
This is the so-called "castle in the air".The proof of the two big guys must be based on the premise that "the Generalized Riemann Hypothesis (GRH) is established".
Once the premise collapses, the conclusion is instantly invalid.
In the past 19 years, countless top scholars have tried to remove this crutch and let themselves stand up. All failed. Because there are no tools. Because the underlying rock has not been dug out yet.
To this day.
Frei, Somos and Widmer saw the "1/32 Safe Zone" that the group in front had grabbed.
This is the base they have been waiting for for 19 years!
Without any hesitation, the three swordsmen unsheathed their 88 swords.
They thundered the latest zero-free region results into the old equations. The logical chain that was once broken, with the support of powerful new theory, snaps together instantly!
Derivation. Simplify. Killer. The conclusion is dazzling:
In 2007, Ellenberg–Venkatesh’s ℓ-torsion boundary of the number field group was unconditionally proved.
No more assumptions! No more prerequisites! The castle in the air suddenly fell to the ground and turned into an indestructible steel fortress!
The ghost of 19 years has been wiped out.
A core puzzle piece of algebraic number theory has been pressed tightly by humans.
I have no use for AI
If the story only ends here, this is just an extremely successful academic relay.
But what really makes this paper completely magical is the sentence at the end.
At the end of the chapter announcing the end of this 19-year problem, Frei, Somos and Widmer did not express long-winded lamentations or flattery towards AI.
They only left a cold, humorous, and somewhat ruthless statement:
We declare that no artificial intelligence tools were used in this work.
Absolutely.
This sentence is like a loud slap in the face, but also like a long and cheerful roar.
Comments