Wiles's Words of Wisdom

News reports about Shen Qi were released quickly.

"Chinese mathematician Shen Qi has won another prize; the Shen Qi Ramanujan Prize is the sixth major mathematics award he has received in two years!" - News report from CCTV Radio's Chinese and English channels.

"China Key has opened the door in Italy with its key; the Ramanujan Prize is in hand, and the Fields Medal won't be far behind!" --- A report from American CNN.

"Shen Qi, the youngest recipient of the Ramanujan Prize, has China Key the record previously held by Peter Schultz." -- A report from the Italy news agency ANSA.

Peter Schultz was only 26 years old when he won the Ramanujan Prize, setting a new record for the youngest recipient at the time.

Just now, the even younger Shen Qi broke Schultz's record.

System: "New achievement! The host has won the A-level Math Prize, the Ramanujan Prize, becoming the youngest winner in history. The base reward is 1 million academic points, multiplied by the primary mathematical talent coefficient of 2.0, resulting in a final reward of 2 million academic points. The remaining academic points are 9,377,510. Please confirm."

Shen Qi finally won an A-level Math Prize, meeting the second requirement for advancing to Math Level 14, and is 1/5 of the way there.

The progress of condition one is close to half, while the progress of condition three is still 0%.

The following day, in the ICTP report hall, Shen Qi delivered a keynote report on "The Latest Research Progress of the RT Third Expression".

Having won his sixth Math Prize, the Ramanujan Prize), a triumphant Shen Qi spoke confidently on stage, "My team and I, after taking the real part of the zero-point expansion of -ζ'/ζ(s), obtained this equation."

The formula on the big screen is:

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Reζ'/ζ(s)=σ-1/∣s-1∣^2-∑ρσ-β/∣s-ρ∣^2+O(1/λ(s)+log(∣s∣+2))

The audience listened intently, so quietly that one could hear a pin drop.

Shen Qi calmly and methodically explained, "Let's review the definition of Shen's twin matching method. Let the set of non-obvious zeros of the Riemann Zeta function be: {ρ1, 1-ρ1, ρ2, 1-ρ2,..., ρk, 1-ρk,..., ρn, 1-ρn}. This set can be represented as: any two non-obvious zeros that have the characteristic of 'summing up to 1 and having the same absolute value of their imaginary parts' are matched as a pair."

"... Combining this equation, where ∑ρ represents the summation over any number of non-obvious zeros, I take only one term ρ=ρ0 from ∑ρ. Thus, there exists a positive constant c1 such that ζ(s) has no zeros in the region σ≥1-c1log^-1(∣t∣+2)."

"In other words, we have obtained the best non-zero region of ζ(s) so far!" Shen Qi's speech suddenly became rapid and forceful.

Wow!

The lecture hall instantly erupted from silence into thunderous applause.

With unwavering determination, Shen Qi said, "In my report just now, I listed four ways to prove the third expression. Although these are only frameworks, and although we haven't yet obtained the third expression for ζ(s), we are not far from success!"

"It's not hard to predict that once the third expression is proven, the value of Riemann Theorem will increase exponentially!"

"I know I have a nickname, the China Key, and in my view, the Third Expression is that precious key. I am merely the gatekeeper, responsible for managing the key. Thank you for listening. My report is finished!" Shen Qi bowed in thanks, concluding his report.

The entire audience rose to their feet. Mathematicians from ICTP, IMU, and various countries applauded and cheered from the bottom of their hearts. China Key's wonderful speech had opened the door in their hearts.

Shen Qi's conference report, "Latest Research Progress on the RT Third Expression," was widely studied overnight.

German science and education media exclaimed, "China Key! Shen Qi has launched an offensive in Europe!"

A little over a week ago, Schultz received the Keith Prize in Edinburgh and published his latest report on the Hodge conjecture. Suddenly, Schultz's career was at its peak; his already immense popularity had reached an even more extreme level.

At this moment, Shen Qi crossed the Atlantic to Europe, using his strength to declare to the European and international Mathematics Community the battle had just begun and the best was yet to come.

After the report meeting, Shen Qi had a long talk with Andrew Wiles.

"A great presentation," Wiles began, then added, "But I still have doubts. Qi, you've obtained the best non-zero region for ζ(s) so far, which is significant. However, based on this result, you haven't achieved the final result I'd like to see."

Old ginger is spicier; Wiles can see through the essence of a problem at a glance.

Shen Qi knew Wiles would say that, and he smiled, "Professor Wiles, the result you want to see is also the result I want to see; it is still in its infancy."

"Qi, following your logic, after obtaining the best non-zero region of ζ(s), you set out four ways to prove the RT Third Expression. I understand these four ways to be four mathematical tools, but in your report yesterday, you did not explain in detail how to use these four tools, only putting forward a conceptual framework."

"The first three approaches, for the function logζ(s), the fundamental theorem of prime numbers, and the zero-point equation, at least have names and basic definitions. But the fourth approach, which you named 'the fourth approach,' has no definition whatsoever. So you've run into trouble?" Wiles asked.

Shen Qi stopped laughing; he had indeed encountered a little trouble.

"I'm actually a layman when it comes to pure number theory. But my intuition as a layman in number theory tells me you're in trouble," Wiles said.

"No, you're not an amateur, you're a genius." Shen Qi had studied Wiles' proof of Fermat's Last Theorem many times. Wiles proved the number theory problem Fermat's Last Theorem using Algebraic Geometry. How could someone like that be an amateur?

"Qi, you know, back in Princeton, I spent a full ten years studying Fermat's Last Theorem. For those ten years, I only did one thing—prove Fermat's Last Theorem, that damned Fermat's Last Theorem."

"I was 41 years old when I finished that 200-page paper," Wiles recalled. He is the only Fields Medal winner in history to be over 40 years old. He received the Fields Special Prize at the age of 45 for successfully proving Fermat's Last Theorem.

"The most devastating thing was that <Inventiones Mathematicae> rejected my 200-page paper. I was desperate at the time. It was a huge blow to me. I had given everything for ten years, and all I got in return was a pile of useless garbage. At that time, I even thought about suicide." Wiles, who was nearly seventy years old, said these words in an unusually calm tone.

As Shen Qi, who was listening in, listened, his nose began to sting with tears.

Wiles patted Shen Qi on the shoulder and said, "Qi, the trouble I encountered back then was much bigger than the trouble you're in now."

"Professor Wiles, we all know what happened next. You successfully proved Fermat's Last Theorem and won the Fields Medal. How did you solve that big problem?" Shen Qi asked curiously.

Wiles looked up at the sky. "I remember that night, I was dead drunk, and I burned it page by page. I had written a 200-page paper by hand over ten years."

"When I got to page 188, I suddenly became lucid, more lucid than I've ever been in my life."

"Then, within 20 minutes, I derived the core logic for proving Fermat's Last Theorem."

"The new paper is only 130 pages long. This time it went very smoothly and has gained worldwide recognition." Wiles looked at Shen Qi and shared his valuable experience.

Shen Qi: "..."