"Dear Junxin,

Hello. Your letter has been received, and I would like to ask for your forgiveness: without your permission, I have submitted your letter to the Annals of Mathematics for printing, and the idea of the Taniyama-Shimura conjecture mentioned in your letter is another rapid development of Fermat's theorem, and he directly connects the geometric study of elliptic lines of the Taniyama-Shimura conjecture with the number theory problem of Fermat's theorem. We agreed to prove the Junxin conjecture, and allow me to call him that, as we unanimously decided. Fermat's theorem can be proved by directly proving the Taniyama-Shimura conjecture.

A historic moment is coming. We look forward to hearing from you and the proof of the conjecture that bears your name. The editorial department of the Annals of Mathematics has re-arranged the papers for the New Year's special issue, leaving a special page for your papers. For that, hopefully, you can mail your paper here as soon as possible.

Finally, on behalf of our esteemed President William G. Bowen1, I would like to convey his invitation, listen to your professor Hua, you are still a freshman, so he came up with the idea of an exchange student, hoping to come to Princeton next year, we will waive all your tuition and fees, and we have prepared the highest level of scholarship. Our professors in the Department of Mathematics are in favor of this decision.

Your Faltins

6 November 1980"

"Xiaojun, what do you think about this matter?" Professor Hu asked. It was not easy for him to make a decision for Junxin, after all, it was the first time that an American university had extended an invitation to a Chinese freshman.

Junxin pondered for a long time and asked, "What do you think of the professor at Princeton University?" ”

"HYCPS, isn't this the top university you told me!" Professor Hu laughed silently, "I thought you had forgotten!" ”

"Among the top universities in the United States, Harvard, Yale, UC, Princeton and Stanford, my favorite is Princeton University in the United States."

"When I was a student at the École Normale Supérieure in Paris, there was no reflection of the American universities. However, my teacher was a researcher at the Institute for Advanced Study in Princeton at the beginning of the founding of the People's Republic of China, and I heard him say that Princeton University is the purest place in the academic world. Although Professor Hu's words were tactful, they already made his meaning clear.

"yes, I see!" Junxin nodded.

"What did you do about that guess?" Professor Hu pressed the question and began to discuss the conjecture named after him with Junxin.

"The proof has an idea, and it will take about a week or so to complete." Junxin said casually.

"Tell me what you think!" Professor Hu pulled Junxin to the blackboard.

"That's what I thought...... Junshin began to explain the connection between the Taniyama-Shimura conjecture and Fermat's theorem, and slowly explained the idea of proof.

"Very beautiful idea!" Professor Hu had to sigh, feeling as if he was getting old, and he couldn't help Junxin in many places, and even in the process of explaining, there were many places that he couldn't understand. "Finish your paper as soon as possible! It's another Fields Medal paper. ”

"The teacher laughed!" Junxin could only say modestly.

"By the way, how are your experiments going?"

"Soon, the trace has been found, and it will take about another day or two of experiments!" Junxin's face couldn't help but show joy.

"Oh, that's good!" Professor Hu nodded, he didn't know much about chemistry, but he was very worried that Junxin would fall into chemistry, which would have a bad impact on his mathematical development.

"There is still a long time before the start of the next school year, and the teacher will soon return to China, so you should think carefully about it at this time." Professor Hu instructed again before Junxin left.

Junxin nodded and came down.

The research on quasicrystals has indeed entered the final stage, as Junxin said. After nearly 100 failures, Junxin revised the experimental protocol four or five times, and finally found a spectrum of 10 symmetries in an unexpected experiment. After many confirmations, Junxin did not think it was an example, and immediately revised the experimental plan and prepared a new experiment. Then he was arrested in Professor Hu's office because of a letter from Faltins.

After leaving the laboratory, Junxin walked briskly towards the laboratory, recalling the unexpected scene that occurred in the experiment.

It is said that after Junxin and Gu Mengxue talked for a long time that day, Gu Mengxue had a new idea for the research of science fiction, so she hurriedly left the laboratory to do her own research. And Junxin was also in good spirits after a day's rest. Re-engaged in experimentation.

The progress of the experiment was indeed not as exciting as expected, and it was a series of blows, so when Gu Mengxue perfected her idea and found Junxin, Junxin had been in the laboratory for another week with a disgraced face, and the number of failed experiments had accumulated to about a hundred.

"Faith, my idea has been perfected, do you want to listen to it?" Gu Mengxue said softly after Junxin stopped to record this failure.

"Oh!" Junxin was a little absent-minded.

Gu Mengxue didn't care about Junxin's attitude, and said excitedly: "I'm thinking about what kind of result will happen if two substances collide, just like two worlds colliding!" ”

"Collision?!" Junxin suddenly fell silent, as if he had grasped something.

"Yes, it's a collision!" Gu Mengxue didn't notice Jun Xin's expression, and continued, "If each substance symbolizes a world, and the world collides with the world, will it merge or destroy? I finally perfected my idea... Alas, how are you? ”

Before Gu Mengxue finished speaking, Jun Xin, who was already a little stunned, suddenly jumped up and came to the pile of marked alloys to look for it, in Gu Mengxue's statement just now, Jun Xin thought of what he had been ignoring.

Soon, in Gu Mengxue's stunned, Junxin selected a few defective products that should have been discarded with a low degree of fusion, and put them under the electron microscope again, after a long time of operation, Junxin found a diffraction pattern of ten light points surrounding an axis, Junxin, who had studied the quasicrystal, knew that this was the quasicrystal.

Junxin carefully saved this picture, and then printed it out with the old-fashioned printer that has disappeared in later generations.

"Mengxue, I seem to have found the trace of what I was looking for, do you think I really found it, a new material form!"