Translator: Henyee Translations Editor: Henyee Translations
Recently, Lu Zhou was busy with superconducting materials research as well as the graduation of his students.
Although he set notifications for Sir Atiyah’s thesis on the Riemann’s conjecture, he didn’t pay attention to the Heidelberg Laureate Forum. Plus due to the sudden Nobel Prize call, he totally forgot about Atiyah.
Until now.
He suddenly received an invitation to write an article for Annual Mathematics.
Lu Zhou only remembered this sensational mathematics news when the editor-in-chief Peter Sarnak wanted Lu Zhou to write a short commentary regarding Atiyah’s thesis. It should be no more than five hundred words.
In the morning, when Lu Zhou went into his office, Hardy walked over with some A4 papers.
“Professor, I’ve already printed the thesis that you wanted.”
Lu Zhou took Atiyah’s thesis from Hardy and was stunned. He then looked at Hardy.
“That’s it?”
“Yes, Professor Lu,” Hardy nodded and said, “I’m sure this is all of it.”
The thesis was only five pages and with only three referred documents. There was even a small typesetting error on the third and fourth subsections, but it wasn’t a big problem.
If this was a PhD thesis, this thesis definitely wouldn’t be accepted. However, the academic community was more tolerant when it was from a famous scholar.
For example, when Wiles first proved Fermat’s last theorem, he even added a “preface” to the front of the abstract. He wrote about his childhood and Fermat’s last theorem, humoring everyone that read it.
Sir Atiyah was also capricious. After all, he was the winner of the Fields Medal and Abel Prize, and the study of the Atiyah-Singer Index Theorem was one of the most important mathematical achievements in the 21st century.
However, this wasn’t the main point.
The mathematics world wouldn’t blindly trust a person just because of their past achievements or honors.
Lu Zhou didn’t have much hope for this thesis. However, the invitation was sent by Professor Sarnak, and the thesis author was a highly respected scholar. Therefore, Lu Zhou sat in his office chair and read the five-page thesis objectively.
However, the more he read, the more he began to frown.
Like Sir Atiyah had previously claimed, he used a very simple method to “solve” this problem.
As expected, claims like this were often unreliable…
Once Lu Zhou read the thesis from the beginning to the end, he had a basic understanding of the proof process.
Basically, in Sir Atiyah’s thesis, he used a weak analytic function called the Todd function. He also used a hypothetical method to associate this Todd function with the fine structures of physics.
The most upsetting thing wasn’t that he didn’t specifically describe what this Todd function was or its relationship with the Riemann zeta function, it was that he used a proof by contradiction.
Yes, he actually used a proof by contradiction.
For example, if the Riemann’s conjecture was wrong, then “my theorem” was a contradiction.
Because there was no way “my theorem” was contradictory, then the Riemann’s conjecture had to be correct…
When Lu Zhou read this, he made a conclusion.
Although this was unfortunate, it seemed like Lu Zhou’s initial thoughts were correct.
Hardy saw that Lu Zhou had a weird expression, and so, he asked, “Professor, what do you think about this thesis?”
Lu Zhou suddenly smiled and put the thesis aside.
“You’re in the field of number theory as well, don’t you have an opinion?”
Hardy scratched his head and said, “I don’t study the Riemann zeta function… Honestly, Sir Atiyah’s thesis is too esoteric, and he seemed to have used some physics terms.”
Lu Zhou: “That’s right, Sir Atiyah did use some physics terms. Professor Witten, who knows Atiyah very well, said that Sir Atiyah only recently entered the field of physics. Atiyah’s physics intuition isn’t flattering, to say the least. As for this thesis, basically, he constructed a weak Todd function and combined the function with a physics concept.”
Hardy couldn’t help but ask, “Is there a problem with the weak Todd function?”
Lu Zhou: “I don’t know if the weak Todd function has a problem… Because the amount of information that I can retrieve from this function is way too small, that’s why I can’t decide yet. The biggest problem in his thesis is that he made reference to the fine-structure constant in physics.”
Hardy: “… Fine-structure constant?”
“Yeah…” Lu Zhou nodded and said, “It’s an important dimensionless number in physics with the symbol alpha that’s commonly used in quantum electrodynamics.”
This was a very important physics concept that was often used to measure the intensity of charged particles and electromagnetic fields.
Interestingly, physicists had spent more than a century to try and derive the value of alpha from a physics perspective. They then try to “invent” a mathematical formula for it.
Unfortunately, no one had succeeded so far, and most people had given up.
However, in Atiyah’s thesis, he recklessly used this concept and used it as the basis for his argument.
This sounded bad, but this was something Professor Enoch would do…
Hardy said: “… You called it, Atiyah is past his prime.”
“Not exactly.” Lu Zhou shook his head as he said, “Even though he is wrong, his courage is still commendable.”
In academia, there was a distinct difference between “honest mistake” and “academic fraud”.
In his later years, Einstein claimed many times that he had discovered the unified field theory, and he continued to research the theory right up to moments before his death… At that time, no one believed in his calculations; they just quietly accompanied him to the end.
In any case, it wasn’t easy to conduct research at 90 years old.
It was even more commendable to gamble one’s honor and reputation just to challenge Mount Everest.
Therefore, just like what Lu Zhou had said, as long as the old man was happy, the final result didn’t matter…
…
Lu Zhou contemplated writing the commentary for Annual Mathematics. In the end, he wrote a polite rejection letter. He conveyed that he was very busy with his research and euphemistically refused the invitation from Peter Sarnak.
This was different from Shinichi Mochizuki’s complicated and lengthy papers. No one was certain whether or not Shinichi Mochizuki was correct; therefore, no one wanted to stand up and testify.
However, the problems in Sir Atiyah’s thesis were very obvious. One didn’t even need to have a deep understanding of mathematics to find the problems.
Despite him staying silent, everyone knew what was going on.
Lu Zhou decided to let Faltings execute this type of humiliating matter.
After all, Faltings was famous in the mathematics world for being ruthless.
However, if instead a 25-year-old was to humiliate Atiyah…
It would be pretty ignorant of the old man’s feelings.
After writing this response, Lu Zhou suddenly realized why no one in the Princeton Institute for Advanced Study was talking about this seemingly huge sensation.
After all, everyone would grow old someday, and everyone needed respect and dignity.
Especially when it was a respectable scholar.
Also, the media loved to use click-bait titles to attract attention. They rather believed the 90-year-old Atiyah wasn’t old at all.
Unfortunately, mathematics was the pursuit of truth, and it would not pander to the public.
