"About the ABC conjecture, it can be said to be a protracted mathematical debate."
"At the beginning, we were happy when we learned that the abc conjecture was proved by Shinichi Mochizuki. This fully demonstrated that even difficult problems have the possibility of being solved in a mathematical sense."
"But unfortunately, after many years of thinking about the IUTT theory proposed by Professor Mochizuki, we came to the conclusion that although these four papers have more than 512 pages, and were later supplemented and revised to more than 600 pages, they have never been easy for people to understand, and the key proofs always appear to be extremely brief and difficult to understand."
"Until now, there are only a dozen people in the world who claim to have read Professor Mochizuki's papers. Most of them are from Professor Mochizuki's hometown and have a certain relationship with Professor Mochizuki."
"In addition, a few months ago, Professor Mochizuki's proof paper was also accepted by the journal "PRIMS" of which he is the editor-in-chief. It is said that in Kyoto University, the abc conjecture has become a theorem."
"I definitely don't think this is the right thing to do, and mathematics should not have such a thing where a proposition directly becomes a theorem based on personal influence, as if it were a tyrant."
"So, it's time to end this."
Peter Schultz mercilessly accused Shinichi Mochizuki and compared him to a tyrant.
However, the vast majority of people in the audience nodded in agreement.
No matter what, it is obviously a very overbearing thing to directly treat a conjecture as a theorem in a certain area when the entire mathematical community has not yet generally recognized it.
The mathematics world is also made up of individuals, so there are many people who are dissatisfied with this kind of thing.
Of course, there were those Shinichi Mochizuki supporters who didn't nod.
That is to say, the dozen or so people who Schultz said "understood Shinichi Mochizuki's paper" are here.
Schultz did not reject these people's applications to attend the meeting, lest he appear too domineering.
In fact, among those 16 seats, there were several Shinichi Mochizuki supporters, all of whom were Japanese.
Next, Schultz's narration begins, starting with the introduction of the abc conjecture.
On the seat, after Xiao Yi heard Schultz's criticism of Shinichi Mochizuki just now, he couldn't help but look at Shinichi Mochizuki on the other side and thought to himself, wouldn't this boss be angry?
However, from the side, Shinichi Mochizuki's expression is very calm and has not changed much.
There is a feeling of intangible joy and anger in it.
Of course, maybe it's because he already has a plan?
Xiao Yi continued to listen, and at the same time, he combined it with the Shinichi Mochizuki paper he had read before, thinking about it in his mind, and occasionally turning over the A4 paper in his hand.
Anyway, although he is sitting here now, because the seat is arranged in the corner, he can be regarded as a small transparent person on the main table.
Schultz The reason why he is placed here is just because his paper is the "trigger" for this discussion. As for whether he can provide any useful opinions on this discussion, it is estimated that no one present has considered it.
In this way, time passed quickly.
Schultz also began to raise his formal questions.
"First point, Frey curve."
"Mochizuki describes all the inequalities with a fixed d≥1 that reduce to all number fields k of degree [k: Q]≤d and all elliptic curves E/k corresponding to the point P∈Mell(k)..."
"... Using local Tate uniformization(rig m→Grig m /qZv′(E×k kv)rig, we get the set of local Tate parameters qv∈kv at the finite position v..."
"... However, please note that the degree of the boundary ∞ = (Mell \ Mell) is 1/2, and the degree of the logarithmic differential is 1/12, which cannot explain the reason for the sixth element I mentioned earlier."
Upon hearing this, more than 90% of the people present were confused about what Schultz was talking about, but those who could really understand it brightened up.
This should be the new point of doubt discovered by Schultz!
This questioning point is different from those he raised two years ago, but is more pointed and goes straight to the essence!
How to explain Shinichi Mochizuki?
However, before Schultz could continue speaking, Shinichi Mochizuki stood up.
"I'm sorry, Peter, since you plan to mention it point by point, then I will also respond point by point."
"As for the first question you mentioned, the sixth element conflict caused by Frey curve and Tate analysis."
Shinichi Mochizuki left his seat and walked to the big blackboard - Xiao Yi discovered that Max Planck Institute for Mathematics almost every room has an oversized blackboard.
Shinichi Mochizuki picked up the blackboard pen from the side and started writing directly on it.
[Grm→Grm/qZv(E×k kv)r]
[deg(qE)=1[k: Q]∑v(qv)log(N (v))]
[h(P)=1/6deg(qE)+O(h(P)^1/2+1)]
[...]
After a few simple expressions, Shinichi Mochizuki put down his pen and said, "My explanation is complete."
People present bared their teeth.
Have you finished explaining now?
Who can understand it at once without saying a word??
Of course, this is actually the character of Shinichi Mochizuki, who acts very casually, rarely explains anything, and is always willful. However, this has aroused the envy of many young students. They envy his "never explain" temperament, and others can't do anything about him.
However, there are still people present who can understand it, and Schultz is one of them.
He frowned and pondered, and soon understood the meaning of the expressions Shinichi Mochizuki.
Just like him, it was created by borrowing all the analysis methods from the Xiao Yi paper.
Solved his first problem.
He let out a sigh of relief. It seemed that today was going to be another fierce collision of mathematical ideas.
Then, he will no longer restrain himself.
"Yes, Professor Mochizuki, you did give a good explanation."
"Of course, this is not the only problem I have."
"The second question comes from your paper, IUTT-4, Theorem 1.10."
"Determine a natural number d≥1, there is a function αd, βd: N→R depends on d, such that αd()→0..."
"So how do you use your IUTT to make your inequality hold?"
As for this question, Shinichi Mochizuki had obviously been prepared for it for a long time, and also started writing on the blackboard.
The two men's confrontation left only their voices in the entire conference hall.
No third party is involved.
Everyone else almost held their breath as they watched the debate in front of them that could probably be recorded in the history of mathematics.
Almost every question raised by Schultz can make those who understand it show a look of enlightenment, and be surprised in their hearts at the advanced nature of this error - it is difficult to detect.
However, Shinichi Mochizuki is well prepared. For almost every problem, he can solve it by just writing lines of formulas on the blackboard.
Only for a few questions would he reluctantly explain aloud.
In this way, time passed slowly.
Compared to the solemn mood of other viewers, there was one person who had a different feeling.
This person is Xiao Yi. As he listened to the arguments of these two big guys, he felt more and more familiar with their way of thinking. At the same time, their questions and answers constantly allowed him to connect with the knowledge in his mind.
Until the end.
[Gv o×μkv×((qj2v)j=1,.,*)N]
"I'm done explaining."
"Peter, do you have any more questions?"
Shinichi Mochizuki once again gave his answer on the blackboard.
However, this time, Schultz was silent.
Almost all of the problems he found for this meeting were cleverly resolved by Shinichi Mochizuki. Only a few of them were still controversial, but he could not raise any further questions.
So, where is the problem?
Could it be that this discussion will end in vain again?
Shinichi Mochizuki...
He is indeed a person that Professor Faltings also considers to be "smart".
Sure enough, it's still so difficult.
The audience also remained silent.
The big guys at the main table also remained silent.
All onlookers could see that Schultz had tried his best.
Even more than five hours have passed!
No one present had lunch, but no one wanted to leave.
Are the results of this discussion about to come out?
However, after a long silence.
Suddenly there was a slightly nervous voice.
"Professor Schultz, Professor Mochizuki, maybe we can go back to the beginning and think about it?"
"If according to what Professor Mochizuki just explained on the fifth question, in any case, a [Hodge Theater] is abstractly derived from the data of a fixed primary truncated elliptic curve X; from the category whose only object is X and whose morphism is the automorphism of X, to the natural functor of the [Hodge Theater] category is equivalent."
"So, starting from this perspective, back to the third question, the content of Far Abelian Geometry is discussed here."
"We all know that Far Abelian Geometry studies how the absolute Galois group of rational numbers and the flattened fundamental group of any algebraic variety, their 'far away from Abelian' parts, that is, the parts that do not comply with the commutative law ab=ba, will affect the properties of the corresponding algebraic structure."
"If you put it this way, in the sense that geometry and group theory are equivalent, Far Abelian Geometry will not be established——"
"In other words, it violated Professor Mochizuki's [Mochizuki Theorem]?"