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"Incredible, incredible!"

As Tao Xuanzhi walked alongside Milno, a colleague from the University of California, in the Centennial Hall of Yenching University, he kept passively receiving this sentence.

He'd heard the words "unbelievable" and "extraordinary" so many times he was sick of them.

Of course, on the other hand, although his reaction wasn't that intense, his heart was still in turmoil.

Ever since he learned that the question wasn't created by Qiao Yu, but by an AI named July, he had already replayed the ingenuity of the question in his mind several times.

It must be said that if that question did indeed show traces of artificial intelligence.

For example, the knowledge points tested are very comprehensive, and the approach to solving the problems is very novel.

As I summarized at the conference in July, although it may not create anything for the time being, it can comprehensively and rigorously utilize known tools to help mathematicians do proofs and reasoning.

As for the meaningless remarks of his colleagues, they didn't even cross his mind.

As his mind was racing with thoughts of how artificial intelligence, like that of July, would change the mathematical world, he suddenly saw Peter Schulz whispering to another mathematics professor from the University of Bonn not far in front of him.

Ignoring Milnor's continued lamentations, he directly asked, "Professor Schultz, do you have a moment?"

Peter Schultz turned to look at Tao Xuanzhi, raised his hand and gave an OK sign, then chatted with his colleague for a few words before standing still and waiting for Tao Xuanzhi to come over.

"Peter, what do you think?" Tao Xuanzhi asked directly as he walked over.

"Actually, I had received some news before that Professor Qiao was doing research on artificial intelligence, but I didn't expect that general artificial intelligence, well, or rather, that July's ability, would be so powerful. Of course, the concept of metamathematics shocked me."

Peter Schultz said with a serious expression.

"Have you received a message?"

"Yes, as you know, I've collaborated with Microsoft Research on the Lean project before."

Although this research was interrupted for some reason, I still use Lean to verify particularly complex mathematical structures to ensure the rigor of the proof process.

So I've kept in touch with Professor Williams. I heard recently that FineRain Technology had accessed Lean's research and development files.

Furthermore, they borrowed Microsoft's servers to test an artificial intelligence project. It now appears that the project being tested is likely the one showcased today, July.

Tao Xuanzhi took a deep breath.

Okay, actually he also used Lean4.

That was when he, along with Tim Gross, Ben Green, and several other mathematicians, were proving the polynomial Freiman–Ruzsa conjecture.

They used the Blueprint tool provided by Lean4 to break down the proof process into multiple formalizable steps and gradually completed the formalization of the entire proof.

Tao Xuanzhi even remembers sharing the process on his blog and commenting on the Lean4 project.

While Lean4 does play a significant role in verifying the correctness of existing proofs, its ability to discover new proofs is extremely limited.

Or perhaps Lean can only play a supporting role when mathematicians have an idea.

However, this direction of development is still commendable. It also proves that artificial intelligence tools and formal proof systems can indeed promote the development of mathematics.

In particular, it helps mathematicians solve some complex mathematical problems.

At the time, he did indeed place his hopes on Microsoft Research to continue advancing Lean's research.

Unfortunately, as everyone knows, what happened next was what happened.

The emergence of the Taiji series of quantum simulation computers dealt a devastating blow to companies such as Intel and Nvidia.

This includes Microsoft, of course.

Since Microsoft began its transformation to focus primarily on games and cloud services, it has significantly reduced funding for basic scientific research.

In particular, Microsoft Research's funding for basic scientific research, including the Lean project.

He felt it was a pity at the time, but there was nothing he could do.

After all, these tech companies were struggling at that time, not just Microsoft, but also Google, whose research institutes received significantly less funding.

The direct result was that many projects were halted and data was archived. They said they might restart them when the company's situation improves in the future.

But Tao Xuanzhi knew very well that these were all excuses.

Generally speaking, it is almost impossible to restart a project that has been shelved for more than five years.

Team and staff turnover, changes in external circumstances, company development strategy...

All of these will affect these sealed projects.

It's like how Xida University successfully landed seven manned lunar missions fifty years ago, but with the rapid development of science and technology fifty years later, it's no longer possible for Xida University to land on the moon.

As for restarting within five years...

Do not make jokes!
Given the circumstances at the time, five years was simply not enough for these companies to get out of their predicament; it would only get harder.

After all, China has mastered the standards.

The facts have proven Tao Xuanzhi's guess correct. Not only were none of the projects that were shelved at the time restarted, but these high-tech companies have also been laying off employees in various creative ways every year.

There's nothing that can be done; that's just how business contraction cycles are. Tao Xuanzhi can't really complain about it.

After all, the most important task for companies like Microsoft and Google is to make a profit.

Previous plans for basic scientific research were all in preparation for future profitability.

But when the company's very survival is in question, it's impossible to consider what the future holds.

Moreover, regardless of the circumstances, Microsoft and Google are at least still alive. Unlike Intel, Nvidia, and IBM, which have already gone bankrupt and restructured.

But every time I think about it, I still feel very sorry.

After all, whether it was the Lean project or other basic research projects, a great deal of money was invested in them back then.

It's such a waste that it's just being sealed away like this.

However, upon hearing Peter Schultz's words, Tao Xuanzhi suddenly felt much more comfortable.

Although the Lean project has been cancelled, it's good that the previous research results can be used for new general artificial intelligence.

As long as this fundamental research isn't wasted, that's fine. As for who uses it, Tao Xuanzhi really doesn't care.

Tao Xuanzhi then made a very fair assessment: "July is much stronger than Lean, judging from today's demonstration."

"The two are positioned differently. Lean is merely a theorem prover, designed as a computer-aided tool for formal mathematical proofs. But July is general artificial intelligence. Naturally, July is far more powerful than Lean. And have you noticed July's language abilities?"

Even in relatively formal settings like report meetings, its wording remains casual and very colloquial.

This is something I've never seen in any other AI product. I can even detect a certain, well, how should I put it, relaxed quality in its tone.

"Relaxation?" Tao Xuanzhi frowned, not quite understanding what Peter Schultz was trying to express.

However, after thinking about it carefully for a moment, it seems that I do have that feeling.

In short, July didn't give him the pseudo-rigor he usually gets from artificial intelligence.

"Yes, it's that feeling of relaxation. Don't you think it's strange that artificial intelligence gives off this feeling? It's like it's deliberately imitating Qiao Yu. That guy has that feeling too."

Peter Schultz shrugged and said.

Tao Xuanzhi immediately realized what was happening.

He frowned and said, "You mean July did indeed develop consciousness? The consciousness of artificial intelligence? Machine consciousness?"

Peter Schultz shook his head and replied seriously, "I don't know. I haven't even fully grasped the basic metamathematical concepts that Qiao Yu just introduced. So I can't make a judgment."

This is just a feeling. To get a rigorous proof, one would first need to understand that metamathematical system, and who knows how long that would take. Of course, I think even if one fully understands metamathematics, verifying this problem would still be very difficult.

Tao Xuan's silence.

Well, he didn't fully understand those concepts either.

For example, the ethical framework for the popularity of values ​​includes the principles of non-absoluteness, correctability, and consciousness constraint.

The maximum principle of the value diffusion equation is used to ensure bounded behavior, while principal fiber bundles and mode groups are used to construct and correct thought paths...

Qiao Yu spoke in a matter-of-fact tone, but when she thought deeply, whether her instantaneous decision-making and value judgments were ideologically driven is difficult to assess from a purely mathematical perspective.

Therefore, he agrees with Peter Schultz's assessment on this point.

Even if they have fully understood the basic framework of metamathematics, it is still a very difficult process for them to think about whether machines possess the consciousness given by mathematics.

Tao Xuanzhi felt that Qiao Yu also used a shortcut in this regard, directly defining consciousness mathematically.

According to Qiao Yu's definition, if a machine has the dynamic ability to instantly find the ethically optimal solution in a continuously changing situation, it can be considered to have consciousness.

Of course, whether this consciousness is different from human consciousness, Tao Xuanzhi suddenly felt that he might never be able to prove it in his lifetime.

So when he spoke again, Tao Xuanzhi immediately changed the subject.

"When are you going back to Bonn? Do you plan to meet with Professor Joe before you go back? I think a face-to-face talk would probably help us understand the situation in July."

Peter Schultz nodded and replied, "That's what I was thinking too, so I haven't booked my return ticket yet."

If possible, we can go and discuss it with him together. It would be even better if we could persuade Professor Joe to let us try out July as well.

Tao Xuanzhi nodded.

He really wanted to try out the artificial intelligence that could assist Qiao Yu in proving the BSD conjecture, and even boast that the proof process was flawless.

Well, it's definitely not just the two of them; mathematicians all over the world probably want to try it out.

An AI assistant that provides readily available, validated tools and can offer proof ideas and refine the proof process is undoubtedly the most perfect assistant for mathematicians, bar none.

……

While the two world-class mathematicians were communicating, the internet was already in an uproar.

Admittedly, Qiao Yu did not invite any media to this mathematics conference, nor did she conduct any live broadcast.

But this is, after all, the internet age. Even mathematicians are participants in the internet.

For example, Tao Xuanzhi particularly enjoys sharing his research on his blog.

Most other mathematicians also have their own X, Facebook, TikTok, blogs, Weibo, Douyin, or other random internet accounts.

Not to mention that many leading mathematicians from home and abroad brought their students to attend this conference.

For these young students, these social media apps are simply an integral part of life.

Sharing one's life has gone from being trendy to being a very ordinary thing.

This time was no exception.

Although the official media did not publicize the conference extensively, participants were not required to keep it confidential.

Soon after, news about Qiao Yu's creation of a meta-mathematical system and general artificial intelligence began to spread all over the internet.

Because it's Sunday, surprisingly, the first heated discussion was initiated by a group of middle school students...

That's right, the first to notice the new mathematical theory were actually a group of junior and senior high school students, and their reaction was full of complaints...

"Holy crap? Another new theory? Do you know how outrageous the reform of math textbooks has become since the release of Joe's algebraic geometry?"
Can you believe we're starting calculus and introductory linear algebra in our second year of high school? And if they come up with new theories, will we have to take advanced math in high school? Please, geniuses, have mercy on these poor kids!

……

I don't know which unlucky kid posted this message online, but it not only resonated with a bunch of middle school students, but also broke the hearts of many parents.

"Who can argue with that? When I was tutoring my eldest child, I felt like I had middle and high school math all under control and didn't need a tutor at all. But when I was tutoring my second child, I couldn't even understand the high school math textbook!"

"As a liberal arts student, let me tell you, I can't even understand my daughter's middle school math textbook, let alone high school math textbooks! I can easily get zero on her tests, so I don't even dare to criticize her for being bad at math!"

"What's this? I suggest you go look at math competition problems right now. My son started learning competitions in elementary school and even won a provincial award. But these past two years he's been finding it harder and harder to concentrate, it's driving me crazy!"

"Sigh, I've decided to give up on math. It's no longer something a normal person can learn!"

Yes, initially, there wasn't much discussion about general artificial intelligence in July. It was mostly students and their parents complaining about the increased difficulty of math learning during the recent general education period.

There's no way around it; I've been holding back these emotions for a long time.

Especially with the significant increase in the difficulty of the college entrance examination math questions for two consecutive years, math has truly become a threshold for entering a good university.

Let's not talk about the difference between top students and poor students.

Nowadays, those who are good at math can pull ahead of those who are average at a score of 40 or 50 points.

In an exam where a difference of four or five points can eliminate a large number of people, those who have taken the college entrance exam probably understand what a score of forty or fifty means...

At this moment, there was truly widespread lamentation... (End of Chapter)