Scholar's Advanced Technological System

Chapter 1378: “Counter-intuitive” Conjecture

The ABC conjecture was not the same as other mathematical conjectures. Its biggest difficulty was not in calculations, nor in the abstraction of the proposition itself, but the fact that its existence was completely counter-intuitive.

Simply put, let three numbers be a, b, and c, where c=a+b. If these three numbers were relatively prime, then to multiply the prime factors of these three numbers to get d. It seemed like d would obviously be larger than c.

For example, let a=2, b=7, c=a+b=9, d=2×7×3=42, d was obviously much larger than c.

However, this was completely contrary to people’s intuition.

There were many counterexamples.

For example, let the triplet be (5, 27, 32), d=30, which was obviously smaller than 32.

Mathematicians went to the next level and modified Joseph Oesterlé’s original expression, magnifying rad(abc) and replacing it with a power of r greater than 1. Which became rad(abc)^(1+ε).

For any real number ε greater than zero, there existed a counterexample of d=rad(abc)^(1+ε)>c!

However, the number of these counterexamples was limited!

Ever since this question was raised, because of its “counter-intuitive” characteristics, it had always been a top problem that plagued mathematics.

In the algebraic sense, the interaction between addition and multiplication corresponded to infinite possibilities. Therefore, the prime factors of two natural numbers and the prime factors of their sum should not be mathematically related.

However, the magic of the ABC conjecture lied here.

It connected two unrelated algorithms in the eyes of mathematicians in a magical way and related the mathematical laws between the two.

Even if it looked wrong at first glance, no one could prove it. Based on the results of distributed computing, it was actually likely to be correct.

History showed that countless scientific conclusions such as “Newton’s Theorem of Inertia” and “Galileo’s Leaning Tower of Pisa Experiment”, which seemed to violate common sense at the time, were finally successfully proven.

Moreover, after these counter-intuitive theories were confirmed, without exception, they greatly promoted the development of science at that time.

Like Professor Dorian M. Goldfeld said, the ABC conjecture was not as well-known as Fermat’s Last Theorem. Many people wonder why mathematicians should research a conclusion that already seemed to be true. But because of its unique counter-intuitive characteristics, its value was no less than Fermat’s Last Theorem.

If this conjecture was proven, many famous Diophantine problems would be instantly solved.

And this included Fermat’s Last Theorem…

After returning from Professor Perelman, Lu Zhou went straight back to his office at the mathematics department.

Compared to the environment at the Jinling Institute for Advanced Study and the launch site, he still preferred the academic atmosphere for studying mathematical problems.

After asking Assistant Zhao to make a cup of coffee, Lu Zhou, who had been sitting at the desk for a long time, took out a pen from the pen holder and thought quietly as he looked at a blank piece of scratch paper.

In fact, he wasn’t just worried about pure academic issues.

There was also the so-called “Holy Relic”.

Compared to the Mars landing office and Chang’an Avenue, he actually knew more about the whole story.

This was not only because he was the person in charge of the Outlier 128 project, but also because he had experienced three pieces of memories about the civilization of the old universe, and he had even communicated face to face with The Observer’s civilization.

All kinds of clues indicated that the Holy Relic was probably not an extraterrestrial civilization; at least, it was not the kind of extraterrestrial civilization imagined by most people. Instead, it was an “item” sent by The Observer civilization to the solar system; one that could change the fate of the universe.

According to them, it was a gift.

But due to various reasons, just like mistakes in an experiment, this gift not only arrived in the solar system billions of years in advance, but it also fell in the hands of a civilization that had nothing to do with their plan.

Analyzing it from this perspective, it was quite possible that it came from the old universe.

According to Dr. Fan Tong’s experience, Lu Zhou made the bold assumption that the so-called Martian civilization that had disappeared might have been “enlightened” by the “item”.

After all, they called it the “Holy Relic”.

“Is solving the ABC conjecture a prerequisite for conversation?

“I originally thought that the first conversation between human civilization and other civilizations would probably start with the dismantling of large prime numbers or other more concise questions…

“The mathematical threshold of this conjecture is too high.”

Unlike the simple and easy-to-understand numbers such as Pi and Planck’s constant, mathematical conjecture involved not only mathematical laws but also human mathematicians’ understanding of mathematics.

In Lu Zhou’s opinion, using mathematical conjectures to converse was definitely not the best choice for communication.

Of course, the premise was that both parties wanted to communicate.

Testing the other party was another story.

Perhaps it was an illusion, but Lu Zhou, who had read the report of project 128, always felt that although the “Holy Relic” was curious about human civilization, it didn’t seem like it really wanted to communicate with them.

In his opinion, this mathematical conjecture was to “embarrass” human civilization.

Lu Zhou was thinking about it randomly while looking at a blank piece of scratch paper. A bunch of bubbles suddenly popped up in the lower corner of the laptop next to him.

[Master, you have mail!]

New mail?

Lu Zhou thought about who would send an email to himself at this time and spoke.

“Open it for me.”

The text bubbles disappeared.

The browser opened, and the email soon appeared in front of Lu Zhou.

The content of the email was short. The body contained only one sentence.

[I’ve been waiting for you for half a year. Have you finished handling the matter at hand?

[Signed by—

[Satoshi Nakamoto.]

When Lu Zhou saw this email, he was still a little bit confused. But when he saw the signed name at the bottom, he immediately knew what the email meant.

At the same time, the expression on his face became weird.

Around the end of last year, when Lu Zhou had just completed the 524-qubit computer and the “Theory of Void”, an anonymous email address with Satoshi Nakamoto’s ID sent him an email saying that he planned to discuss academic issues with him.

Lu Zhou was curious about the mysterious Bitcoin founder. He promised him at the time that he would send him an email back when he finished the matter at hand.

Then, he went to Stockholm and encountered a thrilling incident on the way to Copenhagen on the cruise ship. He had completely forgotten about the agreement after returning home.

But, to be honest, this was not his fault.

After all, he had never actually finished his “matter at hand”…

Even now.

Lu Zhou looked at the e-mail and couldn’t help but feel a little embarrassed.

What do I do?

I’m not in the mood to discuss cryptography…

What is there to even discuss?

Just when Lu Zhou was wondering whether he should just ignore the email, he suddenly had a brilliant idea. He quickly typed on the keyboard and wrote an email.

[I’m sorry I didn’t reply to your message in time. After returning from Stockholm, there were too many things that occupied my time, such as the research I am working on at the moment.

[Of course, if you can help me solve this problem, it would be great. I promise that I will help you with whatever you want to discuss.]

This is probably the best way to reject him.

At the end of the email, Lu Zhou typed out the ABC conjecture and clicked the “Send” button. He then closed his laptop and looked at the blank paper on his desk.

Time slowly passed by.

When Lu Zhou had gradually entered a flow state, the screen of his mobile phone suddenly flickered.

[Master, you have a reply! (๑•̀ᄇ•́)و✧]

Reply?

Already?

When Lu Zhou looked at the text bubbles on the screen, he was stunned.

Out of curiosity about the reply, he couldn’t help but open his computer and log into his email again.

Just like the previous email, this reply only had one short line.

[I have researched this problem before. If you are interested, I have attached the proof method.]

Lu Zhou: “…?!”