Into Unscientific

Chapter 307 Gauss' Treasure (2) (7.6K)

"."

Looking at Gauss who swears, his face is full of blood earned by himself.

Xu Yun opened his mouth lightly, but stopped talking.

He actually wanted to tell Gauss one thing:

Judging from the historical update speed of Faraday's pigeon, his so-called Gagen is probably just a painting

When Xu Yun was writing novels in his previous life, he also knew several pastry painters, but he had seen such things often.

For example, Pei Tugou, Bai Teman, Tianya Yuezhaojin and so on.

Of course.

There are cake-painting masters, and naturally there are honest people.

For example, Xu Yun himself won the praise of a large number of readers with a record of 30,000 daily updates in 2033.

However, judging under normal circumstances, the probability of Faraday being the latter is almost zero.

in the original history.

Not to mention ordinary updates, even the 3,000-word textbook review that the Royal Society asked him to write could be delayed for two years.

Therefore, there is a high probability that Gauss was fooled by this pigeon.

But before the words came out, Xu Yun thought about it.

If I told Gauss about this, I'm afraid there would be no chance to exchange for Gauss's manuscript.

Therefore, he stopped what he was going to say, and just laughed a little bit awkwardly, then pretended to be ignorant, and turned his attention to the manuscript in front of him.

Then look at the manuscripts stuffed into the suitcase.

Gollum—

Xu Yun swallowed heavily, and a hint of excitement flashed in his eyes.

Oh my god, this tmd is Gauss's manuscript!

Throughout the history of human science.

At home and abroad in the Middle Ages, all well-known industry masters basically left some works written by themselves.

For example, there are Yang Hui's "Yang Hui's Algorithm", Lao Su's "Ben Cao Tu Jing" and "Xin Yi Xiang Fa Yao" and so on.

Abroad, there are "Sand Calculation", "Spiral" and so on.

And with the development of scientific level.

When the timeline moved to the 16th century, manuscripts gradually became an alternative carrier for recording scientists' achievements.

Compared with 'writings'.

Manuscripts are undoubtedly much more casual and less accurate and authoritative.

For example, what is recorded above may be the inspiration thought of by a certain scholar, the unconstrained thinking of solving problems, or even the graffiti left at random when bored.

Just like the class notes taken by some students in later generations.

Sometimes in the past one or two months, even the creator himself may not be able to understand the contents of the manuscript.

But on the other hand.

However, the manuscript may also contain some amazing results.

For example, some creators have solved, but are not sure whether there are mistakes or omissions.

Another example is the results that cannot be released due to time constraints, etc.

in human history.

The mathematician who has the most manuscripts is Euler, who is also a god-man who can be called awesome.

He entered the University of Basel at the age of 13 and graduated at the age of 15.

Received a master's degree at the age of 16, began publishing papers at the age of 19, and became a professor at the Petersburg Academy of Sciences at the age of 26.

He wrote 886 books and papers throughout his life, with an average of more than 800 pages per year.

The Petersburg Academy of Sciences has been busy for 47 years in order to organize his works.

What's more interesting.

Euler was almost blind in his right eye when he was 30 years old, and could only see things with his left eye.

Then he got a cataract in his left eye. At the age of 59, he underwent surgery to treat the cataract, and was poked blind by the attending doctor. Since then, he has been completely blind in both eyes.

The result is blindness in both eyes.

Euler still completed several books and more than 400 papers in oral form, and solved complex analysis problems such as Yueli, which caused headaches for Mavericks.

In 1911, the Swiss Natural Science Foundation organized and compiled a "Complete Works of Euler", planning to produce 84 volumes, each of which is a quarto—that is, the size of a newspaper, and a volume is close to 300 pages.

As of 2022, the book has reached 74 volumes and is available on Amazon as OperaOmnia. (eulerarchive.maa.org/This is the search URL for Euler's papers, the appendix of the anti-bar)

What's more, it's even more compelling.

Can you believe that the existing Euler manuscripts are not all of Euler's posthumous works?

True, not all of them.

A considerable part of his manuscript was burned in the Petersburg fire in 1771, and only part of it survives.

So sometimes you really can't help but wonder if someone is a time traveler, because their resume is too outrageous

And on the other hand.

If Euler is a well-deserved writing machine.

Then the title of the most valuable manuscript creator should undoubtedly belong to Gauss.

Compared with Euler's incalculable number of manuscripts, there are actually not many Gaussian manuscripts preserved in later generations, only 20 notes and about 60 incoming and outgoing letters.

But even with such a small number of manuscripts, until 2022 when Xu Yun travels, there are still a lot of them that have not been deciphered yet.

For example, Manuel Bhargava, mentioned earlier.

The project he won the Fields Medal in 2014 was inspired by the chapters related to quadratic forms in Gauss' "A Quadratic Exploration".

Of course.

The reason why many manuscripts in later generations cannot be summarized is largely due to the fact that some creators wrote too sloppily. (sites.pitt.edu/~jdnorton/Goodies/Zurich_Notebook/, this is Einstein's theory of relativity Manuscript, old favorite characters.)

By the way.

Some of these manuscripts can be bought in bookstores, and the handwriting of Mr. Qian Lao and Mr. Huang Weilu is more common in China. Qian Lao's handwriting is super super beautiful.

Same time as Euler.

Some of Gauss's manuscripts were also lost after his death, but most of them were man-made disasters-Gauss and Weber were inseparable, and Weber and Gauss' son-in-law were both one of the Seven Gentlemen of Göttingen.

Therefore, after Gauss' death, his former residence suffered many illegal break-ins and lost many things.

Riemann mentioned the violent destruction of Gauss's study in his letter to Dedekind.

Some of the outflowing manuscripts have entered the hands of collectors. In 2017, a Spanish collector returned two notebooks to the University of Göttingen.

This kind of unsafe thing after death is actually very common in the scientific world. The most unlucky thing is not Gauss, but the old love:

The big guy who competed with the Mavericks for the first place in the history of science until the dog's brain was about to be punched out, was stolen by a doctor named Harvey seven hours after his death and cut into 240 yuan.

It was not until forty-two years after the old love's death that Harvey gave the old love's brain slices to Princeton University Hospital.

This is also the real reason why some novels in later generations will ridicule slices, although it is estimated that many authors who wrote the word "slice" do not know this.

Think here.

Xu Yun couldn't help but sighed faintly, and brought his thoughts back to reality.

He first took out the laboratory gloves from his body - the gloves these days are all latex gloves with basic lead carbonate added, the cost is relatively high, so when doing non-toxic experiments, he basically brings his own and uses them repeatedly .

After putting on the gloves.

Xu Yun bent down and began to search for Gauss' manuscript.

"Thoughts on Advanced Analysis."

"The Euler characteristic number problem in topology"

"Path Interpretation of Complex Variable Function Theory."

Gauss kept a lot of manuscripts in the suitcase with extremely complicated names, but Xu Yun's goal was quite clear:

He only wanted original manuscripts that were lost or had special significance.

As for non-Euclidean geometry, which was not published in 1850, but has been fully formed in later generations, it is definitely not the goal of his trip.

after awhile.

Suddenly, Xu Yun's eyes lit up, and he took out a volume of relatively inward manuscripts:

"Huh?"

I saw a line written on the seal of this manuscript:

"Affinity Number Computation".

affinity number.

The English name of this word is called friendly number, so it is sometimes translated into friendly number or blind date number.

Its interpretation is simple:

Two positive integers whose sum of all divisors of each other (except itself) is equal to the other, such as 220 and 284.

for example.

Friends who have gone to elementary school should know it.

The divisors of 220 are:

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 284;

And the approximate number of 284 is:

1, 2, 4, 71, 142, and exactly 220.

So 220 and 284 are a pair of affinity numbers.

The word first appeared in 320 BC and originated from ancient Greece, one of the birthplaces of Western civilization.

Pythagoras, the academic giant at that time, had unfathomable research on number theory, and he was the proponent of "everything is number".

His disciples were influenced by him, and the study of numbers was even more "obsessed", trying to find numbers from everything in the world.

Results day.

On a whim, his disciples asked Pythagoras a question:

Teacher, when I make friends, will there be a number relationship?

As a result, Pythagoras famously said:

Friends are the shadow of your soul, you should be as close as 220 and 284, there is one in me, and one in you.

This sentence is the root of all evils of affinity numbers.

After the advent of the affinity number, Master Bi did not rest, but led the Bi's school to take the opportunity to publicize "everything is number".

But it's embarrassing.

Bi Jiaozhu has been advocating and researching for decades, but the affinity numbers are still only 220 and 284.

Until the death of Bi Jiaozhu, people's understanding of affinity numbers still remained at 220 and 284.

And what is even more embarrassing is that in the following hundreds of years, the mathematics community still has not found the second pair of affinity numbers.

So everyone began to suspect that 220 and 284 were two numbers that Bi Jiaozhu said casually.

As the enthusiasm for the study of affinity number waned, it gradually faded out of people's field of vision.

It wasn't until AD 850 that the mathematician Tabit ben Kola, the Almighty King of Arabia, came up with an idea:

Among the infinite natural numbers, there must be more than one pair of affinities!

Unlike previous mathematicians, he did not intend to sift through the boundless natural numbers.

Instead, starting from the general law, try to find the general formula of the affinity number.

The almighty king gave up the research of all other subjects in order to study the affinity number, and died in his 20s.

But hard work paid off, and he finally summed up a rule:

a=3X2^(x-1)-1

b=3X2^x-1

c=9X2^(2x-1)-1.

Here x is a natural number greater than 1. If abc is a prime number, then 2xab and 2xc are a bunch of friendly numbers.

For example, take x=2, then a5, b=11, c=71.

So 2×2×5×11=220 and 2×2×71=284 are a pair of affinity numbers.

As soon as the conclusion comes out, it proves that Bi Jiaozhu is not just talking about it, and the affinity number does exist and can be obtained through calculation.

From here, the story starts to get interesting...

since then.

Mathematicians are no longer clueless looking for affinity numbers.

Instead, while looking for a simpler formula, a large number of calculations through the formula are used to find the affinity number.

But unfortunately.

In the following 800 years, mathematicians not only failed to optimize the formula of Almighty King, but also did not find a pair of new affinity numbers.

That is to say.

2500 years after Pythagoras, no one has been able to find the shadow of the second pair of affinities!

This situation lasted until 1636, forcing King Fermat to shine on the stage of history, breaking the historical embarrassment of more than 2,500 years in one fell swoop.

This "amateur mathematician" couldn't stand it anymore. He supported his family during the day and calculated affinity numbers at night, and his mind was buzzing.

Finally, when he counted all the gray hair, he finally found the second pair of affinity numbers:

17296 and 18416.

After Fermat, Descartes also calculated the third pair of affinity numbers:

9437056 and 9363584.

Then there is the debut of Euler, a self-propelled humanoid manuscript printer:

In 1747, when he was 39 years old, he found 30 pairs of affinities in one breath!

Then before everyone reacted, and before they even had time to applaud, he announced that he had found 30 pairs again.

But at this point, the affinity number froze:

It wasn't until 1923 that mathematicians Mai Daqi and Ye Weiler made a surprise plank plank road and darkened Chencang.

They extended the number of affinities to 1095 pairs in one go, the largest of which even reached 25 digits.

Between 1747 and 1923, mathematicians calculated only 217 pairs of affinities using Euler's formula.

Of course.

With the invention of the computer, the calculation of the affinity number is much simpler.

Just as pi has been calculated to 62.8 trillion digits, the affinity number of later generations has been locked to more than 380,000 digits.

You see, all the numbers have girlfriends, but some people are still single.

Oh, so is Xu Yun, that's all right.

all in all.

Under the premise that a large number of affinity numbers have been calculated by later generations.

What Xu Yun expects is not how much help Gauss's manuscript can bring to the future, but rather

Gauss, as the well-known prince of mathematics, has he ever calculated the affinity number?

At least in Xu Yun's perception.

This volume of manuscript must not be included in the "relics" of Gauss in later generations-at least the relevant manuscripts cannot be found in the handwriting that has been made public.

Think here.

Xu Yun couldn't help but glanced at Gauss, and said:

"Professor Gauss, do I have to select a manuscript before I can view the content?"

Gauss nodded:

"Of course, follow-up content needs to be paid to watch."

Gao Si's answer was within Xu Yun's expectations, so he didn't think about bargaining or anything, and immediately replied:

"Then, Professor Gauss, this is the first manuscript I selected."

Gauss waved his hand when he saw it, meaning to do as you like.

After getting the promise of Gauss.

Xu Yun solemnly took the manuscript to the desk, and carefully unsealed it.

The prop used to bind the manuscripts was a red silk thread. Xu Yun held one end of the thread and pulled it like untying a shoelace.

call out--

The manuscript unfolded in an instant.

This manuscript is surprisingly thin, about one or two pages long.

Xu Yun picked it up still wearing gloves, and looked at it seriously.

There are several numbers recorded at the beginning of the manuscript, which are:

220/284, 2924/2620, 17296/18416, 9437056/9363584

These numbers are nothing special, they are the affinity numbers calculated by the predecessors.

Then there is the formula induced by Euler.

But when Xu Yun continued to glance down a few times, his breathing suddenly stopped for a few seconds.

I saw a few numbers in the lower half of the manuscript:

5564/5020

6368/6232

10856/10744

14595/12285

18416/17296

1000452085744/1023608366096

1001583011750/1019368284250

A small, distinct black dot can be seen at the end of the last set of numbers, apparently left by the nib of the fountain pen.

And below this set of numbers, you can also see a formula:

σ(z)=σ(xy)=1 +[σ(x)-1]+[σ(y)-1]+[σ(x)-1][σ(y)-1]=1+σ (x)+σ(y)- 2 +σ(x)σ(y)-σ(x)-σ(y)+ 1 =σ(x)σ(y)

D(x)=x(1 +12+13++1x2)≈x[ln(x/2+1)+r]≈x(lnx- 0.116).

In addition, on the right side of the formula, there are still a few flying letters.

Translated into Chinese characters is:

[Too simple to count, boring to death].

"."

Xu Yun was speechless for a long time, then raised his head and looked at Gauss.

Gauss blinked:

"What are you looking at?"

Xu Yun gently raised the manuscript in his hand towards him, and said to Gauss:

"Professor Gauss, that sentence at the end of your manuscript."

"Oh, you said that."

Gauss recalled for a few seconds, and quickly remembered what Xu Yun said, and explained:

"Literally, it took me two days after I received Euler's manuscript from Joseph. It should have been two days, or three days—anyway, I quickly calculated hundreds of affinity numbers. "

"Later, I originally wanted to sum up a corresponding formula, but it was too simple to calculate half of it, so I put it aside."

"Oh, by the way, Bernhard also calculated this formula three years ago, and his evaluation is as long as you have a hand."

Xu Yun:

"."

The Joseph Gauss spoke of was Joseph-Louis Lagrange, who was also Euler's lover and a mathematician with a long history.

His relationship with Euler is almost equivalent to that of Riemann and Gauss.

Euler-Lagrange-Cauchy, and Gauss-Dirichlet-Riemann, these are two well-known inheritance factions in modern mathematics.

Also in history.

Lagrange is also one of the successors of Euler's manuscript, and it is normal for him to send a letter to Gauss.

only

Gauss's words are too tmd shocking, right?

To know.

Even in 2022, when Xu Yun traveled, the mathematics world still does not have a unified affinity number formula.

Whether it is Euler or Yeweiler, their formulas have a certain error rate-for example, Euler missed the number 1184/1210, and it was not calculated by an Italian prodigy until 1867.

The name of this child prodigy is Paganini. Every time Xu Yun thinks of this name, he will think of Pork Tenderloin and Egg Panini.

The selection of affinity numbers in later generations is mainly based on approximation and comparison, that is, the output YES that meets the conditions, and NO otherwise.

To put it bluntly.

The essence of screening for future generations is actually exhaustive method.

As a result, in the era of 1850, both Gauss and Riemann actually derived the standard formula of affinity number?

However, considering the achievements of these two in history, and Euler has already derived a partial affinity number formula.

Well, it's no surprise that they've made it this far.

at the same time.

This can be regarded as solving a puzzle in the history of mathematics:

Before the invention of computers, almost every school of mathematics devoted a lot of effort and time to affinity numbers.

But Gauss's Göttingen school of mathematics is the only exception.

Whether it is Gauss himself, or Riemann, Jacobi, Dedekind or Dirichlet, none of them have left any works or records on the study of affinity numbers.

This is actually a very strange phenomenon, which is as contrary to the harmony as the masters of quantum theory in later generations who did not study perturbation theory.

Now with the words of Gauss, everything is finally revealed:

The co-authors have already solved the mystery of the affinity number, and they thought it was too simple so they didn't care about it.

Then Gauss glanced at Xu Yun, who was a little unsure.

After pondering for a moment, he took the initiative to go to the side of the suitcase and rummaged a few times.

soon.

He took out another manuscript that was a little thicker, handed it to Xu Yun, and said:

"Luo Feng, since you are interested in affinity numbers, this manuscript may suit your taste."