Into Unscientific Chapter 307

  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 slightly, 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

  Xu Yun also knew a few master cake painters when he was writing novels in his previous life, but he has seen such things a lot.

  For example, Pei Tugou, Bai Teman, Tianya Yuezhaojin, etc.

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.

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

  In the original history.

  Let's not talk about ordinary updates, even the 3,000-word textbook review that the Royal Society asked him to write can 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.

  So he stopped what he was going to say, and just smiled a little bit awkwardly, then pretended to be ignorant, and set his eyes on the manuscript in front of him.

   Then look at these manuscripts stuffed into suitcases.

   Gollum—

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

   Oh my god, that tmd is the manuscript of Lows!

   Throughout the history of human science.

  In China in the middle and ancient times, all unknown industry experts basically left some works written by themselves.

  For example, there is no Yang Hui's "Yang Hui Algorithm" in the local area, Lao Su's "Ben Cao Tu Jing" and "Xin Yi Xiang Fa Yao" and so on.

  There are no "Sand's Calculation", "Spiral" and so on in the country.

   And with the development of the scientific level.

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

  Compared to 'writings'.

  Manuscripts are arguably less random, and more error-prone and authoritative.

  For example, the following records may be the inspiration that a certain scholar thought of, the unconstrained thinking of solving problems, and even the graffiti that was left at random during the chat.

  It's like the class notes some students took in the previous life.

  Sometimes one or two months have passed, and even the creator himself may understand the content of the manuscript.

But on the other hand.

  The manuscript may also contain some amazing results.

  For example, some creators have solved the problem, but are sure whether there are errors or omissions in the calculation answer.

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

   Throughout human history.

  The mathematician with the fewest remaining manuscripts is Euler, who is also a god-man.

  I entered Basel Primary School at the age of 13 and graduated at the age of 15.

  Won a master's degree at the age of 16, published a thesis at the age of 19, and became a professor at the Petersburg Academy of Sciences at the age of 26.

  I have written 886 books and papers in my life, with an average of more than 800 pages written every year.

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

   What's even more compelling.

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

   Then I got cataract in my right eye. At the age of 59, in order to treat the degenerative cataract surgery, the doctor in charge poked my right eye blind again. Since then, my right and left eyes have been completely blind.

  The result is in the case of blindness.

  Euler still completed several books and more than 400 papers in oral form, and solved the simple analysis problems such as Yueli that gave Daniel a headache.

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

  As of 2022, that book has been published to 74 volumes, and Amazon is not selling it. It is called "OperaOmnia". (eulerarchive.maa.org/that is the retrieval URL of Euler's papers, the appendix of the anti-bar)

   What's more, it's even worse.

  Can you believe the existing Euler manuscript in the previous life or all of Euler's posthumous works?

   There is a mistake, yes it is all.

  I don't have a considerable part of the manuscript was burned in the Petersburg fire in 1771, and only part of it survives.

  So sometimes he can really be a goddess or someone who is a time traveler, because our resume is too outrageous

   On the other hand.

   If Euler is a well-deserved writing machine.

   It is doubtful that the title of the most valuable manuscript creator should belong to Deuss.

  Compared to Euler's innumerable manuscripts, there are actually not many Dauss manuscripts preserved in the previous life, only 20 notes and less than 80 incoming and outgoing letters.

   But even if there are only a few manuscripts, until 2022 when Gauss traverses, there is not a small pile that has not been deciphered.

   Such as Manuel Bhargava mentioned later.

  My project that won the Fields Medal in 2014 was inspired by the heptad-independent chapter in Lows's "A Quest for Arithmetic".

Of course.

The reason why there are not many manuscripts that can be summarized in the previous life is due to the fact that some creators' handwriting is too sloppy. (sites.pitt.edu/~jdnorton/Goodies/Zurich_Notebook/, that is Einstein The manuscript of the theory of relativity, old favorite words.)

   By the way.

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

   same as Euler at the same time.

   Some of Dies's manuscripts were lost before his death, but a small part of them were caused by man-made disasters-Dies and Weber were inseparable, and Weber and Dies's son-in-law were both one of the gentlemen in Göttingen.

   Therefore, before the death of Lowes, my former residence suffered several illegal break-ins, and many things were lost.

  Riemann mentioned in his letter to Dedekind that the Deus study was violently destroyed.

   Some of these leaked manuscripts returned to collectors. In 2017, no Spanish collector returned two notebooks to Göttingen Primary School.

  It is actually very common in the scientific world to have a peaceful life before death. The most unlucky thing is actually Deus, but Lao Ai:

In the history of science, the little guy who competed with Daniel for the first place in the dog's brain was slowly knocked out. One hour before his death, a doctor named Harvey stole his real brain and cut it into 240 pieces. .

   It was not until seventy-seven years before Lao Ai's death that Harvey gave the old love's cerebellum slice to Princeton Primary School Hospital.

  That is also the real reason why some big stories in the previous life would ridicule slices, although it is estimated that the author who seldom wrote the word "slice" himself did not know that.

  Think of that.

  Gauss sighed from Youyou, and brought his thoughts back to reality.

  I first took out the laboratory gloves from under my body—the gloves in those days were all latex gloves with basic lead carbonate added, and the cost was relatively low, so when doing toxic experiments, I basically brought them with me and used them repeatedly.

  Before putting on gloves.

  Gauss bent his upper body, and finally rummaged through the manuscript of Dies.

   "Thoughts on Low Level Analysis."

   "The problem of Euler's characteristic number in topology"

   "Path Interpretation of Complex Variable Function Theory."

   Lows kept few manuscripts outside the suitcase, and the titles were extremely simple. It was Jia Xue's goal, but it was also quite clear:

  I just want the original manuscripts of these past lives that were lost or have no ordinary meaning.

  As for the manuscripts of non-Euclidean geometry that were published in 1850 but have been fully formed in the previous life, it is by no means the goal of my trip.

after awhile.

  Gauss's eyes suddenly lit up, and he took out a relatively inner manuscript:

"what?"

  I saw a line written under the seal of the manuscript:

  "Affinity Number Calculation".

   Affinity number.

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

  Its interpretation is very complicated:

  The sum of all divisors of each other (divided by itself) is equal to the other two positive integers, such as 220 and 284.

for example.

   Friends who have gone to college should know it.

  220 is divisible by:

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

  The divisor of 284 is:

  1, 2, 4, 71, 142, and exactly 220.

  So 220 and 284 are a pair of affinity numbers.

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

  Pythagoras, the academic giant at the time, had deep and measurable research on number theory, and I was the one who proposed "everything is number".

  My disciples were influenced by me, and the study of numbers was "obsessed", trying to find numbers from everything in the world.

   Results one day.

  My disciple had a whim and asked Pythagoras a question:

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

   As a result, Pythagoras said a very unknown sentence:

  A friend is the shadow of his soul. You should be as close as 220 and 284. You have no one in you, and he has no you in him.

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

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

   It was embarrassing.

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

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

   What's more embarrassing is that hundreds of years ago, the mathematics community still has not found the seventh pair of affinities.

  So Xiaojia finally believed that 220 and 284 were two numbers that Bi Jiaozhu happened to say casually.

  As the research on affinity number decreases, it gradually fades out of people's field of vision.

   Until AD 850, the mathematician Tabit ben Kola, the Almighty King of Arabia, came up with an idea:

  Among the finite natural numbers, there must be only one pair of affine numbers!

  I am the same as previous mathematicians, and I intend to sift from the boundless natural numbers.

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

  The Almighty King gave up the research of other subjects that I didn't have in order to study the affinity number, and he died when he was only 20 years old.

   It's a waste of time and no intention. I finally came up with a rule when I came here:

  a=3X2^(x-1)-1

  b=3X2^x-1

  c=9X2^(2x-1)-1.

  The x outside that is a natural number less than 1. If abc is a prime number, then 2xab and 2xc are a bunch of friendly numbers.

  For example, take x=2, so 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 came out, it proved that Bi Jiaozhu was talking nonsense, and that the affinity number does exist and can be obtained through calculation.

  From there, the end of the story became boring...

  Since before.

  Mathematicians are no longer clueless looking for affinity numbers.

   Instead, while looking for more complex formulas, find the affinity number through a small amount of formula calculations.

   But unfortunately.

  Besides the previous 800 years, mathematicians are the only formula that has not optimized the Almighty King, and a pair of new affinity numbers have not been found.

   That is to say.

  2500 years before Pythagoras, has anyone been able to find the shadow of the seventh pair of affinities!

  That situation lasted until 1636, forcing King Fermat to step down from the stage of history, breaking the historical embarrassment of 2,500 teenagers in one fell swoop.

   That "amateur mathematician" really seems to be on the top. He supports his family during the day and calculates affinity numbers at night, and his mind is buzzing.

  Finally, when I was counting gray hairs, I finally found the seventh pair of affinity numbers:

  17296 and 18416.

  Following Fermat, Descartes also calculated the eighth pair of affinity numbers:

  9437056 and 9363584.

  Then before that is the debut of Ola, a self-propelled manuscript printer with a humanoid form:

  In 1747, that is, when I was 39 years old, I found 30 pairs of affinities in one go!

   Then Xiaojia still had no reaction, and even had time to applaud, and I announced that I had found 30 pairs again.

   But at that point, the affinity number froze:

   It wasn't until 1923 that mathematicians Mai Daqi and Ye Weiler made a surprise move and built the plank road secretly.

  We extended the affinity number to 1095 pairs in one go, the smallest of which even reached 25 digits.

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

Of course.

   Before the computer was invented, the calculation of the affinity number became much more complicated.

   Just like the number of pi has been calculated to 62.8 trillion digits, the number of affinity in previous lives has been locked below 380,000 digits.

   He sees that most people have no boyfriends, but some people are still single.

  Oh, Gauss too, something is up.

all in all.

  After calculating a small number of affinity numbers in the previous life.

   What Gauss expects is not that the volume of manuscripts of Gauss will bring some help to the future, but

  As a well-known unknown prince of mathematics, have I ever calculated the affinity number?

   At most outside of Gaussian cognition.

  Dose's “relics” in his previous life must have that volume of manuscripts—at least the relevant manuscripts can be found outside of these handwritings that have been made public.

  Think of that.

   Gauss glanced at Lows and said:

   "Professor Lows, do you have to select the manuscript before you can view the content?"

   Lows nodded:

   "Of course, the previous content needs to be paid to watch."

  Gauss's answer was within Gauss' expectations, so I was also thinking about bargaining, so I replied immediately:

   "Professor Lows, this is the first manuscript you selected."

   Lows waved his hand when he saw this, meaning to do whatever he wanted.

  Before getting the promise of Lows.

  Gauss solemnly took the manuscript to the desk, and unsealed it with great care.

  The prop used to bind the manuscripts is a red silk thread. Jia Xue took one end of the thread and pulled it like untying a shoelace.

   Whoosh—

  The manuscript unfolded instantly.

  The manuscript is a little thin, probably only one or two sheets.

  Gauss still picked it up with gloves on, 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

  What is common about those numbers? They are all affinity numbers calculated by later generations.

  Then is the formula induced by Euler.

   But when Gauss continued to glance up a few times, my breathing suddenly stopped for a few seconds.

  I saw the upper half of the manuscript, with a few numbers written impressively:

  5564/5020

  6368/6232

  10856/10744

  14595/12285

  18416/17296

  1000452085744/1023608366096

  1001583011750/1019368284250

   At the end of the first group of numbers, a large cloudy white spot can be seen, which is obviously the mark left by the nib of the fountain pen.

   And above the group 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 left side of the formula, there are still a few flying letters.

   translated into Chinese characters is:

  [Forget it if it's too complicated, some people will die].

  Gauss spoke for a long time, then raised his head and looked at Lows.

   Lows blinked:

   "What is he looking at?"

  Gauss raised the manuscript in Yang's hand to me, and said to Lows:

   "Professor Lows, this sentence at the end of your manuscript."

   "Oh, he said this."

   Lows recalled for a few seconds, and soon remembered what Jia Xue said, and explained:

   "Literally, it took you two days before you received Euler's manuscript from Joseph. It should have been two days, if only eight days—anyway, it was very slow to calculate the affinity number of the next hundred groups."

   "Come here, you originally wanted to sum up a corresponding formula, but after half of the calculations, it felt too complicated, so I put it aside."

   "Oh, by the way, Bernhard also calculated that formula eight years later. My evaluation is that you can do it without hands."

  Gaussian:

  Joseph in the mouth of Lows is Joseph Louis Lagrange, who is also Euler's lover and a mathematician with a long history.

  My relationship with Euler is as special as Riemann and Deuss.

  Euler-Lagrange-Cauchy, and Deus-Dirichlet-Riemann, are two very unknown inheritance factions in modern mathematics.

  The other place is under History.

  Lagrangian is also one of the successors of Euler's manuscript, and I will send a letter to Deus.

only

  Dows's words are too tmd shocking, right?

To know.

  Even in 2022, when Gauss traveled through, there is still no unified affinity number formula in the mathematics world.

  Whether it is Euler or Yeweiler, our formula has a certain error rate-for example, Euler missed the number 1184/1210, and it was not calculated by a child prodigy in Italy until 1867.

  The child prodigy's name is Paganini. Every time he thinks of that name, Gauss will think of Pork Tenderloin Panini

  In the previous life, the selection of affinity number is mainly based on approximation and comparison, that is, the output of YES if the condition is met, and NO if it is not.

   To put it bluntly.

  The essence of past life screening is actually exhaustive method.

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

   It is because of the achievements of the seven in history, and Euler has deduced a partial affinity number formula.

   Well, it seems that we can do that step with good intentions.

at the same time.

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

  After the invention of the computer, almost every school of mathematics will invest a small amount of energy and time in affinity numbers.

  But only Deus's Göttingen mathematics school is excluded.

   Whether it is Deus himself, or Riemann, Jacobi, Dedekind or Dirichlet, have we all left any works or records on the study of affinity numbers.

  That is actually a very strange phenomenon, just like the guy who worked on quantum theory in his previous life went to study perturbation theory.

   Now with the words of Dass, everything is finally the truth:

  Co-authors, we have already solved the mystery of the affinity number, and we feel that only the goddess should take care of it.

   Then Lows glanced at Gauss, who was full of ideas.

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

very slow.

  I took out another slightly thicker manuscript from it, handed it to Gauss, and said:

   "Luo Feng, since he is not interested in affinity numbers, the manuscript may suit his taste."

Note:

  The biological clock difference has been adjusted back. Today, I will offer you 7.6k. Please ask for a guaranteed monthly pass. There will be double in that month, and there will be no such thing as September and October.

  (end of this chapter)

Chapter end