Mathematical puzzles. The Chelyabinsk mathematician solved one of the problems, the millennium, for a million dollars ... Can the equality of the cat scientist be true?
Circle 6 class
Head Evgeny Alexandrovich Astashov
2012/2013 academic year
Lesson 1. Tasks for dating
Teachers have collected written works and recount them before checking. Irina Sergeevna put them in piles of a hundred works. Daniil Alekseevich can count five works in two seconds. What is the shortest time he can count 75 papers to check? a) Propose a set of three weights, each of which weighs an integer number of grams, so that with their help on a pan balance without divisions, you can weigh any integer weight from 1 to 7 grams. b) Wouldn't a set of some two weights (not necessarily with integer masses) suffice for this purpose?Solution. Those interested only in mathematics are four times more interested in both subjects; those interested only in biology are three times more interested in both subjects. This means that the number of those who are interested in at least one of the two subjects must be divisible by 8 (there are 8 times more of them together than those who are interested in both subjects). 8 and 16 are not enough because 16 + 2 = 18< 20 (не забудем посчитать Олега и Пашу); 32, 40 и т.д. — много; 24 подходит. Итак, в классе 24 человека, которые интересуются математикой или биологией (а может быть, и тем, и другим), а ещё есть Олег и Паша. Таким обраом, всего в классе 24 + 2 = 26 человек.
The way to cut off all the heads and tails of the Snake in 9 hits is given in the answer. Let us now prove that this cannot be done in fewer strokes.
Ivan Tsarevich can use three types of strikes:
A) cut off two tails, one head will grow;
C) cut off two heads;
C) cut off one tail, two tails will grow (essentially - just add one tail).
It is useless to cut off one head, so we will not use such blows.
1. The number of Type A strokes must be odd. In fact, only with such strikes does the parity of the number of goals change. And the parity of the number of goals should change: at first there were 3 of them, and at the end there should be 0. If such strikes are made even number, the number of goals will remain odd (and therefore will not be equal to zero).
2. Since it is only by blows of type A that the number of tails can be reduced, one such blow will not suffice. Therefore, there should be at least two such strikes, and taking into account the previous paragraph, there should be at least three of them.
3. After three hits of type A, three new heads will grow, and a total of 6 heads will need to be chopped off. This will require at least 3 Type B hits.
4. To chop off 3 times two tails with blows of type A, you need to have 6 tails. To do this, you need to "grow" three additional tails, making 3 hits of type C.
So, you need to make at least three blows of each of the indicated types; in total - at least 9 strokes.
Every student in our schools studies mathematics. Most of them find this subject difficult, which is true. Teachers and parents do a lot so that students do not give up, overcoming learning difficulties, are not passive in the classroom ... but the problems that arise in this process do not decrease. Therefore, it is necessary to develop an interest in mathematics, using even the slightest inclinations of the student. For this purpose, we have made a selection of competitions that can be used to a greater extent in extracurricular work in mathematics (weeks of mathematics, KVN, evenings, etc.), but creatively working teachers find a place for some of them in the classroom.
< Рисунок 1> .
I. AUNKION
a) Auction of proverbs and sayings with numbers.
By drawing lots, the team that calls the proverb first is revealed, after hitting the leader with the gavel, a member of the second team calls the proverb, etc. The last one to say a proverb wins.
Note that you can limit yourself to a specific number. Name proverbs and sayings where the word seven occurs. For example: “Measure seven times, cut once”, “Seven do not expect one”, “Seven nannies have a child without an eye”, “One with a bipod, seven with a spoon”, “Seven troubles - one answer”, “Behind seven locks ”, “Seven Fridays in a week”, etc.
b) An auction of films with a number in their title.
c) Auction of songs in which there is a number.
It is enough to name a line with this number or sing it.
d) Charade auction.
The charade is a special mystery. It is necessary to guess the word in it, but in parts. You can alternate charades where there is a mathematical element and it is not.
The first is a round object,
The second is something that is not in the world,
But what scares people?
The third is union. (Answer: charade).To the name of the animal
Set one of the measures.
You will receive a full-flowing
river in former USSR. (Answer: Volga).You will find the first syllable among the notes,
And the bull carries the second.
So look for it on the way
Do you want to find the whole? (Answer: road).For the measure, you will suddenly insert a note
And you will find the whole among your friends. (Answer: Galya).
e) Auction on a given topic. Tasks are put up for auction on a topic that is communicated to students in advance. Let, for example, it will be the topic “Actions with algebraic fractions”.
4-5 teams participate in the competition. Lot No. 1 is projected on the screen - five tasks for reducing fractions. The first team chooses a task and assigns it a price from 1 to 5 points. If the price of this team is higher than those given by others, it receives this task and completes it, the rest of the tasks must be bought by other teams. If the task is solved correctly, the team is awarded points - the price of this task, if incorrect, then these points (or part of them) are removed. Pay attention to one of the advantages of this competition: when choosing an example, students compare all five examples and mentally “scroll” in their head the course of their solution.
II. CHAIN OF WORD
The facilitator says one word. The first captain (if this happens at KVN) repeats this word and adds his own. The second captain repeats the first two words and adds his own and so on. One of the referees watches the game, writing down the words in order. The winner is the one who names more words in creating a complete sentence.
a). Triangles are equilateral if all angles are equal or all sides are equal.
b). However, there are isosceles, which means that the angles at the base are then forty-five degrees.
III. EACH HAND IS OWN BUSINESS
The players are given a sheet of paper and a pencil in each hand. Task: draw 3 triangles with your left hand, and 3 circles with your right hand; or the left one writes even numbers (0, 2, 4, 6, 8), the right one writes odd numbers (1, 3, 5, 7, 9).
IV. STEP - IMAGINE
Participants of this competition stand next to the leader. Everyone takes the first steps, at this time the leader calls some number, for example 7. In the next steps, the guys should call numbers that are multiples of 7: 14, 21, 28, etc. For each step - by number. The leader goes with them in step, not letting them slow down. As soon as one makes a mistake, he stays in place until the end of the other's movement. Other topics: repetition of the multiplication table; raising numbers to a power; extracting the square root; finding a part of a number.
V. YOU - TO ME, I - TO YOU
< Рисунок 2>
The essence of the competition is clear from the name. Here is an example of tasks exchanged between captains at KVN.
1. Wolf solved the example: 4872 ? 895 = 4360340 and started doing the division check. The hare looked at this equality and said: “Do not do extra work! And it's clear that you're wrong." The wolf was surprised: “How do you see it?” What did the rabbit say?
(Answer: one of the factors is a multiple of three, but the product is not).
2. In September, Petya and Styopa went to music lessons: Petya - by numbers divisible by 4, and Styopa - by numbers divisible by 5. Both went to the sports section by numbers divisible by 7. The rest of the days were spent fishing. How many days did the guys go fishing?
(Answer: 15).
3. "What time is it?" - asks the Wolf Hare. “The given time is a multiple of 5, and the time of day in hours is a multiple of the given one,” said the Hare. “That can't be!” Wolf was outraged. And what do you think?
(Answer: 15).
4. Vova claimed that this year there would be a month with five Sundays and five Wednesdays. Is he right?
Solution. Consider the most favorable case, when there are 31 days in a month.
31 = 4 * 7 + 3 and among three consecutive days of the week cannot be both Sunday and Wednesday, but only one of these days, then this month can have either 5 Sundays and 4 Wednesdays, or 4 Sundays and 5 Wednesdays. Therefore, Vova is wrong.
5. There are cereals, vermicelli and sugar in three boxes. On one of them is written “Groats”, on the other - “Vermicelli”, on the third - “Groats or sugar”. What is in which box if the contents of each of them do not correspond to the inscription?
(Answer. In the box with the inscription “Groats or sugar” there is vermicelli, with the inscription “Vermicelli” - cereals, with the inscription “Groats” - sugar).
6. The figure shows the houses in which Igor, Pavlik, Andrey and Gleb live. Igor's house and Pavlik's house are the same color, Pavlik's house and Andrey's house are the same height. Who is in what house< Рисунок 3>
VI. RACE FOR THE LEADER
< Рисунок 4>
In order for the guys to leave the event without being upset by the defeat, you can hold this competition and try to make a draw. According to the current situation, by this time, team members or their fans can give answers to the tasks below.
What an acrobat figure!
If you stand on your head,
Exactly three will be less. (Answer: number 9).
I am a number less than 10.
It's easy for you to find me
But if you command the letter "I"
Stand next to me - I am everything!
Father and grandfather, and you and mother. (Answer: family).
Arithmetic sign,
In the problem book you will find me in many lines,
Only "o" you insert, knowing how,
And I am a geographical point. (Answer: plus-pole.)
Zero turned his back to his brother,
He got up quickly.
Brothers have become a new figure,
We can't find the end in it.
You can turn it
Put your head down.
The number will remain the same.
Well, think?
So say! (Answer: number 8).
Dozens turned into hundreds
Or maybe turn into millions.
He is equal among numbers,
But it cannot be divided. (Answer: number 0).
Note that the tasks are not given in the form of tasks, as in the contest “You - to me, and I - to you”, but in verses it is no coincidence. Before this competition, the guys have already worked hard. It is necessary to try to change the intensity of passions, to capture the attention of the majority, which may have already dissipated. And this can be helped by a poem that appears, for example, on a portable board, prepared in advance. With the correct answer to the question posed there (task 5), the presenters present this answer with a colorful picture like this:
< Рисунок 5>
Another approach is also possible: use team artists. According to the model, they will quickly complete drawings on the board. You can pick them up not difficult from different sources. For example, see the bibliography.
VII. A DARK HORSE
< Рисунок 6>
For this competition, we selected tasks in which it is necessary to find out whether the answer to the question posed is possible.
1. We multiply both parts of the inequality 9>5 by a 4 . Is it possible to assert that the inequality 9a 4 >5a 4 is true?
(Answer: no. With a=0 we get 9a 4 =5a 4 since 0=0).
2. Can equality be true?
(Answer: yes, it can. For example, with x=y=1).
3. Can a triangle be cut so that three quadrangles are obtained? (Answer: yes).
For example:
< Рисунок 7>
4. After drawing 2 straight lines, is it possible to divide the triangle into a) two triangles and one quadrangle, b) two triangles, two quadrangles and one pentagon.
a)< рисунок 8>
b)< рисунок 9>
VIII. PORTRAIT COMPETITION
The team is shown a portrait of a mathematician. You need to give his last name. The competition can be complicated if asked to name the area of activity.
IX. COMPETITION OF ERUDITES
a) An erudite member of one team calls the surname of a mathematician, and the other one calls a mathematician whose surname begins with last letter the first scientist, etc.
Or the erudite of the second team names the surname of the mathematician, starting with any letter in the surname of the first scientist, and so on.
b) Two students participate in the erudite competition: A and B.
Questions are asked to each participant in the struggle for the title of erudite.
A. 5 2 =?; 7 2 \u003d?, and what is the angle squared? (Answer: 25; 49; 90 0).
B. There were seven sparrows in the garden. A cat crept up to them and grabbed one. How many sparrows are left in the garden? (Answer: one).
A. What did the word “mathematics” originally mean? (Answer: knowledge, science).
B. From what word does the name of the number zero come from? (Answer: from the Latin word "nulla" - empty).
A. Calculate: (-2)? (-1)…3=? (Answer: 0.)
B. Calculate: (-3)+(-2)+…+3+4=? (Answer: 4.)
BUT; B. Name the old Russian measures of length in turn. (Answer: sazhen, span, quarter ...)
X. HISTORIAN COMPETITION
Required to tell interesting story from the life of a famous mathematician, or to highlight the essence of a fact visually presented in the form of a scene. Example: An old man bent over a drawing, and behind him is a warrior with a dagger.
Legend. Only because of treason Syracuse was taken by the Romans. “At that hour, Archimedes was carefully examining some kind of drawing and did not notice either the Roman invasion or the capture of the city. When suddenly a warrior appeared in front of him and announced that Marcellus was calling him, Archimedes refused to follow him until he had completed the task and found the proof. The warrior got angry, drew his sword and killed Archimedes.
Archimedes was born in 287 BC. in the city of Syracuse on the island of Sicily, which is part of present-day Italy. Archimedes began to be interested in mathematics, astronomy, and mechanics at an early age. The ideas of Archimedes were almost 2 millennia ahead of their time. Archimedes died during the capture of Syracuse in 212 BC.
XI. KNEW CONTEST
Participants in this competition give answers to the questions:
a) about mathematicians;
b) about terms;
c) about formulas;
d) solve crossword puzzles, puzzles.
Rebus example:
< Рисунок 10>
(Answer: fraction).
To prepare students and conduct competitions for scholars, historians, know-it-alls, it is useful to adopt an encyclopedia for children. She will answer all your questions. You will find about two hundred mathematicians in the "Index of Names" section, where there are links to the pages of this book: what is important they have done.
Literature
- Alexandrova E.B. Journey through Karlikania and Al-Jebra / E.B. Alesandrova, V.A. Levshin. - M .: Children's literature, 1967. - 256 p.
- Gritsaenko, N.P. Well, decide!: book. for students / N.P. Gritsaenko. - M: Education, 1998. - 192 p.
- Lanina I.Ya. Not a single lesson: The development of interest in physics. - M.: Enlightenment, 1991.-223 p.
- Mirakova T.N. Developmental tasks in mathematics lessons in grades V-VIII: a guide for the teacher.
- Petrovskaya N.A. An evening of cheerful and savvy in the IV grade / “Mathematics at school”. -1988. - No. 3. - P.56.
- Samoilik G. Educational games.-2002.-№24.
- Encyclopedia for children. T.11. Mathematics / chapters. ed. M.D. Aksenova. – M.: Avanta +, 2002. – 688 p.
The scientist proved the equality of classes P and NP, for the solution of which the Clay Mathematical Institute awarded a prize of one million US dollars.
Anatoly Vasilyevich Panyukov spent about 30 years in search of a solution to one of the most difficult tasks of the millennium. Mathematicians all over the world have been trying for many years to prove or disprove the existence of the equality of the classes P and NP, there are about a hundred solutions, but none of them has yet been recognized. On this topic, which is related to this problem, the head of the SUSU department defended his Ph.D. and doctoral dissertations, but, as it seems to him, he found the right answer only now.
The problem of equality P = NP is this: if a positive answer to some question can be quickly checked (in polynomial time), then is it true that the answer to this question can be quickly found (in polynomial time and using polynomial memory)? In other words, is it really not easier to check the solution of the problem than to find it?
For example, is it true that among the numbers (−2, −3, 15, 14, 7, −10, …) there are such that their sum is equal to 0 (subset sum problem)? The answer is yes, because −2 −3 + 15 −10 = 0 is easily verified by a few additions (the information needed to verify a positive answer is called a certificate). Does it follow that it is just as easy to pick up these numbers? Is checking a certificate as easy as finding it? It seems that picking up numbers is more difficult, but this has not been proven.
The relationship between the classes P and NP is considered in the theory of computational complexity (a branch of the theory of computation), which studies the resources needed to solve a certain problem. The most common resources are time (how many steps to take) and memory (how much memory is required to complete the task).
— I discussed the result of my work at a number of interdistrict conferences and among professionals. The results were presented at the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences and in the journal Avtomatika i Mekhanika, published by Russian Academy Sciences, - Anatoly Panyukov, Doctor of Physical and Mathematical Sciences, told Good News. – The longer professionals cannot find a refutation, the more correct the result is considered.
The equality of classes P and NP in the mathematical world is considered one of the urgent problems of the millennium. And it lies in the fact that if the equality is true, then most of the actual optimization problems can be solved in a reasonable time, for example, in business or in production. Now the exact solution of such problems is based on enumeration, and can take more than a year.
“Most scientists are inclined to the hypothesis that the classes P and NP do not coincide, but if there is no error in the evidence presented, then this is not so,” said Anatoly Panyukov.
If the proof of the Chelyabinsk scientist turns out to be correct, then this will greatly affect the development of mathematics, economics and technical sciences. Optimization tasks in business will be solved more accurately, hence there will be more profit and less costs for a company that uses special software to solve such problems.
The next step in recognizing the work of the Chelyabinsk scientist will be the publication of evidence at the Clay Mathematical Institute, which announced a million dollar prize for solving each of the millennium problems.
At present, only one of the seven millennium problems (the Poincaré hypothesis) has been solved. The Fields Prize for her solution was awarded to Grigory Perelman, who refused it.
For reference: Anatoly Panyukov (born in 1951) Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Economic and Mathematical Methods and Statistics at the Faculty of Computational Mathematics and Informatics, Member of the Association for Mathematical Programming, Scientific Secretary of the Scientific and Methodological Council for Mathematics Ministry of Education and Science of the Russian Federation (Chelyabinsk Branch), member of the Scientific and Methodological Council of the Territorial Body of the Federal State Statistics Service for Chelyabinsk region, member of dissertation councils in the South Ural and Perm public universities. Author of more than 200 scientific and educational publications and more than 20 inventions. Head of the scientific seminar "Evidence-Based Computing in Economics, Engineering, Natural Science", whose work was supported by grants from the Russian Foundation for Basic Research, the Ministry of Education and the International Science and Technology Center. He prepared seven candidates and two doctors of sciences. He has the title of "Honored Worker high school RF" (2007), "Honorary Worker of the Higher vocational education"(2001)," Inventor of the USSR "(1979), awarded a medal USSR Ministry of Higher Education (1979) and a Certificate of Honor from the Governor of the Chelyabinsk Region.
On this page I post puzzles intended for Olympiad classes in grades 5-6. If a math tutor asked you an original rebus and you don’t know how to solve it, send it to me by mail or leave an appropriate entry in the feedback box. It can be useful to other tutors of mathematics, as well as teachers of circles and electives. I look through the Olympiad problems on different sites, sorting them by class and difficulty level for posting on the site. This page contains a collection of entertaining puzzles collected over the years of tutoring. Gradually the page will fill up. Tasks are standard. The same letters represent the same numbers, and different letters represent different numbers. You need to restore the records in accordance with this order. I use puzzles when preparing for the Kurchatov school in the 4th grade, also to awaken my love for mathematics.
Mathematical puzzles for the work of a tutor
1)Multiplication rebus with repeating letters A, B, and C The same letters in the multiplication example must be replaced with the same numbers.
2) rebus mathematics Replace in the word "mathematics" identical letters with the same numbers so that all five actions received have equal answers.
3) Rebus Chai-Ai. Indicate some solution to the rebus (according to tradition, the same letters hide the same numbers, and different ones hide different ones).
4) Mathematical rebus "scientist cat". Can the indicated equality turn into true if instead of its letters we put numbers from 0 to 9? Different to different, same to same.
math tutor's note: The letter O does not have to correspond to the number O.
5) An interesting puzzle was offered to my student at the last Internet Olympiad in mathematics for grade 4.
Ten days ago, Indian mathematician Vinay Deolalikar posted an article on the Web in which, he claims, he proved one of the most important inequalities in mathematics - the inequality of complexity classes P and NP. This message caused an unprecedented resonance among Deolalikar's colleagues - scientists abandoned their main work and began to read and discuss the article en masse. Almost immediately, experts discovered shortcomings in the proof, and a week later the mathematical community came to the conclusion that Deolalicar had failed to cope with the task.
Application for a million
The problem of the inequality of classes P and NP is one of the most intriguing in mathematics, even though most specialists are already sure that they are not equal (all scientists admit that until a strict evidential foundation is put in the basis of certainty, it will remain in the realm of intuition, not science). The significance of this problem, which the Clay Institute of Mathematics has included in its list of seven millennium problems, is enormous and extends not only to "speculative" mathematics, but also to computer science and the theory of computation.
Briefly, the problem of inequality of complexity classes P and NP is formulated as follows: "If a positive answer to a certain question can be quickly checked, then is it true that you can quickly find the answer to this question." The problems for which this problem is relevant belong to the NP complexity class (problems of the P complexity class can be called simpler in the sense that their solution can definitely be found in a reasonable time).
One example of problems of complexity class NP is cipher breaking. To date the only way to solve this problem is to enumerate all possible combinations. This process can take an extremely long time. But when the correct code is found, the attacker will instantly understand that the problem has been solved (that is, the solution can be verified in a reasonable time). In the event that the complexity classes P and NP are still not equal (that is, problems whose solution cannot be found in a reasonable time cannot be reduced to more simple tasks, which can be solved quickly), then all the criminals of the world will always have to open brute-force ciphers. But if it suddenly turns out that inequality is actually equality (that is, complex NP problems can be reduced to simpler class P problems), then brainy thieves could theoretically come up with a more convenient algorithm that will allow them to break any ciphers much faster.
Simplifying very much, we can say that a rigorous proof of the inequality of complexity classes P and NP will finally and irrevocably deprive humanity of the hope of solving complex problems (problems of complexity class NP) except by blunt enumeration of all feasible solutions.
As always happens with problems of particular importance, attempts to prove rigorously that the classes P and NP are equal or not equal are regularly made. Usually, statements on the solution of the Millennium Problem are made by people whose reputation in the scientific world, to put it mildly, is doubtful, or even by amateurs who do not have special education but mesmerized by the magnitude of the challenge. None of the truly recognized experts similar works does not take seriously, just as physicists do not take seriously the periodic attempts to prove that general theory relativity or Newton's laws are fundamentally wrong.
But in this case, the author of the work, uncomplicatedly titled "P is not equal to NP", was not a pseudo-scientific lunatic, but a working scientist, and working in a very respected place - Hewlett-Packard Research Laboratories in Palo Alto. Moreover, a positive review of his paper was given by one of the authors of the Millennium P and NP Inequality Problem, Stephen Cook. In the cover letter that Cooke sent to colleagues along with the paper (Cook was one of several leading mathematicians to whom the Indian sent his work for review), he wrote that Deolalikar's work is "a relatively serious claim to prove the inequality of classes P and NP".
It is not known whether the recommendation of the luminary in the field of complexity theory (it is this area of \u200b\u200bmathematics that deals with the inequality P and NP) played a role, or the importance of the problem itself, but many mathematicians from different countries distracted from their main work and began to understand the calculations of Deolalikar. People who are aware of the inequality of complexity classes P and NP, but not directly involved in this topic, also took an active part in the discussion. For example, they inundated questions about the proof of a specialist in computer science Scott Aaronson of Massachusetts Institute of Technology(MIT).
Aaronson was on vacation at the time of the appearance of Deolalikar's article and could not immediately figure out the proof. However, to emphasize its importance, he stated that he would give the Indian $200,000 if the mathematical community and the Clay Institute recognized him as correct. For this extravagant act, many colleagues condemned Aaronson, saying that a true scientist should rely only on facts, and not shock the public with beautiful gestures.
shoals
Already in the first days of "sucking" Deolalikar's article, experts discovered several serious shortcomings in it. One of the first to publicly declare this was, oddly enough (or, conversely, not at all strange), it was Aaronson. In response to his blog readers' scolding for jumping to conclusions, Aaronson shared a few tricks he used to quickly evaluate an Indian's work.
Aaronsohn, firstly, did not like that Deolalikar kept his article not in the classical lemma-theorem-proof structure for mathematicians. The scientist explains that this nitpicking is not caused by his innate conservatism, but by the fact that with such a structure of work it is easier to catch "fleas" in it. Secondly, Aaronson pointed out that summary the article, which should explain what the essence of the proof is and how the author managed to overcome the difficulties that have prevented solving the problem so far, is written extremely vaguely. Finally, the main point that confused Aaronson was the lack of an explanation in Deolalicar's proof of how it can be applied to solve some important particular problems associated with complexity theory.
A few days later, Neil Immerman of the University of Massachusetts said he found "a very serious gap" in the Indian's work. Immermann's considerations were published on the blog of University of Georgia computer scientist Richard Lipton, where the main discussion about the inequality of P and NP unfolded. The scientist appealed to the fact that Deolalicar incorrectly defined problems that fall into the complexity class NP, but not P, and therefore all his other arguments are also invalid.
Immermann's conclusions forced even the most loyal experts to change their assessment of the work of the Indian from "it is possible that yes" to "almost definitely not." Moreover, mathematicians even doubted that a significant number of ideas could be extracted from Deolalikar's work that could be useful in further attempts to deal with inequality. The verdict of the mathematical community (on English language and with an abundance of mathematical terms) can be read.
Deolalikar himself responded to the criticism of his colleagues that he would try to take into account all the comments in the final version of the article, which would be prepared in the near future (since August 6, when the Indian sent out the first version of his work, he had already made changes to it once). If the assurances of the mathematician turn out to be true and the final version of the proof still sees the light, one must think that experts will once again study the arguments given by Deolalicar. But today the scientific community has already decided on the assessment.
New stage?
Even if we ignore the importance of the Millennium goals as such, this story has another interesting side. The colossal discussion of Deolalikar's work is in itself an absolutely amazing event. Hundreds of mathematicians and computer scientists dropped everything and focused on learning more than 100 pages ( sic!) Indian labor. Judging by the speed with which the scientists discovered the errors, they must have spent many hours of their free - and maybe working - time diligently reading the article "P is not equal to NP". On one of the Wikipedia-like sites, a page was urgently created, where everyone could express their views on the evidence given.
All this frenzied activity suggests that we are witnessing the birth of a new way of creating scientific articles in the example of Deolalikar's work. Placing preprints in open access before official publication in the exact and natural sciences has been practiced for a long time, but in this case a new result - albeit a negative one - was the result of brainstorming conducted by dozens of experts from around the world.
Of course, this way of obtaining scientific data still raises many questions (the most obvious is the question of the authorship of the results and the priority of discoveries), but, in the end, most new undertakings initially faced doubts and opposition. The survival of such undertakings is determined not at all by the attitude of society, but by how much they will be in demand by it. And if brainstorming and getting results is more efficient than traditional methods scientific work, it is very likely that in the future this practice will become generally accepted.