Quantum mechanics suggested a possible proof of the Riemann hypothesis. The mathematician presented a solution to the Riemann hypothesis. Why does the scientific community criticize him?

Russian mathematician found proof of the Riemann Hypothesis January 3rd, 2017

Bernhard Riemann

Remember, I told you about . So, among them was the Riemann hypothesis.

In 1859, the German mathematician Bernhard Riemann took Euler's old idea and developed it in a completely new way, defining the so-called zeta function. One result of this work was an exact formula for the number of primes up to a given limit. The formula was an infinite sum, but analysts are no strangers to that. And it was not a useless game of the mind: thanks to this formula, it was possible to obtain new genuine knowledge about the world of prime numbers. There was only one small problem. Although Riemann could prove that his formula was exact, the most important potential consequences of it depended entirely on one simple statement about the zeta function, and it was that simple statement that Riemann could never prove. A century and a half later, we still haven't managed to do it.

Today, this statement is called the Riemann hypothesis and is, in fact, the holy grail of pure mathematics, which seems to have "found" Russian mathematician.

This may mean that the world mathematical science is on the verge of an international event.

The proof or refutation of the Riemann hypothesis will have far-reaching consequences for number theory, especially in the field of the distribution of prime numbers. And this can affect the improvement of information technology.

The Riemann Hypothesis is one of the seven Millennium Problems, for which the Clay Mathematics Institute (Cambridge, Massachusetts) will pay a reward of one million US dollars for solving each of them.

Thus, the proof of the conjecture can enrich the Russian mathematician.

According to the unwritten laws of the international scientific world, Igor Turkanov's success will not be fully recognized until a few years later. However, his work has already been presented at the International Physics and Mathematics Conference under the auspices of the Institute of Applied Mathematics. Keldysh RAS in September 2016.

We also note that if the proof of the Riemann Hypothesis found by Igor Turkanov is recognized as correct, then the solution of two of the seven "millennium problems" will already be credited to the account of Russian mathematicians. One of these problems is the "Poincaré hypothesis" in 2002. At the same time, he refused the bonus of $1 million from the Clay Institute that was due to him.

In 2015, Professor of Mathematics Opeyemi Enoch from Nigeria claimed that he was able to solve the Riemann Hypothesis, but the Clay Institute of Mathematics considered the Riemann Hypothesis unproven until now. According to representatives of the institute, in order for the achievement to be recorded, it must be published in a reputable international journal, with subsequent confirmation of the proof by the scientific community.

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The 15-line solution was presented by the famous British scientist Sir Michael Francis Atiyah ( Michael Francis Atiyah), winner of prestigious mathematical awards. He mainly works in the field of mathematical physics. Science reports that Atiya told about his discovery at the conference Heidelberg Laureate Forum at Heidelberg University on Monday.

The Riemann hypothesis was formulated, as you might guess, by Bernhard Riemann in 1859. The mathematician introduced the concept of the zeta function - a function for a complex variable - and used it to describe the distribution of prime numbers. The original problem with primes was that they are simply distributed over a series of natural numbers without any apparent pattern. Riemann proposed his distribution function for prime numbers not exceeding x, but he could not explain why the dependence arises. Scientists have been struggling to solve this problem for almost 150 years.

The Riemann Hypothesis is one of the seven Millennium Prize Problems, each of which is worth a million dollars. Of these problems, only one has been solved - the Poincare conjecture. Its solution was proposed by the Russian mathematician Grigory Perelman back in 2002 in a series of his works. In 2010, the scientist was awarded the prize, but he refused it.

Georg Friedrich Bernhard Riemann - German mathematician and physicist / ©Wikipedia

Michael Atiyah claims to have explained Riemann's pattern. In his proof, the mathematician relies on the fundamental physical constant - the fine structure constant, which describes the strength and nature of electromagnetic interactions between charged particles. Describing this constant using the relatively obscure Todd function, Atiyah found a solution to the Riemann hypothesis by contradiction.

The scientific community is in no hurry to accept the proposed proof. For example, an economist from the Norwegian University of Science and Technology Jørgen Visdal ( Jørgen Veisdal), who had previously studied the Riemann Hypothesis, stated that Atiyah's solution was "too vague and uncertain". The scientist needs to study the written evidence more carefully in order to come to conclusions. Atiyah's colleagues contacted Science, also noted that they do not consider the presented solution to be successful, since it is based on shaky associations. UC Riverside mathematical physicist John Baez ( John Baez) and even stated that Atiyah's proof "simply imposes one impressive claim on another without any arguments in favor of it or real justifications."

Michael Francis Atiyah, a professor at Oxford, Cambridge and Edinburgh Universities and winner of almost a dozen prestigious awards in mathematics, presented a proof of the Riemann Hypothesis, one of the seven Millennium Problems, which describes how the prime numbers are located on the number line.

Atiyah's proof is short, taking up five pages, together with the introduction and bibliography. The scientist claims that he found a solution to the hypothesis by analyzing the problems associated with the fine structure constant, and used the Todd function as a tool. If the scientific community considers the proof correct, then the Briton will receive $ 1 million for it from the Clay Mathematics Institute (Clay Mathematics Institute, Cambridge, Massachusetts).

Other scientists are also vying for the prize. In 2015, he announced the solution of the Riemann hypothesis Professor of Mathematics Opeyemi Enoch from Nigeria, and in 2016 presented his proof of the hypothesis Russian mathematician Igor Turkanov. According to representatives of the Institute of Mathematics, in order for the achievement to be recorded, it must be published in an authoritative international journal, followed by confirmation of the proof by the scientific community.

What is the essence of the hypothesis?

The hypothesis was formulated back in 1859 by the German mathematician Bernhard Riemann. He defined a formula, the so-called zeta function, for the number of primes up to a given limit. The scientist found that there is no pattern that would describe how often prime numbers appear in the number series, while he found that the number of prime numbers that do not exceed x, is expressed in terms of the distribution of the so-called "non-trivial zeros" of the zeta function.

Riemann was confident in the correctness of the derived formula, but he could not establish on what simple statement this distribution completely depends. As a result, he put forward the hypothesis that all non-trivial zeros of the zeta function have a real part equal to ½ and lie on the vertical line Re=0.5 of the complex plane.

The proof or refutation of the Riemann hypothesis is very important for the theory of the distribution of prime numbers, says PhD student of the Faculty of Mathematics of the Higher School of Economics Alexander Kalmynin. “The Riemann Hypothesis is a statement that is equivalent to some formula for the number of primes not exceeding a given number x. A hypothesis, for example, allows you to quickly and with great accuracy calculate the number of prime numbers that do not exceed, for example, 10 billion. This is not the only value of the hypothesis, because it also has a number of rather far-reaching generalizations, which are known as the generalized Riemann hypothesis , the extended Riemann hypothesis, and the grand Riemann hypothesis. They are even more important for different branches of mathematics, but first of all, the importance of a hypothesis is determined by the theory of prime numbers,” says Kalmynin.

According to the expert, with the help of a hypothesis, it is possible to solve a number of classical problems of number theory: Gauss problems on quadratic fields (the problem of the tenth discriminant), Euler's problems on convenient numbers, Vinogradov's conjecture on quadratic non-residues, etc. In modern mathematics, this hypothesis is used to prove statements about prime numbers. “We immediately assume that some strong hypothesis like the Riemann hypothesis is true, and see what happens. When we succeed, we ask ourselves: can we prove it without assuming a hypothesis? And, although such a statement is still beyond what we can achieve, it works like a beacon. Due to the fact that there is such a hypothesis, we can see where we are going,” says Kalmynin.

The proof of the hypothesis can also affect the improvement of information technology, since the processes of encryption and coding today depend on the effectiveness of different algorithms. “If we take two simple large numbers of forty digits and multiply, then we will get a large eighty-digit number. If we set the task to factorize this number, then this will be a very complex computational task, on the basis of which many information security issues are built. All of them consist in creating different algorithms that are tied to the complexities of this kind, ”Kalmynin says.

Logical proof of the Riemann hypothesis. SE VIEW OF THE WORLD.

The logical proof of the Riemann hypothesis is also a proof of God.
The Riemann hypothesis is an assumption about the existence of regularities in the distribution of prime numbers. The logical proof of the Riemann Hypothesis is, strictly speaking, the essence of what is known under the name "logic". From now on, this entity is known as it is in itself, in its own form of the Science of Rhetoric.

Information for thought:
“Prime numbers will “bury” cryptography” (NG-TELECOM, October 5, 04): “Mathematicians are close to proving the so-called “Riemann hypothesis”, recognized as one of the unsolved problems of mathematics. If the hypothesis that there are patterns in the nature of the “distribution” of prime numbers is proved, there will be a need to revise the fundamental principles of all modern cryptography, which underlies many e-commerce mechanisms.
The "Riemann Hypothesis" was formulated by the German mathematician G. F. B. Riemann in 1859. According to her, the nature of the distribution of prime numbers may differ significantly from what is currently assumed. The fact is that mathematicians have not yet been able to detect any system in the nature of the distribution of prime numbers. So, it is believed that in the neighborhood of an integer x, the average distance between successive prime numbers is proportional to the logarithm of x. Nevertheless, the so-called twin prime numbers have long been known, the difference between which is 2: 11 and 13, 29 and 31, 59 and 61. Sometimes they form whole clusters, for example 101, 103, 107, 109 and 113. mathematicians have long suspected that such clusters exist in the region of very large prime numbers, but so far they have not been able to prove or disprove this assertion. If such "clusters" are found, the strength of the cryptographic keys currently in use may suddenly become a big question mark.
According to a number of publications, the other day the American mathematician Louis de Brange from Purdue University said that he was able to prove the Riemann hypothesis. Earlier, in 2003, mathematicians Dan Goldston from the University of San Jose (California) and Kem Ildirim from Bogazici University in Istanbul already announced the existence of a proof of this theorem.
The proof of a seemingly abstract mathematical problem can fundamentally change the concepts underlying modern cryptographic systems - in particular, the RSA system. The discovery of a system in the distribution of prime numbers, says Oxford University professor Marcus du Satoy, would lead not only to a decrease in the strength of cryptographic keys, but also to the complete inability to ensure the security of electronic transactions using encryption. The implications of this cannot be overestimated given the role that cryptography plays in today's society, from guarding government secrets to enabling online financial and trading systems."

CALCULATION OF SIMPLE NUMBERS. THE ESSENCE OF MATHEMATICAL
01/16/2003 HTTP://LIB.RU/POLITOLOG/SHILOW_S/CHISLA.TXT

1. The phenomenon of development is calculus.

2. Universal calculus is fundamentally different from differential,
integral and other analytical calculus.

3. Universal calculus proceeds from the concept (formula) of a unit.

4. The idea of ​​an infinitesimal quantity, which underlies modern partial calculus, the idea of ​​Newton-Leibniz flux, is subject to fundamental
reflections.

5. Lorentz transformations, first used by Einstein as
project of a new, synthetic calculus, represent in practice the strategy
search for the foundations of number theory.

6. Set theory is a description, a description of number theory, which is not
is identical to the explication of the foundations of number theory.

7. Einstein's theory of relativity actually reveals numerical foundations
physical processes.

8. The idea of ​​an observer is a lexical description of the project of a synthetic
calculus.

9. In synthetic calculus, measurability is identical to calculus,
meaning is identical to the process, the meaning forms the process, which before
there was no meaning in "nature", in reality a series of numbers.

10. The problem of modern scientific knowledge, therefore, is
the problem of creating a synthetic calculus.

11. The main operation of synthetic calculus is the representation of a number
number.

12. The representation of a number by a digit is the result of the reflection of a number. Like
how the representation of a word by a concept (image) is the result of reflection
the words.

13. Reflection of the word is carried out by reading the letter. Reflection
numbers is carried out through the mathematization of physics.

14. The book of nature (physics) is written in the language of mathematics (read
mathematics). "The Book of Nature", Science is thus an idea,
presentation, description of numbers by numbers. Just like a book is
representation, formalization of words by letters, lexical and grammatical
forms.

15. Thus, the theory of numbers is, properly speaking, the universal theory of nature.

16. Calculus is thus the universal process of nature.
(nature as a process), Development, a process presented in digital form.

17. Representing a number as a digit is a fundamental technology
calculus, the essence of the phenomenology of development, the foundation of Technique as such.
So the representation of a word by an image (concept) is a fundamental technology
thinking is, strictly speaking, reflection.

18. Let's reveal the essence, the phenomenon of representing a number by a figure. Such and
there will be a technology of synthetic calculus.

19. The phenomenon of number representation in true number theory is revealed
as a phenomenon of fundamental difference between numbers in modern number theory.

20. The fundamental difference between numbers in modern number theory is
explication of the set of prime numbers. So the fundamental difference between words in
rhetoric is, first of all, an explication of the primary concepts of rhetoric.

21. A prime number is the possibility of representing a number as a digit, and
represented as a figure, it is the realization, the result of the representation
number as a digit, since there are numbers that cannot be represented as a finite
sign digits.

22. The fundamental position of synthetic calculus is, in the very
unconditional and necessary sense, the formula of unity.

23. An infinitely small value of analytic calculus is, in fact,
speaking, also a unit, as something one fixed by means of analysis.

24. The formula of a unit is the definition of a unit, since the concept itself
unit formulas are the result of the reflection of a number.

25. Since the unit formula is the concept of the language of science, the way
representation of a number by a digit, then the unit is nothing but a set,
set of prime numbers:

26. Sets of prime numbers in reality of a number series are, strictly speaking, phenomena of nature, the measurability of which is identical to their existence in time and space as a synthetic calculus,
calculus that produces numbers.

27. A prime number is the true limit of analytic calculations,
fixed in the form of physical constants indirectly.

28. The essence of synthetic calculus, a single act of computability of synthetic calculus, which can be characterized as a measurement that produces a physical object, and so, the essence of synthetic calculus is such a difference between sets of primes per unit set, which is also a specific set of primes. So the essence of the formation of rhetoric in a dialogue is such a phenomenon of a new basic concept (a unit of meaning, meaningfulness), not included in the circle of used primary concepts, which (a new concept) is also a set of primary concepts.

29. Divisibility as a technology for determining a prime number forms the essence of analytical calculus, which has not been fully reflected today.

30. Division is the path of a digit, entropy as a formal representation of
the reality of the number series.

31. Thus, the direct rule for determining a prime number
through divisibility there is a formula of a formula, the genesis and structure of a physical formula as a result of the reflection of the representability of a number by a digit.

32. The rule for determining a prime number determines the mechanism
synthetic calculus.

33. The rule for determining a prime number is simultaneous divisibility
digital parts of the number to the divisor. In terms of integer divisibility, the number
forms two digital parts, the unity of which is due to its position
with respect to its (all) prime numbers. The divider is working -
simultaneous division "on both sides" (digital) numbers.

34. The transition from analytic to synthetic calculus looks like
most direct form as the simultaneity of two operations of one
divisor in the digital form of the number.

35. A sequence of integer divisors defines a number as prime,
or not simple, that is, it is calculated.

36. Number is calculated in calculus.

37. The calculation of a number is the determination of the quality of a number.

38. In a number engine, the number is calculated.

39. The operation of the numerical engine: there is a sequential determination
(calculation of) prime numbers.

40. The mechanism for determining the simplicity of a number based on divisibility: "we divide
the initially divisible (for the initial sequence of divisors) digital beginning of the number by the initial sequence of divisors, taken, multiplied by an integer up to the maximum integer value of the digital beginning of the number, and we look at whether the remaining digit of the number is divided by an integer (without a remainder) by the real divisor, while the digital the beginning of the number will not be less than the divisor."

41. The physical world thus has a digital form.

42. The measurements of time in the system of measuring the number are identical to the measurements
spaces and are presented as digital forms: the number of digits (and digit) of the first part of the number (initial digital form), the number of digits (and digit) of the second part of the number (middle digital form), the number of digits (and digit) of the third part of the number (final digital form ).

43. Measurability of the physical world - an expression of the initial sequence of divisors in the digital beginning of a number with the simultaneous setting of the ratio of the divisor to the digital continuation of the number (integer, non-integer).

44. The basis of analytic calculus is division as
fundamental operation of number theory.

45. Division is the structure of the representation of a number by a digit.

46. ​​The product is the genesis of the representation of a number in the form of a figure.

47. The work is the fourth dimension, the dimension of time as
the fourth operation of number theory in relation to the triad "division - sum -
subtraction", which forms a single rule for calculating a prime number
(proof of its simplicity).

48. A work is a definition-reflection of a triad of operations.

49. The product is the meaning of the genesis of a number.

50. Division - the meaning of the number structure.

51. 1. The number in the form of the Power of the number (the meaning of the number) is first of all a square
digits of a number (first product).
51. 2. On the other hand, a number as a unit is a set of primes
numbers: 1 = Sp.
51.3. A prime number is a divisor of an integer non-simple number.
Thus, the rule for determining a prime number is written as
Fermat's theorem, which in this case becomes proven:
xn + yn = zn , holds for integers
x, y, z only for integers n > 2, namely:
The square of the digit of a number is the unit set of prime numbers.

52. The essence of Fermat's theorem:
Determination of the power of a number by the power of a set of prime numbers.

53. On the other hand, the geometry of Fermat's theorem is the interconversion of space and time in solving the problem of squaring the circle: The problem of squaring the circle is thus reduced to the problem of interconverting the square of a number into a specific set of primes, which has the "appearance" of the famous Möbius strip. The geometry of Euclid (the lack of proof of the fifth postulate - as a direct consequence of the underdetermination of the point, the lack of reflection of the point) and the geometry of Lobachevsky (the geometrization of the digital form of a number outside the number) are overcome together in the geometry of Fermat's theorem. The central postulate of the geometry of Fermat's theorem is the point postulate, which is revealed by the unity formula.

54. Thus, the reflection of the following operations of number theory based on
unit formulas - raising to a power, extracting a root - will lead to the creation of a physical theory of time-space control.

55. There is a number, a number is a unit that has the strength of a number. Representative
numbers are a prime number. This is the universal structure of a physical object,
the incompleteness of the reflection of which led to the corpuscular-wave
dualism, to the difference between the physics of elementary particles and the physics of the macrocosm.

56. Quantum calculus must be re-reflected into synthetic
calculus, Planck's constant expresses the discovery in the digit of the strength of a number.
Radiation is a phenomenon of representation of a number by a digit, revealed in the formula of unity as a solution to the paradox of black body physics.

57. The unity formula is thus the universal field theory.

58. The formula of unity expresses the intellectual essence of the Universe,
is the basis of the concept of the Universe as the reality of real
series of real numbers.

59. Development The Universe is a synthetic calculus, a calculus of prime numbers, the significance of which forms the objectivity of the Universe.

60. The formula of the unit proves, shows the power of the Word. unit formula
there is a structure of the Universe in accordance with the principle of the Word, when the self-shaping of the word is a product of being, the Book of Genesis. So the self-shaping of a number is a product of nature, the Book of the Universe. Formula
units in the most unconditional and necessary sense is the formula of time.
Synthetic calculus is a form of rhetoric.

CONSEQUENCE OF THE LOGICAL PROOF OF THE RIEMANN HYPOTHESIS:

WHAT IS AN ELECTRON? BEGINNINGS OF ELECTRONIC ENERGY
06/15/2004 HTTP://LIB.RU/POLITOLOG/SHILOW_S/S_ELEKTRON.TXT

1. The 20th and 21st centuries - respectively the Atomic and Electronic Ages - form two successive steps, two essences of the transition from the History of Modern Times to the History of New Being.

2. History, as having, having and the future to have a "place", - from the point of view of the Science of Philosophy, is the identity-difference of being and being. The place itself, as something that provides the possibility and reality for something to exist in time, is a phenomenon that results from the identity-difference of being and being.
Existing is the real, arising from being, existing Now and disappearing into non-being. Being is what creates Now, creates "here and now". As independent, existing in itself, separate from being, being is time. Being is what creates Time. Time tends to Being, as non-existence, as the objectivity of being, as being. Time enters Being, becomes being through the path of two essences of being. Aristotle considered this path from being to time and saw two essences as a descent from being to being, to time. Aristotle's metaphysics, as the beginning of European rationality, prescribes two essences of being, as what makes science possible. Science arises as the first division of being into two essences - into necessary and sufficient grounds, which together determine the being of being as a whole, as it is. Science, according to Aristotle, is the naming of the path (Logic) from being to being. We, in our historical position, consider this same path from the other side, as a path from time, from being - to being. Both Aristotle and I (we) see the same two essences (necessary and sufficient) of being, which connect being and being, but Aristotle sees them from the side of being, and we, on the other hand, from the side of being, from the side of time . Such is the nature of the "new Aristotelianism". Thus, between Being and Time, there are two essences - the necessary and sufficient grounds, which create everything that generally happens, that is really.

3. Being, necessary reason, sufficient reason, Time. Time, sufficient reason, necessary reason, Being. This is a description and presentation of a Mobius strip, which, according to "modern scientists", is impossible to imagine. We quote "modern scientists": "Lobachevsky's geometry is the geometry of a pseudosphere, i.e. surfaces of negative curvature, while the geometry of a sphere, i.e. surfaces of positive curvature, this is Riemannian geometry. Euclidean geometry, i.e. the geometry of a surface of zero curvature is considered to be its special case. These three geometries are useful only as geometries of two-dimensional surfaces defined in three-dimensional Euclidean space. Then it is possible for them to construct in parallel the whole huge edifice of axioms and theorems (which is also described in visible images), which we know from the geometry of Euclid. And it is really very remarkable that the fundamental difference between all these three completely different "structures" is only in one 5th axiom of Euclid. As for the Möbius strip, this geometric object cannot be inscribed in three-dimensional space, but only in no less than four-dimensional space, and even more so, it cannot be represented as a surface of constant curvature. Therefore, nothing similar to the previous one can be built on its surface. By the way, that’s why we can’t visually imagine it in all its glory.”
The speculation, discovered by Parmenides and Plato, as the vision of "eidos", is used by Aristotle directly, and by us, who think from the other side than Aristotle, it is used, achieved indirectly. From this side, which is different from that of Aristotle, we see the formula of that being with which Aristotle deals directly. We do not have a direct relationship with this being, but we can receive it through a certain formula, de-mediation. The Möbius strip is a representation of the movement from being to time and from time to being, that is, the point of the Möbius strip belongs to both time and being - it creates itself. The 5th “unproven” postulate of Euclid is also an indication that, in addition to being, there is also being that generates being, and that being is nothing other than time. The fifth postulate of Euclid arises as a consequence of the under-axiomatization of the point, as a sign-consequence of the absence of a substantial understanding of the point. In essence, the correct axiomatization of the point axiom is the only necessary axiom of universal geometry, the universal geometry of being, and other axioms (postulates) are not required, they are superfluous. In other words, in the geometry of Euclid, only the first necessary essence of the axiom of the point is fixed, which is subjected to problematization in other geometries, problematization from the point of view of an entity whose geometry is not reducible to the geometry of Euclid. The second, sufficient essence of the axiom of a point is that a POINT IS ALWAYS A POINT OF A MOBIUS STRAP (there is NO POINT THAT IS NOT A POINT OF A MOBIUS STRAP). This is the only axiom of Shilov's geometry, as the universal geometry of being. As you can see, this geometry coincides with the existent, as the being of the existent: the objects forbidden in this geometry are non-existent objects. Such is the primary idea of ​​geometry as the law of the formation of the real.

4. The substantial point is both the essence and the problematization of the law of identity. Here logic and geometry coincide in their common source, foundation. Here logic and geometry reveal themselves as two essences of being, as produced by the being of time. Geometry is the necessary essence of existence. Logic is the sufficient essence of being. This is how Aristotle founded European science. By basing it this way, Aristotle directly owned the topic of the substantiality of a point, while we own this topic indirectly (more precisely, this topic owns us with such power that we no longer think about the substantiality of a point). We must thus return from logic to geometry, formalizing the immediate Aristotelian understanding of the substantiality of a point. How do we do it? We problematize the law of identity (A = A) as a process, becoming, an event of how A is, becomes A, how A is held, fixed, grasped, like A. In this problematization, the whole being of logic participates, and in this understanding the law of identity also becomes the only law of logic when all other laws (contradiction, excluded third, sufficient reason) become measurements, participants in the process of identity, the process of becoming, the feasibility of identity. Logic, as sufficient, and geometry, as necessary, coincide in one essential essence, in the name of a single law of identity - the law of the substantiality of a point.

5. What is a substantial point, as real? This is the main question of Science, in the answer to which it becomes a single science not only in the sphere of the foundations of science, but also externally, “eidetically”. What is the root of all "-logies" as "separate scientific disciplines"? In the logical-geometric unity, first of all. What does logico-geometric unity study? point substance. The logical-geometric unity, poorly reflected by modern sciences, is the theory of a substantial point. The theory of a substantial point is the basis of the genesis and structure of scientific knowledge, rationality. In the field theory, truth, like the truth of the theory of a substantive point, is hidden, eludes the scientist. "Field theory", field theory is a scientific myth. The myth of the actual existence of a substantial point.

6. The actual being of a substantial point is a NUMBER. THE TIME OF THE SUBSTANTIAL POINT, THE POINT OF THE MOBIUS STRAP, AND THERE IS THE ONLY POSSIBLE AND EXISTING TIME, THE TRUE MOMENT OF TIME. NO, THERE IS NO TIME WHICH WOULD NOT BE, AS THE TIME OF A SUBSTANTIAL POINT. The logical-geometric unity, which, on the one logical side, is the law of substantial identity, and on the other geometric side, is the law of the substantial point, in its only essential essence, a priori logic and geometry, is the LAW OF NUMBER. Being creates a being, real in the form of a number, in the space of a real number series, as a material being of time. Number is a place that is created between time and being, between being and time, is a being.

7. The true science of number is, therefore, the mechanics of time (Mathematics is the science of the number, of the representation of a number by a figure). This is what makes it possible to understand the new Aristotelianism, "exposing" the "field myth" of modern physics. The space of being reveals itself as the space of a real numerical series. Field theory, the notion of a field, is a myth regarding the logical-geometric unity and its true nature. The quantum-mechanical interpretation is a kind of myth regarding the mechanics of time. The quantum mechanical interpretation does not yet know "nature" as a real number series, does not yet know the universal (universal for interactions of any "level") physical object, as a number. Modern physics has not yet known "nature" as calculus. The quantum mechanical interpretation is stuck in a logical-geometric unity, as in an indefinite duality (Heisenberg's principle).

8. Thus, the possibility of a “non-field” definition and understanding of energy arises. Field understanding-representation of energy comes from the law of conservation of energy and the inviolability of the principles of thermodynamics. NUMERICAL UNDERSTANDING OF ENERGY IS UNDERSTANDING OF THE MECHANISM OF ACTION OF NUMBER AS THE REAL AND ONLY POSSIBLE MOMENT OF TIME. ENERGY IS THE ENERGY OF MOVEMENT (EXISTENCE) OF THE MOBIUS STRIP. MOBIUS TAPE IS A FORM OF EXISTENCE OF ENERGY. ENERGY IN THE MOST NECESSARY AND UNCONDITIONAL SENSE IS WHAT VIOLATES THE LAW OF CONSERVATION OF ENERGY AND THE ORIGIN OF THERMODYNAMICS, AND THIS VIOLATION FORMES THE PHYSICAL ESSENCE OF TIME, THE POSSIBILITY AND REALITY OF THE MOMENT OF TIME AS THE MOMENT OF REALITY.

9. Energy can be defined as the Force of the Unit (the Force of the number), the strength of which consists in a calculable violation of the law of conservation of energy (beginnings of thermodynamics). In essence, atomic energy advanced humanity to a numerical understanding of energy, but stopped in its scientific development, being unable to comprehend atomic energy as a necessary prerequisite for revising the principles of thermodynamics and the law of conservation of energy. Science found itself here in exactly the same position before the need to comprehend its own foundations, in which the church found itself in the face of the achievements of science. Just like the church, science has remained “loyal” to the law of conservation of energy (the principles of thermodynamics), despite the need to comprehend the essence of the foundations of atomic science INDEPENDENTLY, outside of thermodynamic coordination. Atomic science in the matter of using atomic energy came to the idea-representation of a substantial point. The use of atomic energy is, in essence, the self-disclosure of the substance of a point, as a number growing throughout the entire space of a real number series (the idea of ​​a "chain reaction"). Moreover, this idea is quite visible: that is why an atomic explosion is an atomic mushroom, there is GROWTH, metaphysical growth, the running of a number over its own space, the place of a number series.

10. Electronic science will define the face of the 21st century. And this science will arise from the true definition of WHAT THE ELECTRON IS. All previous thoughts, as well as the consideration of atomic science (atomic energy), as a pure phenomenon that has its own truth - the FIRST STAGE, THE FIRST NECESSARY ESSENCE OF DISCOVERING THE NUMERICAL NATURE OF ENERGY, as a physical fixation of the force and being of a number, contribute to understanding the electron already directly, as a number, as an object manifesting itself physically. It is no coincidence that they say that "the electron is the most mysterious particle in physics." The electron is the second step, the second SUFFICIENT ESSENCE OF THE NUMERICAL NATURE OF ENERGY. An atom, an electron are located between being and time (existing), as, respectively, the first necessary and second sufficient essence of the existing. The transition from being to time and the reverse transition from time to being is not the “divisibility of matter” of being, but a substantial point, Number, and, in this sense of Number as “indivisibility of matter”, ELECTRON IS A SIMPLE NUMBER (an indivisible number). A prime number is the physical essence of an electron as a space-time phenomenon of time.

11. Electronic science completes the transition from time to being, necessarily begun by atomic science. Electronic Science discovers the Unity Formula: One is the set of prime numbers. The Unit formula reveals the device, the essence of time, the mechanics of time. Electronic science gives a person access to ELECTRONIC ENERGY, DIRECT ENERGY OF THE NUMERICAL SERIES, ENERGY OF CREATION. Electronic science will solve the problems that atomic science has stopped in front of and thereby incredibly change energy, fixing a “fundamentally new”, and, in fact, a true source of mega-energy - a number, a number series. Understanding WHAT THERE IS AN ELECTRON, we will create ELECTRONIC ENERGY as the mechanics of time, first of all. The mathematical procedure will become a part of the physical-technical process, the part that will bring this process into a new superphysical, superphysical-constant quality.

12. The task of creating electronic energy is the main task of forming a new technotronic mode. This is the task of beginning the History of the New Being, completing the transitional period from the History of the New Age to the History of the New Being, the first necessary foundation, the first necessary step of which was the past 20th Atomic Age. The scientific revolution of the 20s of the 20th century, carried out by Einstein, created the necessary prerequisites for the Mega-Science Revolution of the early 21st century, the result of which will be electronic science, electronic energy. The emergence of electronic science, electronic energy is, first of all, the discovery of what an electron is. The discovery of the “mystery of the electron” is, first of all, understanding, comprehension, the path of which is presented in this sequence of theses as the path of the “new Aristotelianism”.

13. With what experience did Aristotle work when he comprehended the truth of the world as a transition from being to time, when he discovered that possibility that was realized as Logic? The idea of ​​what is known to man as the closest circle of his being, defining him as a proper human being, was the Möbius strip. Where did a person see and know the Mobius strip? Where did a person draw the experience of the substantiality of a point? After all, all this is knowledge, “innate ideas”, which make some living being a man, after all, a person is made human by his human perception (man, in the words of Goethe, “sees what he knows”). How did the “early-ancient” man know everything that modern science, armed with powerful means of technology, experiment, mathematical apparatus, comes only in the 21st century, despite the fact that a person always has this knowledge precisely as a person? Answer: from speech, from human speech, as the direct reality of thinking. Speech is that movement from being to time and from time to being (in the movement from time to being, speech becomes thinking), which is a person, as a kind of movement and experience of real movement. A point, as a substantial point, is known, known to a person, as a point of speech, as a moment of truth, as a judgment. Time, as objectivity, is given to man, as the objectivity of speech (thinking). The meaning of the modern historical moment in the development of science lies in the most important experiment - in verifying modern science with the experience of speech, in the path of a radical logical rethinking of science as scientific speech, in identifying the necessary and sufficient grounds for the truth of a scientific judgment. Speech contains a program of truth, the disclosure of which required all the power of modern science, directed outside of man, but requiring comprehension of the results obtained in the language of science. Speech for a person is not only “between” being and time, but also embraces being, as the being of a person, and time, as the time of a person, with a Mobius strip. Speech is something more than a philological set of words and rules, speech is a being that enters the world at such a time as a person, creates such a being as a person. Speech creates number as the essence of man, the number that is man.
Therefore, the mega-scientific revolution is a humanitarian-technotronic revolution, which begins with the disclosure of the secret of the essence of the electron, as a prime number, BY THE MEANS OF THINKING, THE MEANS OF THE LANGUAGE OF SCIENCE.

THE FIRST MENTION OF THE LOGICAL PROOF OF THE RIEMANN HYPOTHESIS
20.10.2000 HTTP://LIB.RU/POLITOLOG/SHILOW_S/MEGANAUKA.TXT
"CHRONICLE. DEFINITIONS OF MEGA SCIENCE»

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The unshakable and final foundation that Descartes was looking for at the beginning of the Modern Age is understood and revealed at the End of the History of the Modern Age. This base is a number. As being truly described by the language of science. At the End of the History of the Modern Age, this foundation is revealed and becomes visible as the "last" of the Modern Age. One can see the number through the "optics" of the reductionism of the soliptic (methodoritical) doctrine, as the highest form of the Cartesian "methodological" doubt. The number discovered in this way has characteristics characteristic not only of the arithmetic concept of “number”, but also of the philosophical concept of “foundation” (I will add - and the physical concept of “nature” (“matter”) - the concept of “atom” and the concept of “electron”), so that mathematicians (and physicists) will have to make room in the boat of numbers, sailing in the “borderless ocean of the unknown” (which Newton writes about in the Mathematical Principles of Natural Philosophy, treating himself not as “the discoverer of the laws of the universe”, but “like a boy throwing pebbles on the coast ”) and give a place in this boat also to philosophers. Strictly speaking, for the benefit of physico-mathematicians as well, the boat of number (Noah's Ark of modern civilization) under the control of which, crowded on one of its sides, is already almost under water (for example, the collapse of the Hilbert-Goedel "formal-logical" formalization program) . The formalization program of the Science of Rhetoric deduces the notion of a true set theory, bound by the Unity formula, as a set of primes.

Millennium goals. Just about complex

• entertaining puzzles,
• Maths

Hello, habralyudi!

Today I would like to touch upon such a topic as the “millennium tasks”, which have been worrying the best minds of our planet for decades, and some even hundreds of years.

After proving the conjecture (now the theorem) of Poincaré by Grigory Perelman, the main question that interested many was: “ And what did he actually prove, explain on your fingers?» Taking the opportunity, I will try to explain on my fingers the other tasks of the millennium, or at least approach them from another side closer to reality.

Equality of classes P and NP

There are also NP-tasks ( N on-deterministic P olynomial time), the found solution of which can be quickly checked using a certain algorithm. For example, check by brute-force computer. If we return to the solution of the quadratic equation, we will see that in this example the existing solution algorithm is checked as easily and quickly as it is solved. From this, a logical conclusion suggests itself that this task belongs to both one class and the second.

There are many such tasks, but the main question is whether all or not all tasks that can be easily and quickly checked can also be easily and quickly solved? Now, for some problems, no fast solution algorithm has been found, and it is not known whether such a solution exists at all.

On the Internet, I also met such an interesting and transparent wording:

Let's say that you, being in a large company, want to make sure that your friend is also there. If you are told that he is sitting in the corner, then a fraction of a second will be enough to, with a glance, make sure that the information is true. In the absence of this information, you will be forced to go around the entire room, looking at the guests.

This problem is of great importance for various fields of knowledge, but it has not been solved for more than 40 years.

Hodge hypothesis

Hodge's hypothesis in this case is connected with some properties of both "bricks" and objects.

Riemann hypothesis

Many statements about the computational complexity of some integer algorithms are proven under the assumption that this conjecture is true.

Yang-Mills theory

On the basis of the Yang-Mills theory, the standard model of elementary particle physics was built within which the sensational Higgs boson was predicted and recently discovered.

Existence and smoothness of solutions of the Navier-Stokes equations

Birch-Swinnerton-Dyer hypothesis

This hypothesis is connected with the description of algebraic equations of the 3rd degree - the so-called elliptic curves and is in fact the only relatively simple general way to calculate rank, one of the most important properties of elliptic curves.

In proof Fermat's theorems elliptic curves have taken one of the most important places. And in cryptography, they form a whole section of the name itself, and some Russian digital signature standards are based on them.

Poincare conjecture

A special case of the Poincare conjecture tells us that any three-dimensional manifold without boundary (the universe, for example) is like a three-dimensional sphere. And the general case translates this statement to objects of any dimension. It is worth noting that a donut, just like the universe is like a sphere, is like an ordinary coffee mug.

Conclusion

But in fact, this is not so - mathematics was created as a mechanism with which to describe our world, and in particular, many observable things. It is everywhere, in every home. As V.O. Klyuchevsky: “It’s not the flowers’ fault that the blind man doesn’t see them.”

Our world is far from being as simple as it seems, and mathematics, in accordance with this, is also becoming more complex, improving, providing more and more solid ground for a deeper understanding of the existing reality.