Форум по результатам лекций по Молекулярной физике

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by Марат Авдыев -
Number of replies: 0

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Fermat's Last Theorem plays a very interesting role in pedagogy. Today, every student can


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make the discovery by looking at a

school globe or add a wooden cube!


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Are there short and simple ways to prove Last theorem?

Do need to spend a hundred or more pages


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and help of artificial intelligence (AI) to find a prove? Beyond any doubt neural networks are


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a very useful tools for broadcasting knowledge among billions of people.


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Thus Bob and Alice will help us!


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the Fermat's Last Theorem plays a very interesting  role in pedagogy. Nowadays every student can make a


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discovery by looking at a school globe or wooden Cube for child. In this video Let's consider the


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following questions: what is topology and set

theory? Why a ball and a cube are homeomorphic?


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and what homeomorphism is? We'll discuss the

irreducible conflict between form and content


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which is embedded in this theorem. Then we will

make generalizations and conclusions about the


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fundamental properties of our Universe. Begin

from the beginning. Fermat's Last Theorem was


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formulated in 1637 and it states that this

equation for the whole numbers a^n (^ - degree)


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+ b^n  in degree n = c^n has no

solution for n greater than 2, except zero values


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This theorem was formulated by Pierre de Fermat in the margins of the book Arithmetic by Diaphanus


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of Alexandria in the 3rd Century A.D. Thanks to

Diophantus we treat algebraic equations as it is


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convenient and familiar to us. French mathematician

Pierre de Fermat wrote in the margin of the book


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"I have discovered a truly marvellous proof of this, which this margin is too narrow to contain".


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In the 1990s Princeton mathematician Andrew

Wiles shocked the world with a breakthrough


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standing on the shores of Number Theory. He

began dreaming of a bridge to Harmonic analysis


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they also showed that Fry's elliptic curve

can't exist which means that a solution to


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Fermast's equation can't exist either. Subsequently descendants denigrated the French mathematician


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and believed that he made a lightweight judgment simply put bragging a nd lying.


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I'm Andrew Granville I work in analytic number Theory when I was young

I worked on formats Last Theorem before it was


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proved today I work in ideas of L function you

cannot prove them because you cannot go back to


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anything more primitive than those propositions

themselves they are not in need of justification


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this is particularly famous example by Peter

schultzer he had a very very difficult proof


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but he wasn't 100 sure of he would try and say

well this is true and you should know this lead


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and me would say I don't know this at all

you're gonna have to explain this better


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the basis for such an assertion was a hundred

plus page proof by Andrew Wiles prepared by him


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in 1994. the question arise of their short and

simple ways to prove the Fermat's Last Theorem


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to understand this is it necessary to waste

100 or more pages and help of artificial


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intelligence we refer to 500 page work of Shinichi Mochizuki  Japanese mathematician  working in Number


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Theory and arithmetic geometry from Kyoto

University dealing with the "ABC hypothesis"


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in number Theory. But there is another approach

Minhyong Kim, a mathematician at the University


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of Oxford said "it should be possible to use

ideas from physicists to solve problems in


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Number Theory but we haven't thought carefully

enough about how to set up such a framework"


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and one more his quotation: "We're at a point

where our understanding of physics is mature


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enough and there are enough number theorists

interested in it to make a push"


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To the posed question about short and simple ways to prove the Fermat's Last Theorem the answer is "Yes!"


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And this method is associated with a mental

experiment.  Consider a construction of 3


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concentric nested n-cubes or balls with centers

at the origin with edges or radii just equal to


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natural numbers a, b, c. Why these whole numbers which are mentioned in the Last Theorem will


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necessarily be different? Suppose the opposite. If the first two terms and are equal to each other


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then in this case it is easy to see that the root

of 2 must be represented as a fraction say p and q


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Let's reduce p and q by greatest common divisor

and they become mutually prime numbers but then


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we go to this equation and make sure that we

have an even number on the right and left sides


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For instance if degree n equal to 2 the right

part is divisible by 4 because here p^2


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is the result at least twice prime number two so

divide by four the right part of equation and make


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sure that the left part must also be divisible by

2 and again by 2. Thus p and q become even and


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we have a ride at a contradiction. For the case

of degrees higher than 2 the proof is quite


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similar so it is no less general to put that

whole numbers a <  b which in turn is


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less than c. Three years ago in 2020


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I formulated a proof of Fermat's Last Theorem which is that if you take the 3 n-cubes here symbolically depicted on the plane a-Small cube you layer


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around it a certain number of unit cubes, create

the b- Middle cube layer another certain number of


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layers create c-Large cube where volume of a small cube is equals to volume of difference of c-Large


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and b-Middle cubes. It is easy to make sure that in the project of "A house for a capricious rock star"


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the condition of equivalence of the volumes of

the Studio and the Winter Garden excludes central


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symmetry and vice versa and you get a construction that doesn't really exist in nature for the case


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n > 2.  It's amazing! You will never

be able to put each unit cube 1^n from a-Small


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n-cube in correspondence with another unit cube of this subset of layers between the Middle and the


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Large one in such a way that you do not destroy

the symmetry of the construction and do not allow


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voids. Generally speaking these subsets are not

equivalent to each other this is the main idea of


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the proof. This is due to the fact that this figure

has the property of central symmetry and does not


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contain inhomogeneities as a result each layer

in this figure is not comparable to another layer.


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Thus each layer in this figure is not reducible

to another layer here additivity conditions and


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Axiom of Measure do not work. In other words it

is impossible to speak about addition of volumes.


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Why did Andrew Wiles need over a hundred more pages to prove it, if half of page is enough or


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six faces of wooden cube for child? Rospatent

put me "guilty of plagiarism" with Andrew Wiles


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proof for which he received an able award in 2016.

Rospatent refused the State registration of a


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patent 2021501435 for an industrial design under the pretext of "violating public morality". Rospatents claim


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about "plagiarism" of the proof does not stand up to any criticism because the proof you see is


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original new and it really breaks the stereotypes

formed in science about the absence of a short


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proof of Fermat's Last Theorem. Let us imagine

that we have concentric balls nested within


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each other ball with the natural radii a, b,

c that we are looking for we will distinguish


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between a ball and a sphere that encompasses the ball the sphere is the so-called "layer" for the


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ball so the above notations are adopted here here is the ball and here is the sphere a layer it has


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Dimension one unit less n-1. This is clear from physics and math courses remember the formulas for the


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length of a circle 2πR and the area of a circle πR^2 the area of a sphere and the volume of a ball. It is


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interesting to imagine that in the one-dimensional world we would have such an open ball in the form


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of a segment excluding its endpoints or Zero

dimensional spheres located at a distance R from


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the origin of coordinate. Now for the case of the 2-dimensional plane the open ball becomes the familiar circle.


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Excluding the 1-dimensional sphere already

considered finally for the three-dimensional


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case we have the usual ball resembling a soccer

ball it is closed by a two-dimensional sphere we


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again exclude an arbitrary meridian from the

sphere as a result we got acquainted with the


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sequence of geometrical elements on the sphere

of dimension from 1 up to n minus one these are


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the so-called "hypermeridians" which will be

useful for us in the future let's continue


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the experiment with the cascade of spheres this is the encompassing meridian let's try to change the


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step for example what happened and this is the

code that allows us to create this design it's


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based on an understanding of set theory now let's

look at the basics of set theory and make a small


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generalization if a triple of natural numbers a b

c exists C existence quanta for a brief notation


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then in this case we can map every point of space

from this interval between the Middle Ball and the


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Big Ball into a Small Ball and since this whole

construction is symmetric this means that every


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sphere that surrounds these spheres can be mapped

into many other spheres. The Fermat's Last Theorem


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states that this is impossible, why? - Because that's the physics of our Universe! It manifests itself


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in the topological properties of figures let's

talk about continuous functions and relations


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that work in topology. Topology is the science

of geometric objects that modify these objects


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in the most arbitrary way but nothing breaks

and all transformations are reversible here you


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see the Russian figure skater Kamilla Valeeva she is plastic, she performs a beautiful smooth dance.


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Let's imagine a certain function F mapping the set X to the set Y similarly you can see how Kamilla