63
World-famous mathematical problems
20
2 1 century is a century of great development of mathematics. Many main problems in mathematics
Satisfactory solutions are obtained, such as the proof of Fermat's last theorem and the classification of finite simple groups.
Finish, etc.
As a result, the basic theory of mathematics has been developed unprecedentedly. review
20
produce
The development of subject mathematics,
Mathematicians are deeply grateful.
20
The greatest mathematics university of this century
Shi Dawei
Hilbert. Hilbert is here.
1900
year
eight
moon
eight
Held in Paris
In his famous speech at the Second World Congress of Mathematicians, he proposed that
23
A math problem
Title. Hilbert problem has inspired the wisdom of mathematicians and guided numbers in the past hundred years.
Know the way forward.
Knowledge recommendation:
Mathematics is one of the concepts of quantity, structure, change and spatial model.
In short, a basic subject is the science of studying numbers and shapes. In the development of mathematics
In our history, mathematicians not only proved many classical theorems, but also put forward many mysteries.
Leave the topic to future generations. This piece of knowledge, let's walk into those famous mathematics together.
Difficult problem.
1.
Four-color conjecture
One of the three major mathematical problems in the modern world. The four-color conjecture was put forward by Britain.
1852
graduate
Francis of the University of London
.
When guthrie came to a scientific research unit to do map coloring work, he found a kind of
Interesting phenomenon:
"
It seems that every map can be painted in four colors, making the borders of the country the same.
Colour it in different colors.
"
Can this conclusion be strictly proved by mathematical methods? He studies with him in the university.
His younger brother, Grace, is determined to give it a try. The manuscripts used by the two brothers to prove this problem have been piled up.
Big stack, but the research work has not progressed.
What is the four-color conjecture?
What is the four-color conjecture?
What is the name of the computer that proves the four-color conjecture?
Where is the information about the four-color conjecture?
What is the content of the four-color conjecture in the world?
2.
Goldbach's Conjecture
Goldbach is a middle school teacher in Germany.
A famous mathematician,
born
1690
Year,
1725
Elected as an academician of the Academy of Sciences in Petersburg, Russia.
1742
Goldbach found in the teaching of 1998 that every student is not young.
what
six
The even number of is the sum of two prime numbers (numbers that can only be divisible by themselves). such as
six
=
three
+
three
12
=
five
+
seven
Wait a minute. This is the famous Goldbach conjecture. Here comes Euler.
six
moon
30
In his reply, he said:
He believes this conjecture is correct, but he can't prove it. Describing such a simple question, even Euler did it.
No leading mathematician can prove it, and this conjecture has attracted the attention of many mathematicians.
Why Goldbach's conjecture is transformed into proof
1+ 1
?
The content of Goldbach conjecture
What is the difficulty of Goldbach's conjecture?
What's the new development of Goldbach conjecture?
Goldbach conjecture sum
1+ 1
What does it matter?
3.
Horizon: Fermat's Last Theorem
Also known as Fermat's last theorem, people called it at that time
"
theorem
"
I really don't believe Fermat.
Proved it. After three and a half centuries of hard work, this century's number theory problem was solved by Princeton University.
Scientist Andrew
Wiles and his student Richard.
Taylor Yu
1995
Certificate of success in 2008. Prove that it used a lot.
New mathematics, including elliptic curves and modular forms in algebraic geometry, as well as Galois theory and
Heck
produce
Wait, where's Andrew?
Wiles successfully proved this theorem and obtained it.
1998
The Fields Medal in 2008 is very special.
Reward and
2005
Shaw Prize for Mathematics of the Year.
trick
Why does Fermat's Last Theorem prove in different time?
How to prove Fermat's last theorem?
Increasing Element and Increasing Ratio in Fermat's Last Theorem
Where can I see the complete solution of Fermat's Last Theorem?
Illustration of Fermat's Last Theorem (urgent)
4. Notary public
Complete problem
notary
The complete problem is that the uncertainty Turing machine is
P
Problems that can be solved in time,
It is the world's seven largest mathematics.
One of the problems.
notary
The complete question ranks first in the million-dollar prize, which shows its prominent position and infinite charm.
Force. The problem lies in this question mark. What is this?
notary
be qualified for sth
P
, or
notary
unequal to
P
notary
inside
ordinary
breakdown
Nonpolynomial
about
ordinary
be
Uncertainty
(meaning uncertainty)
P
represent
multinomial
That's right.
notary
Precisely
Uncertain polynomial
The problem is,
That is, the uncertainty of polynomial complexity.
Philosophical problems,
notary
Can a completely theoretical person fully understand the world?
What is this?
NP-
Complete problem
notary
A complete problem?
Excuse me, in the optimization problem.
nameplate
difficult
，np
Incomplete medium
nameplate
What do you mean?
Ask for a book about ...
notary
A book with complete questions.
5.
hodge conjecture
Mathematicians in the twentieth century found an effective method to study the shapes of complex objects. basic thought
The method is to ask how much we can change the shape of a given object by increasing the simplification of dimensions.
Single geometric building blocks are bonded together to form. Unfortunately, in this generalization, the geometry of the program begins
The dots become blurred. In a sense, some parts without any geometric explanation must be added. suddenly
The assertion of odd conjecture is a particularly perfect space type for the so-called projective algebra family, which is called Hodge closure.
The components of a chain are actually geometric components called algebraic closed chains.
(
Rational linearity
)
Combination.
What is the Hodge conjecture?
What is this?
"
hodge conjecture
"
?
Heaven/God knows
seven
What is the specific content of the big math problem?
ask
seven
Specific problems of 1000 different problems
What are the eight conjectures in mathematics?
6.
Poincaré conjecture
If we wrap the rubber band around the surface of the apple, then we won't break it, and
Don't let it leave the surface, let it move slowly and shrink to a point. On the other hand, if we imagine the same situation.
The rubber belt is stretched on the tire tread in a proper direction without tearing the rubber belt or the tire tread,
There's no way to narrow it down to a little We say that the surface of apple is
"
Simply connected
"
But the tread doesn't.
Yes About a hundred years ago, Poincare knew that a two-dimensional sphere could be carved by simple connection.
In the painting, he raised the corresponding problem of three-dimensional sphere.
Who cracked the Poincare conjecture?
What are Goldbach conjecture and Poincare conjecture?
Prove Poincare conjecture
Excuse me, what is Poincare conjecture, and the research situation of four-color problem?
Some problems about Poincare conjecture
7.
Riemann hypothesis
Some numbers have special properties and cannot be expressed by the product of two smaller numbers. For example,
2
、
three
、
five
、
7……
Wait a minute. Such numbers are called prime numbers; They play an important role in pure mathematics and its application. exist
In all natural numbers, the distribution of such prime numbers does not follow any laws; However, German mathematics
Garriman
( 1826~ 1866)
According to observation,
The frequency of prime numbers is closely related to a well-constructed so-called Riemann Tsai.
Tower function
Z (S $
Nature of. The famous Riemann hypothesis asserts that the equation
z(s)=0
All the meaningful solutions are in
In a straight line. It's been like this from the beginning.
1,500,000,000
The solution has been verified.
What is Riemann Hypothesis?
What is this?
"
Riemann hypothesis
"
?
If the Riemann hypothesis is confirmed, what's the point?
How's Riemann conjecture going? Is it completely solved?
What are the world-class math problems that reward millions?
8.
white poplar
-
Mills theory
Also known as gauge field theory, it studies four kinds of interactions in nature (electromagnetism, weakness, strength and gravity).
Basic theory,
By physicist Yang Zhenning and
R.L
Mills is at
1954
It was first put forward in 2008.
Its origin
Based on the analysis of electromagnetic interaction, the unity of weak interaction and electromagnetic interaction is established by using it.
The theory has been confirmed by experiments, especially the intermediate bose predicted by this theory to propagate weak interaction.
Son, has been found in the experiment. Young-Mills theory is the basis of studying hadrons (participating in strong interactions).
This particle structure provides a powerful tool.
white poplar
-
What does Mills' field theory say?
What is Yang?
-
Mills equation?
Which is more important, Yang Zhenning or Einstein's scientific achievements and contributions?
What are photons and quanta in physics?
Yang Zhenning's masterpiece
9.
Naville
-
Stokes equation
The ups and downs of the waves accompanied our boat winding across the lake, and the turbulent airflow followed me.
Our modern jet plane. Mathematicians and physicists are convinced that whether it is breeze or turbulence,
They can be explained and predicted by understanding the solution of Naville-Stokes equation. although
These equations are
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Written in the th century, we know little about them. The challenge lies in the understanding of mathematical theory.
Make substantial progress, so that we can solve the hidden mystery in Naville-Stokes equation.
Naville, the world's mathematical problem
-
Stokes equation
What are the math problems in the world?
A very profound question about airflow, Naville.
-
Stokes equation
Hilbert problem and
20
Century mathematics
About the century
seven
Information about big math problems
10. Software of University of California at Berkeley (Berkeley Software Distribution)
guess
The full name of Bell's and Swenetton-Dale's conjecture. In fact, as Matthias Sevic pointed out, Hill.
Bert's tenth question is unsolvable, that is, there is no universal method to determine whether there is such a method.
Integer solution. When the solution is a point of Abelian cluster, Behe and Sveneton-Dale conjecture exist.
The size of rational point group and related Zeta function
z(s)
Order again
s= 1
Sex in the neighborhood. In particular, this
An interesting guess is that if
z( 1)
be qualified for sth
0,
Then there is the point of infinite rationality.
(
solve
)
On the contrary, if
z( 1)
unequal to
0,
Then there are only a few such points.
A mathematical mystery that has not been solved so far
University of California, Berkeley Software Distribution.
guess
Mathematics field
23
What are the big problems?
Does anyone know what the specific mathematical problems of the seventh century are?
introduce
"
Seven mathematical problems in the world
"
?
What are the seven major mathematical problems in the world?
1 1.
The third division of an angle
One of the three major geometric problems in ancient Greece. Between 500 and 600 BC, Greek mathematicians had already thought about it.
To the method of bisecting any angle, as we have learned in geometry textbooks or geometric paintings: use a known angle.
The vertex of is the center of the circle, and the two sides of the arc intersection angle with appropriate radius get two intersection points, and then take these two points respectively.
Draw an arc with an appropriate length with the center of the circle as the radius. The intersection of these two arcs is connected with the corner top to divide the known angle.
Split in half. Since it is so easy to split a known angle into two, it is natural to change the problem slightly: 3
How about equal parts? In this way, this problem naturally arises.
I can. The angle is divided into three parts.
Ruler compass drawing method
The third division of an angle
Can I divide it into three parts with a ruler and an angle?
The angle of graduated ruler and compass is divided into three parts.
How to divide it?
Is it okay to divide the angle into three parts?
12.
Cubic double product
One of the three major geometric problems in ancient Greece has a myth about cubic product: the hope of the past.
The plague is prevalent in Los Angeles, Lartet, and residents dare not pray to Apollo, the patron saint of the island.
Sister Yan told them God's instructions:
"
Double the cube altar in front of the temple and the plague will stop.
Stop.
"
This shows that this great god likes mathematics very much. The residents were very happy after receiving this instruction and took action immediately.
The workers made a new altar, making each side twice as long as the old one, but not only did the plague not exist.
Stop, but more rampant, so that they are all surprised and afraid.
How did three geometric problems lead to the emergence of modern algebra
History of ruler painting (research report required)
What are the three major geometric problems in ancient Greece?
What are the three major geometric problems in ancient times?
Brief introduction of "three difficult problems of plane geometry"
13.
Turn a circle into a square.
Turning a circle into a square is one of the drawing problems of ancient Greek rulers, that is, finding a square with an area equal to 1
The area of a circle. pass by
Pi?
In order to transcend numbers, we should know that this problem can not be completed by a ruler alone. But if the restrictions are relaxed,
System, this problem can be completed by a special curve. Such as the secant of Scipio and Archimedes.
Spiral and so on.
Turn a circle into a square?
Galois was the first to prove the problem of turning a circle into a square.
Used in interrogative sentences and adverbs/to express confusion
What is this?
"
Quadrature problem of circle
"
Turn a circle into a square.
About; In all parts of; about
"
Turn a circle into a square.
"
I hope to have an answer as soon as possible.
14.
Drawing with a ruler is not a problem.
The problem that rulers and rulers can't draw is the problem that they can't draw with rulers and rulers. One of the most famous.
This is a classic problem called the three major problems of geometry. exist
2400
These questions were raised in ancient Greece many years ago.
until
1837
Year,
The French mathematician Mancer first proved.
"
The third division of an angle
"
and
"
Beilifang
"
Draw a ruler
No problem.
1882
German mathematician Lin Deman proved in 1920.
Pi?
After exceeding the number,
"
Turn a circle into a square.
"
Facts have also proved that
Drawing a ruler is not a problem.
certificate
"
Turn a circle into a square.
"
It is a process that a ruler can't draw a problem.
The problem of drawing with three rulers cannot be solved.
How to prove that straightedge drawing can't be an angle trisection?
Can a ruler draw a circle and know it?
2
These lines are tangent and pass through the known
1
individual
main points
Why can't a ruler and a ruler draw any angle in three equal parts?