What are the four major mathematical problems in the world?

Cubic double product is to draw a cube with a ruler to make its volume equal to twice that of a known cube. This problem is also called triple double problem, also called Adrian problem and Deloose problem.

If the side length of a cube is known as 1, then the cubic product problem can be transformed into the equation x? -2=0 ruler drawing problem. According to the rule of ruler and ruler drawing, this equation cannot be solved.

Therefore, the problem of cubic product, the problem of angle bisection and the problem of turning a circle into a square have become the three major geometric problems in ancient Greece. The French mathematician Vanzer (P.-L. Wantzel, 1837) gave a strict proof in 1837 that the cubic product problem could not be solved by the straight-edge drawing method.

2. The problem of bisecting any angle

Angular trisection is one of the three major geometric problems in ancient Greece. Angle trisection is a famous problem in the drawing of geometric rulers in ancient Greece. The problem of turning a circle into a square and folding a cube is listed as one of the three difficult problems in ancient mathematics, but now it has been proved mathematically that there is no solution to this problem. The complete description of this problem is as follows: a given angle is divided into three parts, only a compass and an uncalibrated ruler.

On the premise of ruler drawing (ruler drawing refers to drawing with ruler and compass out of proportion), there is no solution to this problem. If the conditions are relaxed, such as allowing a scale, or it can be used with other curves, then a given angle can be divided into three equal parts.

3. 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 that of a given circle. From π as the transcendental number, it can be seen that this problem can't be completed only with rulers and compasses. But if the restrictions are relaxed, this problem can be completed through a special curve. Such as the secant of Scipio and the spiral of Archimedes.

4. Goldbach conjecture

Goldbach put forward the following conjecture in his letter 1742 to Euler: any even number greater than 2 can be written as the sum of two prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler and asked him to help him prove it, but until his death, Euler could not prove it.

Because the conventional saying that "1 is also a prime number" is no longer used in today's mathematics, the modern saying of the original guess is:

Any integer greater than 5 can be written as the sum of three prime numbers. (n>5: When n is even, n=2+(n-2) and n-2 is even, it can be decomposed into the sum of two prime numbers; When n is odd, n=3+(n-3), and n-3 is even, it can be decomposed into the sum of two prime numbers)

Euler also put forward another equivalent version in his defense, that is, any even number greater than 2 can be written as the sum of two prime numbers.

Today's popular conjecture is said to be Euler's version. Any sufficiently large even number can be expressed as the sum of a number with no more than one prime factor and a number with no more than b prime factors, and the proposition is called "a+b".

1966 Chen Jingrun proved that "1+2" holds, that is, "any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number".

Baidu encyclopedia-cubic product problem

Baidu Encyclopedia-Tripartite Arbitrary Angle Problem

Baidu Encyclopedia-Turning Round into Square

Baidu encyclopedia-Goldbach conjecture