1, Corazze conjecture

Corazze's conjecture, also called even-odd normalization conjecture, means that for every positive integer, if it is odd, multiply it by 3 and add 1, if it is even, divide it by 2, and so on, and finally get 1.

2. Goldbach conjecture

Goldbach conjecture is one of the oldest unsolved problems in mathematics. It can be expressed as: any even number greater than 2 can be expressed as the sum of two prime numbers. For example, 4 = 2+2; 12 = 5 + 7; 14 = 3 + 1 1 = 7 + 7。 In other words, every even number greater than or equal to 4 is a Goldbach number, which can be expressed as the sum of two prime numbers.

3. Twin prime conjecture

This conjecture originated from the German mathematician Hill Bert, who proposed at the 1900 International Congress of Mathematicians that there are infinitely many prime numbers P, making p+2 a prime number.

Among them, the prime pair (p, p+2) is called twin prime numbers. 1849, the French mathematician Alfonso de Polignac put forward the conjecture of twin prime numbers: for all natural numbers k, there are infinite prime pairs (p, p+2k). The case of k = 1 is the twin prime conjecture.

4. Riemann conjecture

Riemann conjecture was put forward by German mathematician Bernhard Riemann in 1859. It is an important and famous unsolved problem in mathematics, known as the "crown of conjecture", which has attracted many outstanding mathematicians to rack their brains for many years.

For each S, this function gives an infinite sum, and some basic calculations are needed to find the simplest value of S. For example, s = 2, then (S) is the well-known sequence1+1/4+1/9+1/6. / 6。 When s is a complex number (a complex number that looks like a +b), it is very tricky to find it by imaginary number.

5. Bell and Swinerton-Dell conjecture

Behr and Swinaton-Dale conjecture are expressed as follows: For any elliptic curve in the rational number field, the zeroing order of its L function at 1 is equal to the rank of Abel group formed by rational points on the curve.

Let e be an elliptic curve defined on algebraic number field k, and E(K) be a rational point set on e, and it is known that E(K) is a finite generating commutative group. Remember that L(s, e) is the l function of e, then Behr and Swinaton-Dell conjecture formulas in the above figure are generated.

6. The number of kisses

When a bunch of spheres are piled up in an area, each sphere has a "number of kisses", that is, the number of other spheres it touches. For example, if you want to touch six adjacent spheres, then your number of kisses is six. A bunch of spheres will have an average number of kisses, which helps to describe this situation mathematically. However, the number of kisses has not been solved mathematically.

7, slipknot fast knot problem

Mathematically, the problem of slipknot deadlock is to determine the number of knots in the algorithm given a knot.

Connecting the two ends of the rope at infinity forms a topological knot. If this knot is topologically equivalent to a circle in a sense, it means that the original knot is a slipknot, otherwise it is a dead knot.

8. Large base

In the mathematical field of set theory, the nature of large cardinality is the nature of finite cardinality. As the name implies, cardinality with this property is usually very large, and they cannot be proved by the most common axiomatization of set theory.

Minimum infinity, recorded as. That's the Hebrew letter aleph；; It says "aleph- zero". It is the size of a set of natural numbers, so it is written as |? |=。 Next, some common sets are larger than the size. The main example of cantor's proof is that the real number set is large, but |? | > means.

9、π+e

This problem is all algebraic real numbers. Definition: A real number is algebraic if it is the root of some integer coefficient polynomials. Like x? -6 is a polynomial with integer coefficients, because 1 and -6 are both integers. x？ The root of -6= 0 is x =√6, and x =-√6, which means that √6 and -√6 are algebraic numbers.

All rational numbers and their roots are algebraic. So it may feel that "most" real numbers are algebraic, but the result is just the opposite. Real numbers can be traced back to ancient mathematics, and E did not appear until17th century.

10 and γ are rational numbers?

This is another problem that is easier to write than to solve. It is Euler-Mas Ceroni constant, which is the difference between harmonic series and natural logarithm.