Horizon: Fermat's Last Theorem
Fermat's Last Theorem was first put forward by the French mathematician Fermat, and was finally proved by andrew wiles in 1994 through the efforts of many mathematicians. This theorem shows that for any integer n greater than 2, the equation x n+y n = z n has no positive integer solution.
Cauchy-Schwartz inequality
Cauchy-Schwartz inequality is an important basic inequality in mathematics, which shows that the value of the inner product will not exceed the product of their respective lengths. It is widely used in various fields, such as signal processing, probability theory, measure theory and so on.
Five basic theorems of linear algebra
Linear algebra is an important branch of mathematics, which uses symbols such as vectors and matrices to express and solve mathematical methods such as linear equations and linear transformation. These five basic theorems include the associative law of matrix multiplication, uniqueness theorem of inverse matrix, rank theorem, determinant theorem and positive definite theorem.
Hamilton quaternion theorem
William Hamilton, an Irish mathematician, discovered Hamiltonian quaternion, and he described the algebraic structure of quaternion. It is widely used in physics, engineering and computer science.
group theory
Group theory is a branch of abstract algebra, which studies the basic properties of symmetry and transformation in algebraic structure. It often appears in geometry, number theory, physics and other fields.
Lagrange's theorem
Lagrange theorem is a basic theorem in group theory, which shows that subgroups of any finite group can be divisible. It is widely used in algebra, geometry, topology and other fields.
Riemann hypothesis
Riemann conjecture is a famous problem in number theory, which was put forward by German mathematician Bernard Riemann. This conjecture shows that the zeros of all nontrivial natural numbers fall on the straight line 1/2+it, where t is a real number and I is an imaginary unit.
Twelve-tone sequence
Twelve-tone sequence is a technique in early 20th century music, which was invented by Austrian composer arnold schoenberg. This technique takes 12 notes as raw materials, so that each note only appears once in a piece of music.
Shortened curve algorithm
Shortened curve algorithm is an algorithm in cryptography, which can be used to encrypt and decrypt information. Invented by American mathematician Eugene Kubowski, it is widely used in digital signature, data encryption and other fields.
Bernoulli number
Bernoulli number is an important concept in mathematics, which describes the relationship between the coefficients of polynomial functions. Bernoulli numbers are widely used in number theory, combinatorial mathematics, geometry and physics.