The above equation was put forward by Einstein in 19 15, which is a part of his groundbreaking general theory of relativity. This theory completely changed scientists' understanding of gravity by describing gravity as a distortion of space-time structure.

Mario Livio, an astrophysicist at the Institute of Space Telescope Science, said: "It is still amazing for me to describe space-time with such a mathematical equation."

The right side of the equation describes the energy content of our universe, and the left side describes the geometric structure of time and space. This equation reflects that in Einstein's general theory of relativity, mass and energy determine the geometric shape and curvature, which is what we call the manifestation of gravity.

Standard model

The standard model is another leading theory of physics, which describes the collection of elementary particles that are currently considered to constitute our universe.

This theory can be summarized in a master equation called standard Lagrangian model. Except gravity, it successfully describes all the basic particles and forces we have observed in the laboratory so far. Completely in line with quantum mechanics and special relativity. But the standard model theory is not unified with general relativity, which is why it can't describe gravity.

calculus

The first two equations describe specific aspects of our universe, and this equation can be applied to all kinds of situations. The basic theorem of calculus constitutes the backbone of the mathematical method of calculus, and links its two main ideas, the concept of integral and the concept of derivative.

The germination of calculus began in ancient times, but most of it was put forward by isaac newton in17th century. Newton used calculus to describe the motion of planets around the sun.

restricted theory of relativity

Einstein made the list again with his formula of special relativity. Special relativity describes that time and space are not absolute concepts, but relative, depending on the relative speed of observers. The above equation shows that the faster a person moves in any direction, the more time will expand or slow down.

This formula is really concise, but it embodies a brand-new way of looking at the world, an overall attitude towards reality and our relationship with reality. Suddenly, the unchanging universe was swept away and replaced by a personal world related to what you observed.

euler equation

This simple formula summarizes the essence of polyhedron: if the surface of a sphere is cut into polyhedrons with faces, edges and vertices, let f be the number of faces, e be the number of edges and v be the number of vertices, then v–e+f = 2 will always be obtained.

Take a tetrahedron as an example. It consists of four triangles, six sides and four vertices. So in this sense, a sphere can be cut into four faces, six sides and four vertices.

Euler-Lagrange Equation and Nott Theorem

These are abstract, but they have amazing power. The coolest thing is that this way of thinking about physics has survived some major revolutions in physics.

Here, L stands for Lagrangian quantity, which is a measure of energy in physical systems such as springs, levers or elementary particles. Solve this equation and you will know how the system will evolve with time.

A branch of Lagrange equation is called Nott Theorem, named after the 20th century German mathematician emmy noether. This theorem is the basis of physics and symmetry. In layman's terms, this theorem goes like this: If your system is symmetrical, then there is a corresponding law of conservation. For example, the basic laws of physics are the same today and tomorrow, and so are the laws of physics here and in outer space.

Karan-Simanzik equation

The equation has many applications, allowing physicists to estimate the mass and size of protons and neutrons that make up the nucleus. Basic physics tells us that the attraction and electromagnetic force between two objects are inversely proportional to the square of the distance between them. On a simple level, the same is true of powerful nuclear forces, which combine protons and neutrons to form nuclei, and quarks form protons and neutrons. However, small quantum fluctuations can slightly change the dependence of force on distance, which has a dramatic impact on strong nuclear forces.

The scientist said: "It prevents this force from weakening over a long distance and causes it to capture quarks and combine them to form protons and neutrons in our world. What Karan-Simanzik equation does is to connect this dramatic and difficult-to-calculate effect with a more subtle but easier-to-calculate effect, which is important when the distance is about equal to one proton and can be measured when the distance is much less than one proton. "

Minimum surface equation

Frank Morgan, a mathematician at Williams College, said, "The minimum surface equation encodes a beautiful soap film to some extent. When you soak them in soapy water, they will form on the border. " In fact, this equation is "nonlinear", including the product of power and derivative, which is a mathematical hint of the surprising coding behavior of soap film. This is in contrast to more familiar linear partial differential equations, such as heat equation, wave equation and Schrodinger equation in quantum physics.