17 Math Formulas That Changed the World

Jin Lei from the qubit of the concave temple | public account QbitAI

Mathematics has always been a subject that I think is very magical. When I was in school, I didn’t know the use of mathematics. I even felt that the mathematics major could not even find a job, so ghosts would go to school. Of course, there was no concept of AI at that time.

Since I came into contact with machine learning and deep learning, I realized that my original cognition was simply too small. Mathematics is not only powerful, but it has been changing the world.

Below are 17 formulas that can change the world. Some have learned it, some have not. Let’s review it together. My personal favorite is the 6th Euler formula.

1. Pythagorean

English:

Pythagoras’ Theorem

official:

definition:

In a right triangle in the plane, the sum of the squares of the sides of the two right angles equals the square of the hypotenuse.

This basic geometric theorem, in the 11th century BC, the mathematician Shang Gao (in the early years of the Western Zhou Dynasty) proposed "go three, share four, and string five".

In the West, the Greek mathematician Pythagoras proved the Pythagorean theorem in the 6th century BC, so Westerners are accustomed to calling this theorem Pythagoras' Theorem.

"Old Bi" also proved the golden section line. The Pythagoras school he founded was one of the four major schools of ancient Greece.

The Pythagorean theorem is considered to be the origin of the demonstration of geometry. It is the first theorem in history to link numbers and shapes, and the first indefinite equation in history to give a complete solution.

This theorem is not only a dazzling pearl in geometry, but also known as "the cornerstone of geometry" .

2. Logarithmic

English:

Logarithms

official:

definition:

If a raised to the power of x is equal to N (a>0, and a≠1), then the number x is called the logarithm of N with base a.

The logarithmic method was invented in 1614 by the mathematician John Pinar.

But this method is of great significance both at the time and now, and its emergence has made many difficult calculations possible.

For this reason, it was used for a long time in surveying, navigation, and other practical branches of mathematics before the advent of calculators and computers.

3. Calculus

English:

Calculus

official:

The formula given here is the definition of derivative in calculus.

In fact, calculus is a branch of mathematics that studies functions of differentiation, integration, and related concepts and applications in advanced mathematics.

Differential calculus includes the operation of taking derivatives and is a set of theories about the rate of change. It enables functions, velocities, accelerations, and slopes of curves to be discussed with a common set of symbols.

Integral calculus, including the operation of integrals, provides a general method for defining and calculating areas, volumes, etc.

Von Neumann once commented on calculus as follows:

It was the first achievement of modern mathematics, and its importance cannot be overstated.

Calculus, I think, more clearly than anything else shows the beginnings of modern mathematics; moreover, the system of mathematical analysis as its logical development still constitutes the greatest technological advance in precise thinking.

Many problems that cannot be solved by elementary mathematics can often be solved by calculus, and many natural phenomena can also be described by establishing differential equations.

Because of this, calculus is widely used in kinematics, astronomy, economics, sociology, chemistry, biology, etc.

4. The law of universal gravitation

English:

Law of Gravity

official:

definition:

Any two particles have a mutual attraction force in the direction of the center line:

The magnitude of the gravitational force is proportional to the product of their mass and inversely proportional to the square of their distance, and has nothing to do with the chemical composition of the two objects and the type of medium between them.

Among them, F represents the gravitational force between two objects; G represents the gravitational constant; m1 and m2 represent the mass of object 1 and object 2, respectively; r is the distance (size) between the two objects.

The law of universal gravitation was published by Newton in "Mathematical Principles of Natural Philosophy" in 1687. It can be said to be one of the greatest achievements of natural science in the 17th century.

He used the law of universal gravitation to prove Kepler's laws, the motion of the moon around the earth, the causes of tides, and natural phenomena such as the flattening of the earth's poles.

Therefore, Newton's law of universal gravitation is the basis of celestial mechanics . The orbits of artificial satellites, lunar and planetary probes are calculated based on this law.

5. Square root of -1

English:

The square root of -1

official:

Mathematicians have been expanding the concept of numbers, from natural numbers to negative numbers, fractions, to real numbers.

In the 16th century, the Milanese scholar Cardan introduced the concept of plurals for the first time.

After the work of D'Alembert, De Morpher, Euler, Gauss and others, this concept was gradually accepted by mathematicians.

From a mathematical point of view, complex numbers can be said to be extremely elegant. Any equation has a complex solution, but this situation does not hold for real numbers.

For example, for x2 + 4 = 0, there is no real solution, but for complex numbers, the solution is -4 or 2i.

And calculus can also be extended to complex numbers, and mathematicians have also discovered some symmetries and properties of numbers.

These properties make complex numbers important in electronics and signal processing.

6. Polyhedron Euler's Theorem

English:

Euler’s Polyhedra Formula

official:

definition:

For a simple polyhedron in n-dimensional space, the number of zero-dimensional objects (that is, the number of vertices) D0, the number of one-dimensional objects (that is, the number of edges) D1, the number of two-dimensional objects (that is, the number of faces) D2, the number of three-dimensional objects (that is, the number of bodies) ) D3, ..., the number of n-dimensional objects Dn:

The signs are alternately appearing with positive and negative signs, one side of the equation is the repeated addition and subtraction of the number of objects in each dimension, and the other side of the equation is 1.

Generally, V (Vertex) represents the number D0 of zero-dimensional objects (ie vertices), E (Edge) represents the number D1 of one-dimensional objects (ie edges, edges), and F (Flat surface) represents the number of two-dimensional objects (ie faces) D2, S (Solid) represents the number of three-dimensional objects (ie, volumes) D3, and P represents the number of four-dimensional objects D4.

For a general three-dimensional space, the formula is expressed as: V - E + F - S= 1 .

Since for a three-dimensional object, its body number S is always 1, so the above formula is obtained.

This observation by Euler is now regarded as one of the earliest examples of topological invariance.

Together with his solution to the Konigsberg bridge problem, it can be said that it paved the way for the development of topology, making it an indispensable branch of mathematics in modern physics.

This is also the formula that Musk likes. The translation is: eiπ + 1 = 0, which is Euler's formula known as the most beautiful formula in history.

Due to space reasons, other formulas will not be expanded one by one. Interested friends can click the link at the end of the article to view the details.

All in all, after reading this list of formulas, many netizens expressed the following emotions:

Which is your favorite formula? Welcome to share in the comment area.

Reference link:

[1]https://www.businessinsider.com/17-equations-that-changed-the-world-2014-3#1-the-pythagorean-theorem-1
[2]https://twitter.com/gunsnrosesgirl3/status/1500925968956993540