Who is the best mathematician in the field of mathematics?

There have always been four kings in the history of mathematics, and the development of mathematics has been related to them for thousands of years. They tortured your primary school, middle school and university. They are Archimedes, the god of mathematics, Newton, the father of classical mechanics, Euler, the hero of mathematics, and Gauss, the prince of mathematics.

Archimedes, the God of Mathematics

In ancient Greece, mathematics had begun to sprout. A large number of mathematicians were born. The Greeks regarded rational numbers as an arithmetic continuum from the beginning, and mathematicians represented by Plato tried to establish a mathematical model based on numbers.

However, the Pythagorean school discovered irrational numbers at this time, which triggered a mathematical crisis of more than 2,000 years. In order to avoid irrational numbers, ancient Greek mathematicians made a lot of efforts. Eudoxus of Pythagoras School directly declared the bankruptcy of establishing mathematical model based on numbers and established deductive system based on explicit axioms, which greatly promoted the development of geometry. Since then, geometry has become the mainstream of Greek mathematics.

Euclid put forward the idea based on geometry, and the ancient Greeks developed logical thoughts in this idea, which deepened their understanding of the essential characteristics of mathematics such as abstraction and idealization.

Raphael reappears the glory of ancient Greek mathematics and art

The work of eudoxus, Euclid and others not only summarized all previous geometric knowledge, but also established the first geometric axiom system (Euclid-Hilbert geometric axiom system). He also wrote the book The Elements of Geometry. This is undoubtedly a great revolution in mathematical thought. Classical logic and Euclid geometry are the products of the first crisis.

At this time, Archimedes was born. Archimedes studied under Euclid. Archimedes further improved the geometric system, and he published a series of geometric works.

For example, on balls and cylinders (in

Sphere and cylinder), the quadrature of parabola method

Parabola), "measurement of circle", "on the balance of the plate" (on the plane

Balance), "on cone ellipsoid", "sand calculation" (sand

Calculator), on methods (Archimedes' letter to erato Sese, some theorems about geometry), on floating bodies (on floating)

Corpse), "Lemma". In the geometry of these works, he supplemented many original studies on the quadrature method of plane curves and the determination of the volume surrounded by surfaces.

But Archimedes did not abandon Plato's idea of mathematical model based on numbers, and the seeds of numbers were preserved here, which is very important for the future, because the West regarded Euclid geometry as the Bible for a long time.

He foresaw the concept of minimum division, which played an important role in17th century mathematics. It is the predecessor of calculus, and Archimedes quadrature method is the bud of integral thought. In this way, Archimedes discovered many theorems.

Archimedes also studied spirals and wrote them. Some people think that, in a sense, this is the most wonderful part of Archimedes' all contributions to mathematics. Many scholars foresaw the calculus method in his spiral tangent method. To his credit, he defined mathematical objects from the perspective of movement. If a ray rotates around its endpoint at a uniform speed, at the same time, a point moves along the ray from the endpoint at a uniform speed.

All the conclusions made by Jimmy are obtained without algebraic symbols, which makes the process of proof quite complicated. But with amazing originality, Jimmy combined skillful calculation skills with strict proof, and closely combined abstract theory with concrete application of engineering technology.

Archimedes' work on geometry is the pinnacle of Greek mathematics, which pushes it to a new stage. He harmoniously combined Euclid's rigorous reasoning method with Plato's colorful imagination, reached the state of perfection and beauty, and laid a solid foundation for the development of mathematics for more than 2,000 years. So Archimedes is called "the God of Mathematics" by many mathematicians.

Newton, the father of classical mechanics

Newton's greatest achievement in mathematics is that he and Leibniz independently created calculus. 1May 20th, 665 is a very meaningful day in the history of mathematics. Newton, a great physicist, put forward "flow counting" (differential method) for the first time, and "counter-current counting" (integral method) in May 1666, which marked the establishment of calculus.

Newton put forward calculus mainly to solve the following problems:

1. Find the velocity and acceleration at any moment with the "distance-time" function relation of the known object motion. The time interval of "any moment" is 0, so his displacement must be 0, which leads to the difficulty of v=0/0.

2. Find the tangent of the curve

3. Find the maximum and minimum value of the function

4. Find the length of the curve, the area enclosed by the curve, the volume enclosed by the surface and the center of gravity of the object.

So calculus mainly includes these aspects, including limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and the slope of the curve can be discussed with a set of universal symbols. Integral calculus includes the calculation of integral, which provides a general method for the definition and calculation of area and volume.

Newton calculus manuscript

Since then, Newton's calculus has been further improved under the movement of "arithmetic analysis" by Euler, Cauchy and Wilstrass.

The appearance of calculus greatly promoted the development of mathematics. Many problems that cannot be solved by elementary mathematics in the past can often be solved by calculus, which shows the extraordinary power of calculus. Drake formula, divergence theorem and classical Stokes formula. Conceptually and technically, they are all extensions of Newton-Leibniz formula.

Von Neumann once said: Calculus is the first achievement of modern mathematics, and its importance cannot be overestimated. In my opinion, calculus shows the beginning of modern mathematics more clearly than anything else; Moreover, as its logical development, mathematical analysis system still constitutes the greatest technological progress in precision thinking.

In addition, calculus has promoted the great development and prosperity of physics, and physical problems are generally expressed in the form of differential equations. It also ushered in the era of great development and prosperity of science, which lasted for a whole period of time.

More than 200 years, until the last month of the 20th century, these 200 years.

Over the years, countless famous mathematicians and scientists have emerged. They applied calculus to astronomy, mechanics, optics, heat and other fields, and achieved fruitful results. In mathematics itself, the theories of multivariate differential calculus, multiple integral calculus, differential equation, infinite series and variational method have been developed, which greatly expanded the scope of mathematical research. For example, the most famous problem is the steepest descent line.

Calculus also promoted the development of industrial revolution, promoted the improvement of social productivity and made great progress in social civilization.

"Mathematical Hero" Euler

Euler is really a chosen son. Not only does he have a photographic memory, but only when he is blind can he solve many problems by mental arithmetic.

Euler's greatest contribution is that he invented a series of symbols that have far-reaching influence on mankind. The use of mathematical language symbols can avoid the ambiguity of this written language, ensure the accuracy and clarity of mathematical language, and make its language form completely conform to the substantive content expressed in the form.

1748, Euler published "Introduction to Infinite Analysis", which is one of the seven masterpieces of mathematics, and is as famous as Gauss's arithmetic research. This book is an epoch-making masterpiece in the history of mathematics. At that time, mathematicians called Euler "the embodiment of analysis".

Why talk about this book alone? Because the development of mathematics in the next few hundred years is largely related to this book.

Euler's Introduction to Infinitesimal Analysis first systematically discusses the concept of taking logarithm as exponent and trigonometric function as numerical ratio to replace some line segments, and then taking function as the center and main line, and taking function as the main research object to replace curve, so that infinitesimal analysis no longer depends on geometric properties.

In Euler's Introduction to Infinitesimal Analysis, he defined trigonometric functions as infinite series, expressed Euler's formula and used the abbreviation of sin. Because. Don. ，cot。 , seconds. And cosec. Yes, these symbols were invented by Euler.

Euler made trigonometry a systematic science. He first gave the definition of trigonometric function by ratio, but he always used the length of line segment as the definition before. The learning of trigonometric functions is mostly carried out in a circle with a certain radius. For example, Ptolemy in ancient Greece set a radius of 60; India's Ayabata (about 476-550) has a radius of 3438; German mathematician Giovannas (1436- 1476)

In order to accurately calculate the trigonometric function value, the radius is set to 600,000; Later, in order to make a more accurate sine table, the radius was set to 10'. So the trigonometric function at that time was actually the length of some line segments in the circle.

Euler's definition makes trigonometry jump out of the circle of studying triangular tables only. Euler analyzed and studied the whole trigonometry. Before that, every formula was only derived from the chart, and most of them were expressed by narration. Euler analytically deduced all the triangular formulas from the first few formulas, and got many new formulas. Euler used a

, b and c represent the three sides of a triangle, and a, b and c represent the angles opposite to the first side, thus greatly simplifying the narrative. Euler's famous formula:

Euler later linked trigonometric functions with exponential functions. Introduction to differential analysis is not only the beginning of trigonometry research, but also the further improvement of calculus.

Simply put, trigonometric function was perfected by Euler, and exponential and exponential functions also contributed.

In addition, he also invented the symbol π of pi, the symbol f(x) of function, the symbol I of imaginary number, the base E of natural logarithm, σ and so on.

Trigonometry, mathematical analysis, topology, exponential function, perfect expansion of calculus, perfect expansion of functions, algebraic number theory, analytic number theory, graph theory, etc. all have outstanding achievements and are known as "all-round mathematicians".

According to statistics, in his tireless life, he wrote 886 books and papers, among which analysis, algebra and number theory accounted for 40%, geometry for 18%, physical mechanics for 28%, astronomy for 1 1% and ballistics, navigation and architecture for 3%. In order to organize his works, the Petersburg Academy of Sciences.

It can be said that since Euler, it has largely got rid of the dependence on geometric intuition, which is more logical and easier to analyze.

Mathematics began to get rid of its dependence on geometry. Euler broke through the ideological framework of the ancient Greeks and further transformed it into symbolic algebra. Geometric problems are often solved by algebraic methods in turn. Euler's perfection of calculus has transformed the basic method of mathematical research from geometric deduction in ancient Greece to analytical methods of arithmetic and algebra.

"Prince of Mathematics" Gauss

When Gauss was three years old, his father was a foreman. When he was checking the workers' weekly wages, Gauss took a look at the ledger and was able to help his father correct the mistakes in the ledger.

When Gauss 18 years old, he discovered the prime number distribution theorem and the least square method. Based on this discovery, he created a set of measurement data processing methods. According to this new method, he obtained a measurement result with probability property, and plotted this measurement result as a curve. This curve function distribution is later called Gaussian distribution diagram, also called standard normal distribution.

At the age of 0/9, Gauss/Kloc-discovered the regular drawing method of regular heptagon, which solved the problem that puzzled the mathematics field for more than 2000 years. He is also the first mathematician in the world who successfully solved geometric problems by algebraic methods.

19 years old proved the law of quadratic reciprocity, which is at the center of the development history of number theory. Gauss not only gave the first strict proof, but also proved the law of quadratic reciprocity, and later gave seven proof methods. Put forward one that can be regarded as a great mathematician, and Gauss put forward eight!

When Dr. Gauss graduated, he also discovered the famous basic theorem of algebra. He believes that any unary algebraic equation has roots. This paper shocked the world. Later, after Gauss died, many mathematicians proved the truth of the basic theorem of algebra. Gauss was also the first mathematician in the world to discover this theorem.

There are 1 10 items named after him, which are the most among mathematicians, such as Gaussian distribution (normal distribution), Gaussian fuzzy, Gaussian integral, Gaussian integer, Gaussian elimination, Gaussian curvature, Gaussian filter and Gaussian gravitational constant. It can be said that there are Gauss in great events, Gauss in high numbers and Gauss in geometry ... You close your eyes and pick one of the science and engineering (technical) books. You can definitely find the name Gauss in it ... You just need to open an app and look at the code. Generally speaking, there must be more than one formula related to Gaussian (or the formula of the contents in the bag).

You finally learned a graphic design, which has Gaussian ambiguity. . . It can be said that Gauss is everywhere.

Gauss tomb

This is still the case that Gauss has not published all his research results. Gauss is a very cautious person, probably afraid of hitting his face. His attitude towards his work is to strive for perfection, and he is very strict with the research results. He himself once said: I would rather publish less, but I publish mature results. Many contemporary mathematicians asked him not to be too serious, and to write and publish the results, which is very helpful for the development of mathematics.

Bell once commented on Gauss: Only after Gauss died did people know that he had foreseen some mathematics in the19th century, and had predicted that they would appear before 1800. If he can reveal what he knows, he is likely to be half a century or more advanced than today's mathematics.

Our present mathematics cannot be separated from these four, and their great innovations are the source of many branches of mathematics. It can be said that without these four great mathematicians, there would be no complete mathematical system today.