Euler is "Shakespeare in mathematics". 1707 On a sunny day, he came to the earth in Basel, Switzerland. It is such a genius that he will change the history of mathematics, the whole history of science and even the history of mankind. At the age of 13, Euler was admitted to university of basel and studied under the most famous mathematician at that time, johann bernoulli. 17 got his master's degree. From then on, he began his scientific career. It is said that Euler wrote 886 books and thousands of papers in his life, and it took him 47 years to sort out his works! In mathematics, it is recognized that there is a most beautiful formula, which was discovered by Euler of Basel and appeared in 1784. Before looking at that formula, let's look at its general form: eiθ=cos θ+isinθ. This is Euler's formula. Where e is the base of natural logarithm and I is the unit of imaginary number. Ok, ok, if we make θ = π, what do we get? Well, eiπ= cosπ+isπ=- 1+0 or another variant, eiπ+ 1= 0. This is the most beautiful formula in mathematics, a special case of Euler formula. Why is it the most beautiful? Look, it connects the most important constants in mathematics. 0, 1, e, π, I, where 0 and 1 represent the oldest and most basic branch of mathematics-arithmetic; E stands for analysis; And pi can represent geometry; The imaginary unit I stands for algebra. Wow, a formula that connects the four branches of mathematics is undoubtedly the most beautiful! Actually, it's more than that. Euler's formula is very powerful, which makes its beautiful position more stable. For example, we can turn trigonometry problems back to complex problems to solve, and so on. This reminds me of a book by Shen Zhiyuan that science is beautiful. Be more specific-math is beautiful.

The beauty of perfection (1)

No subject can show a series of complete and perfect worlds with so many symbols like mathematics. Let's just say that the set of real numbers is complete, and any number of real numbers can be added, subtracted, multiplied and divided at will, and the result is still real numbers (note: mathematical completeness is strictly defined according to the convergence of sequence. I am not a complete statement in the strict sense here, but it can be considered as a general statement). The imaginary unit is introduced, and the real set is extended to the complex set, or any number of complex numbers. If you do those operations, the result is still a complex number.

By abstracting concrete numbers into points in space, under certain assumptions and conventions, a complete space can be obtained, which can be one-dimensional, two-dimensional, three-dimensional or even multi-dimensional. Beyond three dimensions, you can't imagine it, but you can't deny its existence. Points and sequences in a certain space can be operated according to certain rules, but they still cannot leave that space. This is integrity. This integrity is wonderful. You can imagine it as a sphere. No matter how you move, you can't get out of the sphere.

A complete space can bring many benefits. Hilbert space is the most used space in engineering. By the way, Hilbert is one of the greatest mathematicians in the twentieth century.

In addition, many systems in mathematics are also complete, such as Euclidean geometry, which is well known. On the basis of several axioms, a series of beautiful conclusions are derived, which have enduring vitality, especially in engineering applications.

(2) the beauty of symmetry

When it comes to the beauty of symmetry, the first thing that comes to mind is geometry. In fact, geometry is only one aspect, which is a "visible" aspect. In fact, symmetry is everywhere in mathematics. For example, the basic theorem of calculus shows the close relationship between differential and integral, which has strong symmetry itself. For example, dual operators in functional not only have obvious symmetry in operation, but also show consistency in properties everywhere.

(3) the beauty of simplicity

There is a beautiful formula in mathematics, that is Euler formula. This formula relates several "great" numbers in mathematics, they are natural logarithm, pi, imaginary unit and 1, among which the first two are transcendental numbers, which have been discovered only by human beings at present and have great influence on mathematics. I dare to guess that when the next transcendental number is found, mathematics will experience another great revolution. Imaginary unit seems nothing special today, but when it was first introduced, it was questioned and opposed by many mathematicians. Finally came in, mathematics opened up a broad road, that is, complex variable function.

There is no doubt that Euler's formula is simple and perfect, and another formula that can compete with it has appeared in physics, that is Einstein's formula of mass-energy conversion. I may be a little arbitrary in this statement, but I can only think of this at present, hehe.

(4) the beauty of abstraction

This may cause many people to disagree, because in many people's eyes, abstraction is not good, because it is too far from reality. But I don't think so. If mathematics is not abstract, it is difficult to develop, although many problems come from reality. Mathematics is based on symbolic logic. Even if we solve practical problems, we should abstract them and express them with mathematical symbols, so that we can solve them well. On the other hand, abstract mathematics can drive you to roam in the infinite thinking space, put aside all other thoughts and become a beautiful enjoyment. Of course, this is a bit idealistic, but there is no denying that it is indeed a wonderful experience.