Simplicity itself is a kind of beauty, and the primary feature of mathematics lies in simplicity. The world is diverse. Mathematical theories are abstracted from chaotic objective phenomena and expressed in simple and clear mathematical forms, which in turn explain and deal with more objective things and phenomena. This is the beauty of simplicity in mathematics. Just as excellent poetry pays attention to expressing the richest content with the least words, formulas, rules and theorems in mathematics use refined language and symbols to highly summarize the relationship and structure of real world quantities. You see, there are so many triangles in the world, and the shapes are unimaginable. But their area calculation can be highly condensed into such a relationship to calculate the area of all polygons. The form is so simple and the application is so extensive, 5 = 10. A, from which we can conclude that. The emergence and development of mathematical symbols make mathematical expressions extremely concise. A lot of numerical calculations, a series of numerical formulas, how annoying it is to sort out a mess. But we can sum them up with a mathematical expression. The continuous product n (n-1) (n-2) ... 3.2.1is so troublesome to write. You can use the factorial symbol "n!" Very succinctly expressed. Using the symbol ""for reasoning gives people a rigorous, orderly, clear and vivid aesthetic feeling.
Second, the unified beauty of mathematics
Using a higher level concept, formula or theory to unify many concepts, formulas and theories will make people get a kind of psychological pleasure, which is the unified beauty of mathematics. In mathematical research, people are always looking for a higher degree of abstraction in order to have a wider generalization and a wider scope of application, so many concepts belong to one concept and many formulas have a unified formula. For example, there are many concepts in primary school geometry: square, rectangle, trapezoid and parallelogram, but they are all quadrilaterals. In primary school mathematics, we have the area formulas of triangle, parallelogram and trapezoid. Although they are different, they can be unified by the formula S = 1/2 (A 10 b)h (in the formula, "A is the upper bottom, B is the lower bottom, and H is the height"). In mathematics learning, many excellent students are always pursuing the unified beauty in mathematics problems in the process of solving problems. They think that only by finding a unified law for solving a class of problems can they truly master mathematical knowledge and enjoy beauty from it.
Third, the singular beauty of mathematics.
Singularity refers to the originality or unexpected result of law. The singular beauty in mathematics is as exciting and enjoyable as the ups and downs of literary stories and precious and peculiar works of art. No matter what kind of triangle you draw, its three high lines intersect at one point and its three middle lines intersect at one point. The bisectors of the three angles intersect at one point, showing an ingenious beauty, which makes people feel that there seems to be a magical law in the triangle, which is surprising and mysterious. In the operation, we will be surprised by the equations of 39 13× 9 = 39, 49 14× 9 = 49. Because the numbers on the left and right sides are so symmetrical, we will also be 4109589041096× 83 = 34109589041008. Many conclusions in mathematics are magical because they are ingenious. It is precisely because of this that mathematics has infinite charm. In the history of mathematics development, it is often the singular beauty of mathematics itself that attracts mathematicians to explore at a newer and deeper level and get to the bottom of it.
Fourthly, the singularity of mathematical beauty.
Beauty is strange and magical. bacon
Singularity is an important feature of mathematical beauty. Singularity includes two aspects: one is surprise, and the other is variation. Many conclusions in mathematics are magical, because they are ingenious, and because of this, mathematics has infinite charm. Variation refers to the starting point of new methods, new ideas, new concepts and new theories after the expansion or unity of mathematical theories is destroyed. Variation is contrary to people's imagination and expectation. Therefore, it has aroused people's attention and curiosity. Anything novel and unusual can arouse a sense of pleasure in imagination, because it will make people feel a pleasant freshness in their hearts, and satisfying their curiosity will give people an idea that they have never had before. The birth of many new branches of mathematics is the result of people's discussion on the singularity of mathematics. In the history of mathematics development, it is often the singular charm of mathematics itself that attracts mathematicians.