Gauss's famous mathematical sayings
1. Mathematics is the queen of science and number theory is the queen of mathematics.
2. Half of the proofs are equal to 0.
3. What gives me the greatest happiness is not knowing knowledge, but learning constantly; Not what you already have, but what you keep getting; Not the height that has been reached, but the constant climbing.
You, nature, are my goddess, and my contribution to your law is limited.
Shallow knowledge keeps people away from God, while extensive knowledge keeps people close to God.
Gauss's Mathematical Achievements
Euclid once pointed out that the geometric drawing of equilateral triangles, equilateral quadrangles, equilateral pentagons, equilateral pentagons and equilateral polygons with twice the number of sides mentioned above can be realized with compasses and rulers, but the research on this issue has not made much progress since then. On the basis of number theory, Gauss put forward a criterion to judge whether a regular polygon with a given number of sides can be drawn geometrically. For example, you can use compasses and rulers to make a regular heptagon inscribed in a circle. This is the first discovery after Euclid.
These works on number theory have contributed to the modern arithmetic theory of algebraic numbers (that is, the solution of algebraic equations).
Gauss also introduced complex numbers into number theory, which initiated the arithmetic theory of complex integers. Before Gauss, complex integers were only introduced intuitively. In 183 1 (published in 1832), he explained in detail how to develop an accurate complex theory by means of representations on the x and y planes.
Gauss was one of the first people to doubt that Euclidean geometry was inherent in nature and thought. Euclid was the first person to establish system geometry. Some basic ideas in his model are called axioms, which are the starting point of building the whole system through pure logic. Among these axioms, the parallel axiom stands out from the beginning. According to this axiom, only a straight line parallel to a given straight line can pass through any point that is not on this straight line.
It was soon speculated that this axiom could be deduced from other axioms and thus deleted from the axiomatic system. But all the proofs about it are wrong. Gauss was one of the first people to realize that there may be an axiom that geometry does not apply to parallel lines. He gradually came to a revolutionary conclusion: such geometry does exist, and its inherent compatibility is not contradictory. But he dared not publish it because it was contrary to the views of his contemporaries.
When Bolyai of Hungary and Lobachevsky of Russia independently published non-Euclidean geometry around 1830, Gauss claimed that he had reached the same conclusion about 30 years ago. Gauss hasn't published any works about special complex functions, perhaps because he can't deduce them from more general principles. So this theory had to be reconstructed by other mathematicians from his works decades after his death.
1830 or so, the principle of extremum (maximum and minimum) began to occupy an important position in Gauss's physical problems and mathematical research, such as the condition that the fluid remains static. When discussing capillary action, he put forward a mathematical formula, which can consider the interaction of all particles in the fluid system, gravity and the interaction between fluid particles and solids or fluid particles in contact with them. This work contributes to the development of the principle of conservation of energy. Since 1830, Gauss and physicist William? Edward? Weber works closely together. Because of their common interest in geomagnetism, they established a worldwide systematic observation network together. Their most important achievement in electromagnetism is the development of telegraph. Due to limited funds, these experiments are all small-scale.
Goss's personal data
John? Carl. Friedrich? Gauss (C.F.Gauss,1April 30, 777-1February 23, 855), male, is a famous mathematician, physicist, astronomer and geodetic scientist in Germany. Gauss is one of the founders of modern mathematics and is regarded as one of the most important mathematicians in history. The prince of mathematics? Known as. Gauss ranks alongside Archimedes and Newton as the three greatest mathematicians in the world. He has achieved great success in his life, in his name? Gauss? The result of naming is 1 10, which is the highest among mathematicians. Gauss has a great influence in history, and can be juxtaposed with Archimedes, Newton and Euler.
1792, Degaus entered Brunswick College at the age of 15. There, Gauss began to study advanced mathematics. The general form of independent discovery binomial theorem, number theory? Quadratic reciprocity law? , prime number distribution theorem, arithmetic geometric average.
1795 Gauss entered the University of G? ttingen. 1796, 17-year-old gauss got a very important achievement in the history of mathematics, that is, the theory and method of drawing a regular 17-sided ruler, which provided the first important supplement for Euclidean geometry that has been circulated for 2000 years since the ancient Greek era. 1807, Gauss became a professor at the University of G? ttingen and director of the local observatory. With the help of his survey adjustment theory based on least square method, Gauss calculated the trajectory of celestial bodies. So we found the trajectory of ceres. Ceres was discovered by Italian astronomer Piazi in 180 1 year, but he delayed his observation due to illness and lost the trajectory of this asteroid. Piazi in Greek mythology? The goddess of harvest? (Ceres) named it Planetoiden Ceres, and announced the previously observed position, hoping that astronomers all over the world can find it together. Gauss calculated the trajectory of Ceres through the previous three observation data. Austrian astronomer Heinrich Olbers successfully discovered this asteroid in the orbit calculated by Gauss. Since then, Gauss has become famous all over the world. Gauss wrote this method in his book The Theory of Celestial Motion. 1855 died in gottingen on the morning of February 23rd.