Russian mathematicians believe that parallel lines can intersect. Why are they ridiculed and questioned?

Can parallel lines intersect? Everyone must think that people who think this way have either not completed nine years of compulsory education or are crazy. However, a Russian mathematician does not think so. This person is the Russian Lobachevsky. ?

Lobachevsky was born in a noble family. He developed a love for mathematics very early and showed his talent. In 1807, when he was only 15 years old, he entered Kazan University. After studying at Kazan University, he received a master's degree in mathematics at the age of 18. In 1822, this 30-year-old youth became the youngest mathematics professor since the founding of Kazan University. He published many mathematics papers and was well received by the industry. In 1827, he was elected as the president of Kazan University. ?

The geometric theorems at that time were basically based on the foundation provided by the mathematician Euclid. ?Parallel lines do not intersect?, which comes from the fifth postulate proposed by Euclid in "Elements of Geometry": ?If a line segment intersects two straight lines, the sum of the interior angles on one side is less than the sum of the two right angles , then after the two straight lines continue to extend, they will intersect on the side where the sum of the interior angles is less than the sum of the two right angles. The Scottish mathematician Playfair proposed a simpler version based on this, which is what people learn in textbooks: Given a straight line. Through any point outside this straight line, there is one and only one straight line parallel to it. ?

In 1826, Lobachevsky proposed a completely different geometric system, which was called "hyperbolic geometry" by later generations. It turned out that Lobachevsky imagined that on a curved surface, The properties of the geometry can change. Two parallel lines can naturally intersect, and the sum of the interior angles of a triangle can be less than 180 degrees. On March 26 of that year, at the academic conference of the Department of Physics and Mathematics of Kazan University, Lobachevsky presented the "Abstract of the Rigorous Proof of the Principles of Geometry and the Parallel Line Theorem" in front of many well-known Russian mathematics scholars and deans at that time. 》 as the title, published his own results. ?

At the meeting, Lobachevsky’s words not only did not receive any response, but were questioned. Some people began to wonder if he was just making a name for himself. However, by 1829, Lobachevsky, who did not give up, was already the principal. He continued to publish the paper "Principles of Geometry" to defend his views. Two scholars named Bla?ek and Tereny ridiculed Lobachevsky, thinking that he was trying to impress others, and that his talent was completely unworthy of the position of principal.

Lobachevsky struggled to argue for himself, but at that time there was no one in Russia or even in Europe who spoke for him. Due to external pressure, Lobachevsky lost his position as principal. Lobachevsky was extremely painful in his later years, and no one stood on his side academically. Finally, in 1856, the scholar completed the last journey of his life.

However, 12 years later, in 1868, the Italian mathematician Bette Nano published an article "An Attempt at the Interpretation of Non-Euclidean Geometry", which mentioned Lobachevsky's point of view and believed that non-Euclidean geometry can be used in The realization of the curved surface of space only attracted the attention of the outside world. Soon after, people realized that Lobachevsky's view that "parallel lines can intersect" was actually correct to a certain extent. The theory he proposed has also been confirmed by the mathematical community.

However, this scientist has passed away suddenly, but the honors he received after his death are countless. People call him the "Copernicus of the scientific world". The story of this scholar has also inspired countless people. People feel admired.