Mathematical genius Lobachevsky

The mathematics we learn from childhood tells us that parallel lines never intersect. But if someone has a different opinion and puts forward his new theory, which is eventually confirmed by later people, who is this person and what is his story, today we will reveal this mathematical genius Lobachevsky.

The path of growth

Lobachevsky was born in the eighteenth century to an ordinary Russian family and showed a keen interest and talent for mathematics from his childhood. He was not just a genius, as he was admitted to Kazan University at the age of less than 15.

In just four years, Lobachevsky completed his undergraduate and master's degree and obtained a master's degree in physics and mathematics. After completing his basic studies, he stayed on as an assistant professor and was already a permanent professor before he turned 30.

During his stay, he was not a "nerd" who only closed his door and poured out his knowledge. He was actively involved in the administrative affairs of the school, was elected to the school committee, and was twice appointed to the position of head of the Department of Physics and Mathematics for many years.

To say that Lobachevsky was a young man who was highly regarded and expected would not be an overstatement.

The road less traveled

Lobachevsky was indeed a genius, so it seems that he was destined to take the road less traveled, a genius who had to bear the price of breaking through the misunderstandings and loneliness of innovation.

During his time at Kazan University, Lobachevsky was actively involved in the administration of the university, while on the other hand, he did not stop with his academic studies. He encountered an unprecedented challenge just when he was absorbed in trying to prove the fifth metric in Euclidean geometry.

The doctrine of Euclidean geometry is a set of axioms or axioms that have been compiled by Euclid and completed by the achievements of human geometry up to the third century, that is, they have been recognized as correct and can be directly used as the results of other derivations of the basic theory without proof.

According to Euclid's compilation, he believed that the axioms could be universally applied to all sciences, while the axioms were only applicable to the field of geometry.

The problem arises with the fifth axiom of Euclidean geometry, also known as the axiom of parallelism: if a line segment intersects two lines with an interior angle sum smaller than the sum of the two right angles on one side, then the two lines, after being continuously extended, will intersect on the side with an interior angle sum smaller than the sum of the two right angles.

From the third century until the nineteenth century, generations of mathematicians tried to give their proofs, but no miracle happened. Lobachevsky was also interested in proving the parallel axiom at first, but he was also confused and had nothing to gain.

Suddenly, one day, Lobachevsky had an idea: if this axiom cannot be proved directly, then I can prove that its converse is also a path that can be explored, so he started his research on the converse of the fifth axiom.

In 1826, Lobachevsky publicly presented his research paper "Summary of the Principles of Geometry and the Strict Proof of the Parallel Lines Theorem" at a school conference, which concluded that there was a fallacy in the fifth axiom and, to put it bluntly, proved that parallel lines could also intersect.

However, the audience was indifferent in the face of the fanciful arguments presented by a novice mathematics researcher, and there was no lively discussion of the contents of the paper. Even a few other respected professors present at the time directly evaluated his research results with a "no pass".

Perseverance in the truth

Since he first published his challenge to the fifth axiom, Lobachevsky did not win any academic applause, but he was convinced of the correctness of his new doctrine and continued to improve his proofs.

Moreover, due to his outstanding performance in the administrative affairs of the university, he was elected as the rector of Kazan University, which was also a kind of shining light from the east.

In the course of his continuous research on his new geometric theory, Lobachevsky encountered more and more attacks, because there were also hard-liners in the mathematical research community.

Instead of refuting the loopholes of Rochevsky's geometry from an academic point of view, these hard-liners attacked it in a bottomless manner by denigrating it, because the proofs of Rochevsky's geometry were completely unavailable in the reality of the time, and were attacked as heresy.

Many publications, as a result, refused to publish Robachevsky's articles. Lobachevsky was like a Copernicus of the new age, but he was still the head of a school and could still publish in his school.

Lobachevsky persisted in his decades of dedicated research, building his edifice of Rochevsky's geometric doctrine even stronger.

In his later years, he suffered more hardships in life, one of his children passed away and he lost his eyesight due to eye disease, but he still used the last days of his life to finish his work "On Geometry" by dictating it to himself and recording it by others.

It was not until 12 years after he departed from this world that the doctrine of Rochevsky's geometry was recognized and accepted, thanks to the proof of Rochevsky's geometry published by an Italian scientist.

In the course of human development, the development of theory always precedes practice for many years or even spans hundreds of years. Lobachevsky's contribution to the doctrine of Roche's geometry laid the foundation and provided the ideas for the later understanding of space physics, astronomy, and other research, and his contribution speaks for itself.

Science is also a very rigorous study, scientists proposed a variety of doctrines that need to go through scientific colleagues after sufficient time to refine, and verify to become a new scientific cornerstone, scientific workers are indeed a group of people worthy of our respect.