Russian mathematical genius: claimed that parallel lines can intersect, but was questioned and ended in frustration, which was confirmed 12 years later

Tech 2023-05-04 21:34:54 Source: Network

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On the path of human technological development, there are many great scientists who have played a very important role in human technological development. Without the contributions of these scientists, human technological development may have regressed by several hundred years. Modern science believes that humans were born more than 2 million years ago, and at that time, there were many other ferocious creatures living on Earth. Ape like organisms in order to survive for a long time, So they chose to live in groups, which not only promoted opportunities for mutual communication, but also effectively resisted foreign invaders. Scientists have studied that frequent communication can make brain development faster and faster. Due to long-term living together, the brain of apes has become increasingly intelligent, and ultimately evolved into humans.

On the path of human technological development, mathematics is very important for humanity. Mathematics can help humanity achieve many wishes, but it is also a field that pursues extreme accuracy. In such a very rigorous field, it is normal for some mathematicians' theories to be questioned. In human history, many great mathematicians have devoted their lives to studying a theory, Many mathematicians have also lost their precious lives due to being questioned by the outside world. If the preservation of fire brought about the development of reality and mysterious colors to primitive humans, then the discovery of numbers marks the primitive progress of reality and aesthetics. Each of us has been learning the concept of numbers since childhood, and different things can have the same quantity in the sense of counting, and this abstract quantity is called number by humans.

According to the research of scientists, the history of mathematics began with tying ropes to record things. About tens of thousands of years ago, people in the Primitive Society used ropes to tie knots to express things and numbers, and used ropes to express the size of wild animals. The concept of number developed slowly. 5000 years ago, the ancient Egyptians learned agricultural production earlier. Later, more than 2000 years ago, the ancient Greeks inherited and developed mathematical knowledge, It also developed numbers into a discipline. The study of the true meaning of human science began in ancient Greece. The first mathematician in modern history of mathematics was Pythagoras. Although Plato and Aristotle had a great influence on later generations, the greatest achievement of ancient Greece was to establish a relatively perfect mathematical world, This mathematical world is not like Plato's Republic and Aristotle's metaphysical view of nature.

It has had a significant impact on human history. Mathematics has brought rationality to humanity, and it is a persistent spirit of exploration. The earliest to abstract numbers and elevate their status to an unparalleled level was the ancient Greek mathematician Pythagoras, who was also the first mathematician in human history. Since then, more and more scientists have studied mathematics, In Russia, there is such a mathematical genius as Lobachevsky, whose theory was only confirmed by humans after his death. Lobachevsky is a famous Russian mathematician and one of the earliest discoverers of non Euclidean geometry. In 1807, Lobachevsky successfully entered the famous Kazan University with extraordinary intelligence.

At the age of 19, he obtained a master's degree in physical mathematics. In the field of mathematics, the most mainstream discussion in geometry is the study of Euclidean geometric theory, which is actually the study of plane geometry and space geometry. Euclidean was a very famous mathematician in history, and many of his ideas were unshakable truths at that time, leaving many room for speculation for future generations, Years ago, Lobachevsky also launched speculations about plane geometry and space geometry. At that time, while studying Euclidean's fifth idea, he suddenly raised a strange question: why do two parallel lines never intersect? After this theory was proposed, it quickly received ridicule from mainstream mathematicians, who believed that Lobachevsky's speculation was a bunch of nonsense.

However, these doubts did not affect Lobachevsky's research. He continued to complete his "Non Euclidean Geometry Thought". At that time, like Copernicus, he was not recognized, but he still adhered to his ideals and beliefs in his heart. However, reality dealt a very cruel blow to Lobachevsky. In the midst of everyone's questioning, Lobachevsky not only stepped down from the altar of mathematical genius, And in 1856, he left the world at the age of 64. In Lobachevsky's heart, he had always believed in a viewpoint: to do something satisfactorily, either you must do it yourself, or you must be proficient in it, ensuring that you can provide precise and clear advice to the people involved in it. It was because of his fifth postulate with Euclid that he lost his life.

So what are the five postulates of Euclid? Hypothesis 1. A straight line can be drawn from any point to another point, Hypothesis 2. A finite line segment can be infinitely extended, Hypothesis 3. A circle can be drawn from any point at any distance, Hypothesis 4. All right angles are equal to each other, Hypothesis 5. If both lines intersect with the third line and the inner angles on the same side are only less than two right angles, then these two lines must intersect on this side. In the history of human mathematics, many mathematicians attempted to overthrow these five postulates, but ultimately failed. Prior to this, Lobachevsky, like his predecessors, studied the five postulates of Euclid. When he encountered difficulties in his research, he made a major decision and no longer pursued the footsteps of his predecessors. He believed that the fifth postulate may not exist at all, as long as he could find an answer that the fifth postulate cannot be proven, So all the problems have been solved.

Unfortunately, during his lifetime, Lobachevsky did not see his theory believed. In human history, many scientists were the same as Lobachevsky. Copernicus proposed the heliocentric theory, which was also questioned and mocked by many. In 1543, before his death, Copernicus published "On the Motion of Celestial Bodies," which is known as the starting point of modern astronomy and opened up the Copernicus Revolution, It also promoted the Scientific Revolution and made significant contributions. In the Copernican era, people believed in the geocentric theory, and believed that the earth was the center of the universe. The sun and the moon were rotating around the earth. At that time, Copernicus discovered the loophole of the geocentric theory. In the next 20 years, he insisted on observing and measuring the position of the planets every day.

Based on years of observation, Copernicus believed that the Earth could not be the center of a planet's orbit, and that the annual variation of the Sun was not significant, which means that the distance between the Earth and the Sun has never changed significantly. At this time, if the position of the Sun was placed at the center of the universe, the Earth should rotate around the Sun. Later, he proposed the heliocentric theory, but at that time, his heliocentric theory was not recognized, Moreover, his "Theory of the Movement of Celestial Bodies" did not dare to be published in the public. It was not until Copernicus died that his "Theory of the Movement of Celestial Bodies" was recognized by the world. In the 17th century, Galileo and Johannes Kepler proved Copernicus' theory was correct from both the observation and theory levels.

To commemorate Copernicus' achievements, one of the most prominent craters on the moon was named Copernicus Crater. The most prominent feature of this 93 kilometer diameter crater is the bright radiation patterns distributed around it. Copernicus had a great impact on future generations. If it did not propose the heliocentric theory, human astronomy might have regressed to several hundred years. These stories tell us that truth always emerges in the long river of history, Just like Lobachevsky's theory, 12 years after his death, this theory was proven by Italian mathematician Bertrami, who had always believed that Lobachevsky's theory was correct, but due to the oppressive social environment at that time. Many mathematicians who support Lobachevsky are also unable to express their views, so they can only conduct theoretical research on Lobachevsky alone.

After a long period of research, he finally published the "Explanation of Non Euclidean Geometry" in 1868 and proved that parallel lines can actually intersect. He proposed that Euclidean parallel lines cannot intersect only in Euclidean plane systems, and Lobachevsky's parallel line intersection must also be completed in non Euclidean geometry systems. Later, in order to commemorate Lobachevsky, the University of Kazan, A commemorative statue was built for him in the school, reminding everyone to adhere to the truth and never give up. In our ordinary understanding, parallel lines cannot intersect, which is actually due to the limitations of our knowledge. The plane geometry we studied in school is based on the Euclidean geometry framework, where the definition of parallel lines is two non intersecting straight lines in a two-dimensional plane.

In Euclidean geometry, parallel lines can be extended indefinitely and never intersect, which is also in line with human intuition. However, if the sum of the inner angles of a triangle on a two-dimensional surface can be less than 180 degrees, it can also be greater than 180 degrees at that time. Due to the sharp angle formed by two straight lines, a perpendicular can be drawn to one side, and this perpendicular can not intersect with the other side. In a two-dimensional surface, it passes through a point outside the line, Multiple straight lines can be made parallel to known lines, but there are also situations where parallel lines cannot be made. In other words, on a two-dimensional surface, there is no true parallel line, and any two lines have a common intersection. In the early 20th century, the famous physicist Einstein proposed the theory of relativity based on four-dimensional space and non Euclidean geometry, reshaping the spatiotemporal structure of the entire universe for humanity.

According to Einstein's theory of relativity, we can know that flat spacetime is only a special case of the universe at small and medium-sized scales. On large scales, there is no so-called flat spacetime, so non Euclidean geometry is the essence of the universe, because the entire universe has a certain curvature. Although the universe we observe is almost flat, this only indicates that the range we observe is very small, Just like the ground we see on Earth is actually flat, but if we stand outside the Earth, the Earth we see is actually a spherical shape, and the Earth itself is also spherical. The reason why we see the Earth on the ground as flat is because our observation range is too small to only observe local areas. If we stand on the scale of the entire universe, there are no absolute parallel lines, Two infinitely extended lines will intersect due to the curvature of the universe.

The great philosopher Plato once said: Truth may be on the side of a few people. In human history, there are many truths that have been questioned before they were proposed, and only a few people can hold onto them. Truth needs to go through a long process from being discovered to being recognized by the public. The surface geometry established by Lobachevsky allows two parallel straight lines to intersect under changes in curvature, This concept violates the laws of plane geometry, but it is more in line with the reality of the universe. It was ultimately confirmed by Einstein that every scientist's success was not accidental. Einstein was able to become one of the greatest scientists in human history and also experienced many hardships. Before Einstein, everyone believed in Newton's absolute view of time and space.

Newton believed that time and space are the same, just a geometric parameter that describes the motion of an object. This is a spatialized external time, and the increase and decrease of time describe the displacement of an object as a point in space without involving or affecting its internal properties. After Einstein appeared, he broke this theory and explained the relationship between velocity and time in Einstein's theory of relativity, And it also explained the relationship between gravity and time. Einstein believed that time, matter, and space are all related. Now we have proven that time, space, and matter are all one. This theory has overturned humanity's traditional understanding of time and given scientists a new understanding of the universe.

On the path of human development, there are many twists and turns. Only those who adhere to the truth and have the courage to face the doubts of the world can reach the end. The high achievements of human science today cannot be achieved without the persistence of these scientists. Currently, human technology is still constantly advancing and developing, and human understanding of the world is not very comprehensive. There are still many mysteries hidden in the universe that we do not know, These mysteries are waiting for humanity to explore and study. The editor believes that as the most intelligent life on Earth, humans have been continuously exploring the mysteries of the world since their birth. Currently, humans have been able to explore the universe outside of the Earth, indicating the rapid development of human technology. With the progress of human technology in the future, perhaps we can unravel the mysteries of the universe. We hope that this day can come soon, Do you have anything to say?

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