Lobachevski

Nicholas Ivanovich Lobachevsky (December 1st, 1792 (Yenzi year) February 24th, 1856), Russian mathematician, African One of the early discoverers of Ou Geometry.

Name
Nikolas lvanovich Lobachevsky
Country of Citizenship
Russia
Date of birth
(1792 (Yen Zi Year) December 1
Date of death
February 24, 1856
Profession
Russian mathematician
Place of birth
Russia

Life

Lobachevs entered Kazan University in 1807, obtained a master's degree in physics and mathematics in 1811, and stayed at the school to work. In 1814, he served as assistant to the professor. He was promoted to an additional professor in 1816. Became a permanent professor in 1822. From 1818, Lobachevsky began to hold administrative positions and was first elected to the Kazan University Council. In 1822, he served as a member of the New School Building Engineering Committee. Was elected as the chairman of the committee in 1825. During this period, he served twice as the head of the Department of Physics and Mathematics (1820-1821, 1823-1825). Due to his outstanding work performance, in 1827, the university committee elected him as the president of Kazan University. After 1846, he served as deputy superintendent of the Kazan School District until his death.

When Lobachevsky tried to prove the parallel axioms, he found that all previous proofs could not escape the error of circular argumentation. Therefore, he made the assumption that if you pass a point outside the straight line, you can make countless straight lines parallel to the known straight lines. If this assumption is rejected, then the parallel axiom is proved. However, he not only failed to deny this proposition, but also used it with other propositions in Euclidean geometry that had nothing to do with the parallel axioms, and obtained a logically reasonable new geometric system— non-Euclidean geometry. It is what people call Roche's geometry later on.

The creation of Rochevsky's geometry played a huge role in the development of geometry and mathematics as a whole, but it did not attract attention at the beginning, and it was gradually recognized by Lobachevsky 12 years after his death. Lobachevsky also has certain achievements in mathematical analysis and algebra

Personal story

In 1893, the world's first statue of a mathematician was erected at Kazan University. This mathematician is Lobachevsky, a great Russian scholar and an important founder of non-Euclidean geometry.

Non-Euclidean geometry is a great creative achievement in the history of human cognition. Its establishment has not only brought about tremendous progress in mathematics in the past century, but also has a profound impact on the transformation of modern physics, astronomy, and the concept of human time and space.

However, for a long time after Lobachevsky proposed this important mathematical discovery, not only did it fail to win recognition and praise from society, but it was also subject to various distortions, criticisms, and attacks, which made non-Euclidean geometry. The new theory has not been recognized by academia for a long time.

Discover the background

In the process of trying to solve the problem of Euclidean Fifth Post, Lobachevsky embarked on his path of discovery from failure. Europe's fifth postulate problem is that the history of mathematics, one of the oldest well-known problems, it is from the ancient Greek scholar was first put forward.

In the third century BC, Euclid, the founder of the Greek Alexandrian school, compiled the great achievements of predecessors in geometry research and compiled the mathematics masterpiece "The Originals of Geometry ", which has an extremely profound influence on the history of mathematical development.

The important significance of this work is that it is the earliest example of the establishment of a scientific theoretical system using axioms. In this work, Euclid gave five axioms (applicable to all sciences) and five postulates (applicable to geometry only) as logical deductions for deducing all the propositions of geometry. premise. " Elements of geometry " of commentators and the commentators who are very satisfied with the first four of five axioms and postulates, with the exception of the fifth postulate (ie parallel axiom) raised the question.

The fifth postulate is about parallel lines. What it says is: if a straight line intersects two straight lines, and the sum of the two internal angles formed by the same side is less than two right angles, then extend the two straight lines and they must intersect on one side two internal angles. Mathematicians do not doubt the authenticity of this proposition but think that it is not much like a postulate in terms of the length or content of the sentence, but rather like a proving theorem, only because Euclid could not. Only after finding its proof did it have to be listed in the postulate.

In order to give proof of the fifth postulate and complete the work that Euclid could not complete, from the 3rd century BC to the beginning of the 19th century, mathematicians invested endless energy and tried almost every possible method. , But they all failed.

Discovery

Lobachevsky started to study the theory of parallel lines in 1815. In the beginning, he also followed the ideas of his predecessors and tried to prove the fifth postulate. In the preserved notes of his students' lectures, there are some proofs given by him in geometry teaching in the 1816-1817 academic year. However, he soon realized that his proof was wrong.

His predecessors and his own failures enlightened him from the negative side, and made him boldly think about the opposite formulation of the problem: there may be no proof of the fifth postulate at all. So, he changed his mind and set out to find an unprovable answer to the fifth post. This is a completely new way to explore, which is completely contrary to traditional thinking. It is precisely along this path that Lobachevsky discovered a brand new geometric world in the process of trying to prove that the fifth post is unprovable.

Anyway, how did Lobachevsky demonstrate that the fifth post is unprovable? How could you find the new mathematical world from it? It worked out that he innovatively utilized a legitimate strategy regularly used to manage the complex numerical issues the technique for evidence by inconsistency.

The fundamental thought of this inconsistency technique is that to demonstrate that "the fifth post isn't certain", the fifth post is first invalidated, and afterward, this nullified recommendation and different aphorisms are utilized to shape another adage framework, and intelligent allowances are done from this.

As indicated by this coherent line of thought, Lobachevsky kept the same recommendation from getting the fifth to hypothesize—Plefel's aphorism, "On the off chance that you pass a point outside a straight line on the plane, you can just present a straight line that doesn't converge the known straight line". Acquired the negative recommendation "crossing a point outside a straight line on the plane, something like two straight lines can be referred to as not converging with the known straight line", and utilize this negative suggestion and different maxims to frame another adage framework to complete coherent allowances.

During the time spent derivation, he got a progression of odd and truly preposterous recommendations. Be that as it may, after cautious assessment, there is no sensible inconsistency between them. Consequently, the foresighted Lobachevsky intensely attested that this new aphorism arrangement of "there is no inconsistency in the outcome" can establish another sort of calculation, and its legitimate trustworthiness and thoroughness can be tantamount to that of Euclid. It's mathematically similar. Also, the presence of this new math without inconsistency is an invalidation of the provability of the fifth hypothesizes, which is coherent confirmation of the unprovability of the fifth proposal. Since the model and similarity of the new calculation, in reality, have not yet been discovered, Lobachevsky cautiously calls this new math "nonexistent math".

Lack of concern and forswearing

On February 23-1826 Lobachevs, taking into account the academic social affair of the Division of Material science and Math of Kazan Schooldetailed his first paper on non-Euclidean computation: "Rundown of the Severe Evidence of the Standards of Math and Equal Line Hypothesis". The coming of this spearheading paper denoted the introduction of non-Euclidean calculation. Notwithstanding, when this significant accomplishment was disclosed, it was met with detachment and resistance from universal mathematicians.

Numerous specialists with significant numerical accomplishments took an interest in this scholarly meeting. Among them were the popular mathematician and space expert Simonov, Gupfer who later turned into an academician of the Foundation of Sciences, and Bora who was notable in arithmetic. Sman. In the personalities of these individuals, Lobachevsky is an exceptionally skilled youthful mathematician.

Nonetheless, incredibly, after the short introductory statements, the youthful educator proceeded to express some mysterious things, like the inward point of a triangle and under two right points, and it turns out to be limitlessly more modest as the side length increments. , Until it approaches zero; the upward line on one side of the intense point may not converge with the opposite side, etc.

These recommendations are strange, clashing with Euclidean calculation, yet additionally in spite of individuals' everyday experience. In any case, the columnist brought up truly and certainly that they have a place with a new, intelligently thorough calculation, which has a similar right of presence as Euclidean math. These peculiar words came from an unmistakable leaning and thorough scholastic teacher, and they really wanted to astound the members. They originally showed a sort of uncertainty and shock, and sooner or later, they showed different negative articulations.

After the introduction of the proposition, Lobachevsky warmly welcomed the members to talk about and propose changes. Notwithstanding, nobody was able to disclose any remarks, and the gathering was uninterested. A unique and significant revelation was made. Those companion specialists who were quick to pay attention to the revelation by the pioneer himself, but since of moderate reasoning, not just neglected to comprehend the meaning of the disclosure however embraced cold talk and hatred. Demeanor, this is actually something lamentable.

After the gathering, the scholarly board of the division endowed Simonov, Gupfer, and Bolasman to frame a three-man examination group to make a composed evaluation of Lobachevsky's proposal. Their demeanor is without a doubt negative, yet they have been hesitant to compose their viewpoints recorded as a hard copy so that in the end even the composition was lost.

Insults and assaults

Lobachevsky's spearheading paper neglected to attract the thought and thought of the scholastic world, and therefore the actual paper seemed to fall under the ocean, and that I haven't got the foggiest plan wherever it had been deserted. In any case, he wasn't debilitated on these lines, but perpetually unbroken on investigating the secrets of recent maths alone. In 1829, he composed another postulation named "Standards of Math". This paper imitates the basic thoughts of the first paper and encompasses a few enhancements and advancements. Right now, Nikolai Ivanovich Lobachevsky has been chosen because of the leader of the urban center school, presumptively because of his "regard" to the president. The "Kazan school Notice" distributed this paper fully.

In 1832, at Lobachevsky's solicitation, the critical Panel of urban center school conferred this paper to the military campaign Foundation of Sciences for the survey. the muse of Sciences appointed the favored scientist Academician Ostrogradsky to form the appraisal. Ostrogradsky may be a recently chosen academician. He has created exceptional accomplishments in numerical natural science, numerical examination, mechanics, and divine mechanics, and encompasses a high standing within the scholastic circles around then. it's a pity that even a very extraordinary scientist did not comprehend Lobachevsky's new mathematical thoughts, and he was way more traditionalist than the lecturers of the urban center school.

Assuming the educators of the urban center school area unit were still "lenient" towards Nikolai Ivanovich Lobachevsky himself, Ostrogradsky utilized surprisingly mocking language and offered a public expression regarding Nikolai Ivanovich Lobachevsky. Allegations and assaults. On Nov seven of that terribly year, he composed jokingly toward the beginning of his analysis to the muse of Sciences: "It seems to be that the author plans to compose a piece that's immeasurable. He accomplished his objective.", Twisted and place down Lobachevsky's new mathematical musings. Eventually, I showing bad manners affirmed: "From this, I found the resolution that this work by President Nikolai Ivanovich Lobachevsky is deceptive to such associate degree extent that it does not advantage the thought of the muse of Sciences."

This paper excited the disturbance of scholastic specialists, nonetheless, in addition, stirred antagonistic clatter from traditionalist powers within the public arena. 2 people named Blaček and Terene, in secret composing articles within the "Child of the Homeland" magazine, freely named Nikolai Ivanovich Lobachevsky truly attack.

Because of this sinning unknown article, Nikolai Ivanovich Lobachevsky composed a counter article. even so, the "Child of the Mother country" magazine suppressed Lobachevsky's article on the grounds of defensive the magazine's standing and ne'er distributed it. In such a way, Nikolai Ivanovich Lobachevsky was unbelievably furious.

Lobachevsky, World Health Organization has battled in separation for as long as he will keep in mind, created another field of arithmetic, however, his innovative work has not been perceived and perceived by the critical world throughout his period. solely 2 years before his ending, the notable Russian scientist Boone Yakov Noam Chomsky likewise his book "equal lines" a book on the Nikolai Ivanovich Lobachevsky dispatch associate degree assault, he tried to look at non-Euclidean calculation and therefore the irregularity of experimental info keeps the legality from obtaining non-Euclidean calculation.

The popular English scientist Morgan's protection from the non-Euclidean calculation is significantly a lot obvious. He even subjectively aforementioned while not specifically concentrating on non-Euclidean math: "I do not suppose there'll be any struggles with non-Euclidean calculation whenever. geometrician maths is largely not an equivalent joined a lot of variety of calculation." Morgan's words address the demeanor of the scholastic circles towards non-Euclidean maths around then.

Weakness and dejection

In the hard course making|of constructing} and creating non-Euclidean maths, Nikolai Ivanovich Lobachevsky ne'er met his public allies, even Gauss of FRG, an extra pioneer of non-Euclidean calculation, declined to transparently uphold him. Work.

Gauss was the most scholastic skilled in science around then, and he was called the "ruler of European math". As right time as 1792, that is, the year Nikolai Ivanovich Lobachevsky was formed, he had effectively created the germination of non-Euclidean calculation, and by 1817 it had found a grownup level. He initially referred to this new maths "against geometrician calculation", later referred to as "brilliant math", last referred to as "non-Euclidean math". In any case, Gauss expected that the new maths would excite disappointment within the scholastic world and resistance from society, which might influence his pride and honor. throughout his period, he had not started to form this vital revealing of his own to the global public, but simply incompletely warily. The outcomes area unit wrote within the journal and correspondence with companions.

At the purpose once Gauss saw Lobachevsky's German non-European maths work "Mathematical Investigations of Equal Line Hypothesis," he clashed. From one viewpoint, he in secret counseled Nikolai Ivanovich Lobachevsky as "Russian" before his companions. Quite presumably the foremost exceptional" not extremely set in stone to be told Russian with the goal that he might squarely examine everything of Lobachevsky's chips away at non-Euclidean calculation; nonetheless, he did not allow his companions to reveal his insight into non-Euclidean maths to the remainder of the globe. Admission, and ne'er overtly remarked on Lobachevsky's work on non-Euclidean maths in any structure. He effectively selected Nikolai Ivanovich Lobachevsky because of the Correspondence Individual of the majestic Institute of Sciences in Göttingen. the foremost exceptional commitment is that the formation of non-Euclidean calculation, however, tries to not discuss it.

Gauss, together with his standing and impact in maths, is completely conceivable to reduce Lobachevsky's pressing issue and advance the acknowledgment of non-Euclidean calculation within the critical world. In any case, even with obstinate traditionalist powers, he lost the natural virtue of battle. Gauss ' quiet and defect not simply seriously restricted the tallness he will accomplish within the investigation of non-Euclidean calculation, nonetheless in addition impartially urged the traditionalist powers to assault Nikolai Ivanovich Lobachevsky.

In his later years, Lobachevsky's temperament was considerably heavier. He was suppressed scholastically moreover as confined in work. As per the rules of the Russian school Gathering at that time, the foremost extreme term of a teacher's arrangement was thirty years. As per this guideline, in 1846 Nikolai Ivanovich Lobachevsky conferred associate degree charm to the Service of Individuals' Schooling, mentioning that he be mitigated of his add the mathematics Instructing and Exploration workplace and prompt that he be supplanted. To his understudy Popov.

The Service of Individuals' Schooling has since a long time ago held biases against Lobachevsky, who didn't follow their will, yet couldn't track down an appropriate chance to eliminate him from the post of leader of Kazan College. Lobachevsky's application for abdication as an educator was blamed not exclusively to eliminate him from leading the instructing and exploration segment yet additionally against his own desires by eliminating every one of his posts at Kazan College. Being driven away from the college work that he adored for his entire life, Lobachevsky experienced a serious mental blow. He communicated incredible outrage at this preposterous choice of the Service of Individuals' Schooling.

The setback of the family has added to his trouble. His top choice and skilled oldest child passed on of tuberculosis, which made him extremely pitiful. His body became more diseased and more ailing, his eyes bit by bit became visually impaired, lastly, he neglected to focus on anything.

On February 12, 1856, the extraordinary researcher Lobachevsky finished the last piece of his life in sorrow and gloom. The educators and understudies of Kazan College held a fabulous dedication administration for him. At the commemoration administration, a large number of his partners and understudies exceptionally lauded his extraordinary accomplishments in building Kazan College, raising the degree of public instruction, and developing science abilities, yet nobody referenced his work in the non-Euclidean calculation, in light of the fact that as of now, Individuals likewise, for the most part, believe that non-Euclidean math is unadulterated "gibberish".

Lobachevsky has been battling for the endurance and advancement of non-Euclidean math for over 30 years. He has never shaken his firm faith in the extraordinary eventual fate of new math. To extend the impact of non-Euclidean calculation and endeavor to get early acknowledgment from the scholastic local area, as well as utilizing Russian, he likewise composed his own books in French and German. Simultaneously, he additionally carefully planned a galactic perception program to test the mathematical attributes of enormous scope space.

Not just that, he likewise fostered the insightful and differential pieces of non-Euclidean calculation, making it a total and orderly hypothetical framework. In the difficulty of being truly sick and laid up, he didn't quit concentrating on non-Euclidean calculation. His keep going work of art "On Calculation" was finished by directing his understudies a year prior to he was visually impaired and passed on.

Acknowledgment and acclaim

History is the most attractive on the grounds that it will ultimately make the right assessments of different considerations, conclusions, and feelings. In 1868, the Italian mathematician Bertrami distributed a popular paper "An Endeavor to Decipher Non-Euclidean Calculation ", demonstrating that non-Euclidean math can be acknowledged on the outer layer of Euclidean space. This implies that non-Euclidean calculation suggestions can be "interpreted" into relating Euclidean math recommendations. On the off chance that Euclidean math has no inconsistencies, non-Euclidean calculation normally has no inconsistencies.

Up to that point, the non-Euclidean math, which has not been focused on for quite a while, has started to get general consideration and inside and out research in the scholastic local area. Lobachevsky's unique examination has likewise been exceptionally commended and collectively lauded by the scholastic local area. Lobachevsky was adulated as "the Copernicus in calculation ".

On the excursion of logical investigation, it isn't hard for an individual to withstand transitory difficulties and blows, however, the trouble is to dare to battle in misfortune for quite a while or in any event, for a lifetime. Lobachevsky is a hero who battles for life in misfortune.

Additionally, a logical specialist, particularly a profoundly esteemed scholastic master, isn't hard to effectively recognize those logical outcomes that are mature or have clear pragmatic importance, however, it is hard to distinguish those that are youthful or that have not yet uncovered their viable importance on schedule. Logical outcomes. Every one of our logical laborers ought to be a 2scientific voyager who dares to gesture in affliction, yet in addition a firm ally of new things in the logical field.