Euler: He stopped living and calculating
A giant who appeared in a small country
The birth of a scientific giant in a small country is rare in the history of the world, and the Swiss mathematician and physicist Lionel Euler is one of the most outstanding. Although he has lived as an adult in two far-flung, exotic cities—Petersburg and Berlin—his portraits appear on the Swiss franc, and along with the Newton on the pound, he is the only two large-scale banknotes still in circulation in Europe to this day. the scientist. On April 15, 1707, Euler was born in Basel, near France and Germany in northwestern Switzerland. This German-speaking city still has a population of less than 200,000, but it has the oldest university in Switzerland, the University of Basel (1460). ), the Rhine meanders through its center. The German philosopher Nietzsche served as a professor of classical philology at the University of Basel for ten years when he was young, where he completed his masterpiece "The Birth of Tragedy", and became a close friend with Wagner, a musician who spent his later years in the suburbs.
Let's go back in time to Euler's twenty-year-old, 1727. It was a pivotal year for Euler, the year Newton died in London, the year Euler began his academic career, and entered for the first time in a prize-winning competition at the Paris Academy of Sciences – placing a mast on a ship. This traditional competition began in 1721, attracting and motivating countless young people in European countries, and its contribution to science exceeds the establishment of the Nobel Prize. Unfortunately and fortunately, Euler lost the election, and since then he failed to apply for his alma mater, so he left for Russia that year and was employed by the Petersburg Academy of Sciences. However, on the day Euler set foot on Russian territory (May 17), the country's Queen Catherine I died. As the mistress and wife of Peter the Great, Russia's greatest monarch, this humble Lithuanian woman was very open-minded in many ways, fulfilling her husband's desire to establish an academy of sciences in just over two years of her reign. .
The reason why Euler, who came from a priest family, chose his later path of science, cannot but say that it has something to do with a local mathematician surnamed Bernoulli. The Bernoulli family originally lived in the Belgian port city of Antwerp (then part of the Netherlands), but because of religious persecution, they fled to Frankfurt inland at the end of the 16th century, and then moved to Switzerland to settle in Basel. Eight highly accomplished mathematicians emerged in three generations of the family, the eldest of whom, Jacob, became a professor of mathematics at the University of Basel and became a teacher of Euler's father. Although the old Euler was quite talented in mathematics, he almost made the mistake of teaching his son mathematics while asking him to succeed his village priesthood. In fact, for young Westerners from non-noble families in those days, pastor, doctor and lawyer were three good occupations to settle down.
So little Euler went to the University of Basel to study theology and Hebrew, but his mathematical talents soon caught the attention of Jacob's brother John. John succeeded his brother after Jacob's death, and his two sons, Nikolai and Daniel, also became close friends with Euler (both brothers were mathematicians). At the age of seventeen, Euler received a master's degree in philosophy and faced a choice about his future career. Old Euler is still stubborn, thanks to the enthusiastic advice and guarantees of the Bernoulli predecessors, the father finally gave up his own ideas, and the mathematics kingdom would not lose such a great creator. Nikolai and Daniel later applied for employment at the newly established Petersburg Academy of Sciences. It was on the recommendation of their brothers that Euler bid farewell to his fathers and villagers and embarked on the road of mathematics of no return. Although Euler did not become a priest, his father's strong Calvinism gave him a warm and kind heart, and he was very humble throughout his life.
Euler is recognized as one of the founders of pure mathematics and one of the most outstanding and prolific scientists in history. , Mechanics has made significant original contributions, and the results are widely used in the fields of physics and engineering technology. In my opinion, one of Euler's unparalleled virtues is his refinement and patience, which makes mathematical discoveries named after him ubiquitous and always prominent in fields such as Euler's function and Euler's theorem (number theory), Euler's constant (calculus), Euler's formula (complex function), Euler line and Euler circle (geometry), Euler graph (graph theory), Euler characteristic (topology) science), Euler angles (dynamics), Euler equations (fluid mechanics), etc.
Although Euler has never held a teaching position, he is an excellent textbook author. His "Introduction to Infinite Small Analysis", "Principles of Differentiation" and "Principles of Integral" are all landmark works in the history of mathematics. Contains a large number of his own creations, which have been used for a long time as a model for analyzing textbooks. In addition, Euler wrote elementary mathematics courses for Russia, helped reform the weights and measures system, and designed formulas for calculating tax rates, annuities, and pensions. Euler is also one of the mathematicians who made the greatest contribution to the mathematical notation system. The significance of this work is extremely important, but it is often overlooked by people. Euler first used f(x) to represent the function, e represents the base of the natural logarithm, i represents the imaginary number, s represents the perimeter of the triangle, a, b, c represent the sides of the triangle, π represents the pi, Σ represents the summation, and the sine sin, cosine cos and tangent tg were also introduced by Euler, and these symbols are still used today and are well known to the world.
2. Getting along with the Queen and the King
Just as Napoleon was the king with the most mathematicians, the mathematician with the most kings was Euler. Until the 18th century, European universities were not the main centers of academic research, but mathematics was valued because it was closer to the classical tradition than branches of modern science such as physics. However, despite the fact that calculus was born a century ago, the main energy of university professors is still dealing with elementary mathematics, and they devote little energy to cutting-edge research. Unlike the great amateurs in 17th century France, true scholars have their own backers and patrons, that is, professional scientific research institutions. As a result of Leibniz's strong advocacy, with the support of visionary rulers, the Berlin Academy of Sciences and the Petersburg Academy of Sciences were established successively, together with the Italian (Lynx) Academy of Sciences, the Royal Society of England and the Royal Academy of Sciences of France (Messen Academy) , the most active period in the history of mathematics has come.
However, when Euler first arrived in Petersburg, the situation was very difficult. After the death of Catherine I, power fell to a gang of rude and brutal people, and even the young tsar died before he could exercise his power. Those in power saw the Academy of Sciences and its researchers as a dispensation, and they even considered scrapping it and repatriating all foreigners. Fortunately, the Bernoulli brothers originally recommended Euler to go to the medical department, because there were only vacancies there. For this reason, he rushed to study physiology and attended medical lectures at the University of Basel. The chaotic management of the Academy of Sciences gave Euler an opportunity to sneak into the Mathematics Department. For the next six years, Euler immersed himself in his research, completely immersed in the realm of mathematics, until one of his guides, Daniel Bernoulli (Nicolas Bernoulli drowned a year before Euler's arrival) death) decided to leave Russia and return to his homeland.
After Daniel returned to Switzerland, Euler succeeded him as a professor of mathematics at the Petersburg Academy of Sciences. At the age of twenty-six, Euler was about to settle down in Russia. The bride was the daughter of a painter brought back from Peter the Great's westward journey. Euler's Swiss compatriot. Russia had already had a new empress, Anna Ivanovna, the niece of Peter the Great. While Russia endured one of the bloodiest horrors in history under the indirect rule of Anna's lover, the Academy of Sciences did not fare any worse, and mathematicians like Euler were harmless to those in power. Euler loved children, and his two wives (the second was the half-sister of the first) had thirteen children. Euler often wrote papers while holding the baby, while the older children frolicked around their father, one of the few great scientists who could work anywhere and under any conditions.
In 1740, when Queen Anna abdicated and died that year, Euler accepted the invitation of Frederick the Great, King of Prussia, to serve as head of the Mathematics Department at the Berlin Academy of Sciences. Legend has it that the Queen Mother liked Euler, who was honest and serious. Once she deliberately teased him, but Euler's answer was always concise, "yes" or "no". "Why don't you want to talk to me more?" asked the queen mother. "Queen Mother, I just came from such a country, where if you talk too much, you will be hanged." In contrast, Euler did not get along well with the Prussian king, because the king liked ministers who were slapping their horses. He supported mathematics only because he felt that it was a duty, but he hated it from the bottom of his heart, because his own mathematics was so lame that he could not compare with the French emperor Napoleon, who called himself a geometer, And made friends with all the Parisian mathematicians of his time.
On many occasions Euler acted as president of the Berlin Academy of Sciences. Another reason for his unpopularity in Berlin was his ignorance of the philosophical questions that Frederick the Great relished. Once, the French Enlightenment thinker Voltaire came to visit, and after doing everything he could to please the king, he made Euler amused with an almost metaphysical vocabulary. The honest and honest Euler patiently accepted all this, but the king felt that he had lost face. He was determined to find an articulate mathematician to lead his academy. As a result, the Frenchman D'Alembert was invited to Berlin. D'Alembert, who was ten years younger than Euler, was a pioneer of partial differential equations, and he wrote the first work on the principles of dynamics. In addition, he was the deputy editor of the famous "Encyclopedia, or Explanatory Dictionary of Science, Arts and Crafts" (the editor in chief was the philosopher Diderot). Obviously, such an all-rounder was enough to satisfy the vanity of Frederick the Great. Unexpectedly, D'Alembert was a man of clear-headedness and precise judgment, although he and Euler were academically There was some unhappiness. The French guest told the King of Prussia quite frankly that it would be a mistake to put any other mathematician above Euler. Unfortunately, this not only did not make the conceited king change his opinion of Euler, but made Euler even more unbearable. For the future of his children, Euler had to pack and leave Berlin, where he had lived for 25 years, and returned to the cold Petersburg again, along with his wife and children and grandchildren.
At this time, Russia had a new queen, Catherine II, who was originally the daughter of the German prince. Because she came to Russia to marry the grandson of Peter the Great, she had the opportunity to approach and seize the throne. During the thirty-four years of Catherine II's reign, he inherited the unfinished business of Peter the Great, leading Russia to fully participate in the political and cultural life of Europe, formulating codes and implementing reforms, and at the same time capturing Poland and Crimea Most of the territory, so it is also called Catherine the Great. After Euler returned to Petersburg, the Queen received him in royal manner, gave him a large house and furnished sets for a family of eighteen, and went to one of her own cooks. The enraged king of Prussia had to write to the French mathematician Lagrange: "The greatest king of Europe wants the greatest mathematician of Europe in his palace." Obviously, he was bitter about Euler's departure.
There is one thing that shows that Catherine II and Frederick the Great acted in radically different styles. She once invited the French philosopher Diderot to visit, the editor-in-chief of the famous "Encyclopedia". Petersburg was originally built by Peter the Great in imitation of Paris, and the Russians have always respected French culture. Unexpectedly, Diderot tried to persuade the ministers present to convert to atheism in order to show that he was very worthwhile to be invited. This annoyed the queen, and she ordered Euler to use French to silence the talkative philosopher. Euler walked straight to Diderot and said in a very calm and serious tone: "Sir, because (a+b^n)/n=x, God exists!" He refused because his heart was higher than the sky. Diderot, who was in college, knew nothing about mathematics. He was at a loss when he heard it, and the ministers around him responded with warm laughter. The poor philosopher, feeling humiliated, begged the Queen for permission to return at once, and she graciously agreed.
Three tireless blind people
In the history of human civilization, there are many blind singers, from Homer in ancient Greece to Rudaki in medieval Persia, from Milton in modern England to Borges in Argentina in the last century. However, such figures are extremely rare among scientists. Just like Beethoven, who created the immortal melody, lost both ears successively, Euler, who is engaged in mathematics research, is also blind in his later years, but this does not reduce their creativity in the slightest. Beethoven wrote nine symphonies, five piano concertos, ten piano and violin concertos, as well as countless works for piano sonatas, string quartets, vocal and opera. Euler completed more than 800 papers (departments) and books, of which 58% were in mathematics, physics-mechanics and astronomy accounted for 28% and 11% respectively. The remaining three percent are about navigation and architecture. Since the bicentennial of Euler's birth in 1907, the Swiss government has ordered the relevant departments to edit the "Complete Works of Euler", which is a huge work in 72-volume quarto edition, which has not yet been completed.
It must be pointed out that Euler's blindness was not due to family inheritance. Euler was only twenty-eight years old when the first disaster struck. In order to win a Paris prize for astronomy, he worked three days and three nights in a row to solve this problem, which other leading mathematicians believed at the time. It will take several months. The result was a disease, and Euler lost sight in his right eye, as we can see from several portraits he himself left behind. Euler developed a cataract in his left eye during his second stay in Russia, when he was almost sixty years old. Although Euler's correspondents such as French mathematicians Lagrange and D'Alembert expressed deep concern, he himself was able to take it calmly. Before going completely blind, he struggled to chalk the formula on a large slate, then had his son or secretary copy it, and he dictated the formula and other texts himself. In this way, instead of reducing the efficiency of his thesis writing, it has improved.
Like many blind people, Euler has an extraordinary memory. In addition to memorizing nearly all the mathematical results of that era, he was also good at mental arithmetic. What is even more incredible is that Euler can recite the first and last sentences of each page of the twelve volumes of the ancient Roman poet Virgil's epic "Aeneid". This epic describes the hardships of the prince Aeneas after the fall of Troy to re-establish his settlement in a foreign land (Rome), and its beautiful and intelligent verse, structure and rhythm have reached such perfection that Dante in " In the Divine Comedy, Virgil leads him to heaven. Perhaps, Euler got some resonance from it, and his mathematical inventions always came in beautiful form. In his later years, when a friend asked him where he had the best time, he answered without hesitation that it was Petersburg. During the seventeen years that Euler was completely blind, his most proud work was to discover the laws of motion of the moon, which was the only problem that gave Newton a headache, and was deduced by Euler through complex analysis and mental arithmetic.
In Euler's time, there were no journals devoted to mathematical papers. But more than half a century after the publication of the Philosophical Proceedings of the Royal Society in London and the Proceedings of the French Academy of Sciences, the Letters of the Petersburg Academy of Sciences and the Proceedings of the Berlin Academy of Sciences were also born. The advent of the latter two journals is of course related to Euler, who himself is one of the main authors. Legend has it that Euler was able to write a dissertation within half an hour of being called to dinner twice by his family. For ordinary researchers, at most one theorem can be deduced in such a short time. Euler never bothered with submissions, and after writing a paper, he put it at the top of a growing pile of papers. When the journal needs it, the editor takes a paper or two from the top. As a result, it is often the case that the writing and publication dates of the papers do not coincide. What's more interesting is that since Euler often writes a series of articles around a problem, readers sometimes get confused when reading his papers.
In addition to being blind, Euler also suffered many misfortunes in his life: eight children died one after another; a fire in his later years almost took his life and manuscripts, but thanks to the hard work of Swiss servants, his house and collection of books were burned down . Catherine II immediately compensated for all the economic losses after learning about it, and Euler went back to work. It is worth mentioning that between Anna and Catherine II, there is another Empress Elisabeth of Russia, the daughter of Peter the Great. During her twenty years on the throne, Euler had lived in Berlin, although the Russian side paid him an academician's allowance. It was also during her reign that for the first time the Petersburg Academy of Sciences had its own academician, the scientist and poet Lomonosov. One year, when the Russian army invaded the outer suburbs of Berlin, Euler's farm was looted, and the queen paid double compensation for his losses. It can be said that Euler's life was favored by the four empresses of Russia.
On September 18, 1783, on a clear autumn afternoon, Euler wrote something on the slate as usual, which was probably calculating the balloon's ascent. He then had dinner with his family and talked about the newly discovered planet Uranus. At that time, in Braunschweig in north-central Germany, a small town less than 200 kilometers from Berlin, the gardener's son Gauss was six years old, fully showing the talent of a mathematical prodigy. After dinner, Euler was drinking tea and playing with his little granddaughter when suddenly the pipe fell from his hand. He said "I am dead" and Euler "stopped living and calculating". This latter phrase, often quoted by historians of mathematics, comes from the French philosopher and mathematician Condorcet, who was a pioneer during the Revolution and died in prison. For some reason, this sentence reminds me of Euler's favorite verse from Werner: "The anchor is dropped, and Flying's ship has stopped."
Everyone has the limitations of the times. Among the many problems studied by Euler, some have not been completely solved, such as the three-body problem in astronomy, that is, how the sun, the earth and the moon move under the mutual gravitational force. This problem It still exists today. Because of the wide range of Euler's research, there are still many unsolved problems even in the field of mathematics he is interested in: for example, the problem of perfect numbers and friendly numbers left over from the time of Pythagoras, which is based on Euler's The contribution is the biggest; another example is Fermat's last theorem, Euler also has an excellent contribution, but the final solution was given by the British mathematician Wiles at the end of the last century; another example is the Goldbach conjecture, which is the result of Euler and mathematicians Goldbach's correspondence has not yet been confirmed or denied - Goldbach's hometown is Königsberg in Prussia, and the "seven bridges problem" born in this city is the starting point of topology, and this secular It was Euler who abstracted the problem to a mathematical level and solved it.
To be precise, Euler was the most famous court mathematician in history, and he spent his life traveling back and forth between two hostile kingdoms, Russia and Germany, serving different kings and queens. Once, when Frederick the Great ordered Euler to teach his niece, he wrote a series of beautifully written essays that later became the best-selling "Letter to a German Princess" in dozens of countries. An early example of popular science writing by scientists. Nevertheless, since Euler neither established a new science (calculus) and a complete mechanical system like his predecessor Newton, nor established a school of mathematics (Göttingen school) like the later Gauss, plus He comes from a small country and his public profile is not particularly high. There were many times when Euler silently did the work that other great mathematicians were unwilling to do with a humble heart, just as Euler's early mentor John Bernoulli wrote him in a letter: "I am teaching advanced analysis. When it was a child, you are bringing it to adulthood."
When it comes to mathematicians in the 18th century, although the French preferred to exalt their compatriots, Lagrange, Euler was admired by more of his peers as the most accomplished. There are also many historians of mathematics who rank Euler with Archimedes, Newton and Gauss as the four greatest mathematicians of all time. They have one thing in common, that is, while creating pure theories, they also apply the mathematical tools they invented to solve a large number of astronomical, physical and mechanical problems. They continue to draw nourishment from practice, and at the same time are never satisfied with solving specific problems; they regard the universe as an organic whole and try to reveal its inner mysteries and laws. Laplace, who has the reputation of "French Newton", praised: "Learn Euler, he is the teacher of all of us." "Prince of Mathematics" Gauss also once said: "The study of Euler's work will Still the best irreplaceable school for a mathematician." In a sense, since Euler's death, mathematics has never been as good as it once was.
∑ Editor | Gemini
Source | "Mathematical Legends: Those Unattainable Characters"
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