Euler's life can be divided into four periods. He was born in Basel, Switzerland, on 15 April , where he grew up and went to university. At the age of 20 he went to Russia, to the St Petersburg Academy, where he became head of the mathematics division. Things eventually got so bad there that he went to Berlin in , where he stayed for twenty-five years. Things then got bad there but for different reasons , and he returned to St Petersburg in where he spent the rest of his life, eventually dying in Leonhard Euler's father was a Calvinist pastor of modest means who wished his son to follow him into the ministry.
On entering the University of Basel at the age of 14, not an unusual age in those days, the young Euler duly studied theology and Hebrew, law and philosophy. While at the University, he encountered Johann Bernoulli , possibly the finest mathematician of his day, who was impressed with Euler's mathematical abilities and agreed to give him private teaching every Saturday, quickly realising that his pupil was something out of the ordinary.
Euler also became close friends with Johann's sons, Daniel and Nicholas, although Nicholas was to die soon after. Euler took his Master's degree in , at the age of 17, and entered divinity school to train for the ministry:.
I had to register in the faculty of theology, and I was to apply myself to the Greek and Hebrew languages, but not much progress was made, for I turned most of my time to mathematical studies, and by my happy fortune the Saturday visits to Johann Bernoulli continued.
Eventually, Bernoulli persuaded Euler's reluctant father that his talented son was destined to become a great mathematician, and Euler left the ministry. His first significant mathematical achievement occurred when he was just twenty. The Paris Academy had proposed a prize problem involving the placing of masts on a sailing ship, and Euler's memoir, while not gaining the prize, received an honourable mention.
Later, Euler actually won the prize — twelve times! Euler next applied for the Chair of Mathematics at the University of Basel. He didn't get it, but meanwhile Daniel Bernoulli had taken up a position at the St Petersburg Academy in Russia, and invited Euler to join him there. The only available position was in medicine and physiology, but jobs were scarce — so Euler learned these subjects, in the process of which his study of the ear led him to investigate the mathematics of sound and the propagation of waves.
In the event, fate dealt a cruel blow. Her heir was still a boy, and the faction that ruled in his place regarded the Academy as something of a luxury. Euler kept his head down and got on with his work, while living at the home of Daniel Bernoulli and working closely with him. By this time Euler was working in physics, rather than in medicine.
In , Daniel Bernoulli had had enough of the problems of the Academy and returned to an academic post in Switzerland, while Euler, still aged only 26, replaced him in the Chair of Mathematics. He determined to make the best of a difficult situation and settle down, so he got married and had thirteen children, although only five survived to adolescence.
Euler apparently enjoyed having his children around him, and even managed to carry out mathematical researches with a baby on his lap! The s were indeed very productive years, with substantial advances in number theory, the summation of series and mechanics. At the same time he was acting as a scientific consultant to the government — preparing maps, advising the Russian navy, testing designs for fire engines, and writing textbooks for the Russian schools — although he apparently drew the line when he was asked to cast a horoscope for the young Czar.
An area to which Euler contributed throughout his life was the theory of numbers. In December , he received a letter from his colleague Christian Goldbach , who is best remembered for the still-unproved Goldbach conjecture , which states that every even number can be written as the sum of two prime numbers: for example,.
Are all such numbers primes? Since then, no other Fermat number has been shown to be prime, so Fermat's conjecture was an unfortunate one. Euler's prodigious calculating abilities soon became legendary.
One day, two students were trying to sum a complicated progression and disagreed over the 50th decimal place. Euler simply calculated the correct value in his head. He calculated without any apparent effort, just as men breathe, as eagles sustain themselves in the air. Another challenge given to Euler was to find four different numbers, the sum of any two of which is a perfect square. Euler produced the quartet: , , and A different preoccupation in the s was his work on infinite series.
For example, he became interested in the harmonic series. However, if we look at the first n terms of this series, then their sum turns out to be close to log n — in fact, as Euler proved in the s, as n becomes large, the difference between the sum of the first n terms and log n gets closer and closer to a fixed number — a strange number now called Euler's constant.
Its value is about 0. One other puzzle, known as the Basel problem , exercised many minds at the time. It was to find the exact sum of the series. He then extended his calculations to find the sum of the reciprocals of all the 4th powers, 6th powers, and so on, right up to the 26th power.
This led him to define what we now call the Riemann zeta function. Euler employed a counting argument, counting the number of bridges emerging from each land area, and proved that this cannot be done. Euler considered the bridges problem in the context of a query by Leibniz who, in a letter to Christiaan Huygens in , had asked for a type of geometry that involves no metrical ideas such as length, distance or angle.
We now call this topology , or rubber-sheet geometry — the problem remains the same if we draw the map on rubber and stretch it. In Euler wrote a letter to Giovanni Marinoni, Court Astronomer in Vienna, describing what he thought of the problem: "This question is so banal, but seemed to me worthy of attention in that neither geometry, nor algebra, nor even the art of counting was sufficient to solve it.
In view of this, it occurred to me to wonder whether it belonged to the geometry of position, which Leibniz had once so much longed for. And so, after some deliberation, I obtained a simple, yet completely established, rule with whose help one can immediately decide for all examples of this kind whether such a round trip is possible.
However, he is known primarily as a mathematician. Leonhard Euler is the most prominent scientist from those who come from Switzerland. He was born in Basel, on the 15th of April, Having received his first schooling at home, Leonhard was sent to the Latin school in his hometown and after finishing it, aged thirteen, he enrolled at the University of Basel, at the Philosophical Faculty.
At that time the University was rather small — nearly a hundred of students were taught by 19 professors. However, there was Johann Bernoulli among the teaching staff — a prominent star on the horizon of the world's science. Leonhard had a good memory and an acquisitive mind. In his free time he attended lectures on mathematics, which were read by Johann Bernoulli. Bernoulli quickly discovered his new pupil's incredible talent for mathematics and started working with Euler - every Saturday he spent time with the professor's family and it had continued for several years.
Leonhard made friends with Bernoulli's sons — Daniel and Nicolaus, who studied physics and mathematics in-depth. The friendship with Bernoulli brothers predetermined further trajectory of Euler's life.
The first meeting of the Academy took place in August , six months after the death of Peter the Great. It is because of Bernoulli brothers' favour, in Leonhard Euler also received an invitation to the Academy at Saint Petersburg. In the Academy Euler found comfortable facilities for the development of creative capacity: material security, opportunity to do his favorite job, ability to regularly publish his articles in a yearly journal. Euler started his position as an adjunct of the Academy. In August the young scientist had already gave his first talk.
In he became a professor of physics, and in was offered an important post in the mathematics department, which had earlier been occupied by Bernoulli before he came back to Switzerland.
In the Academy received a task to do promptly very complicated and cumbersome astronomical calculations. A group of academicians needed three months to execute this work, as it required much time and energy. Euler took matters into his own hands and did the calculations in three days, but the flow of information exhausted Leonhard to the bitter end — the scientist almost died of high fever and strong infection and, thus, it cost him his right eye.
Almost certainly his youth he was 19 at the time was against him. However Calinger [ 24 ] suggests:- This decision ultimately benefited Euler, because it forced him to move from a small republic into a setting more adequate for his brilliant research and technological work.
As soon as he knew he would not be appointed to the chair of physics, Euler left Basel on 5 April Through the requests of Daniel Bernoulli and Jakob Hermann , Euler was appointed to the mathematical-physical division of the Academy rather than to the physiology post he had originally been offered.
At St Petersburg Euler had many colleagues who would provide an exceptional environment for him [ 1 ] :- Nowhere else could he have been surrounded by such a group of eminent scientists, including the analyst, geometer Jakob Hermann , a relative; Daniel Bernoulli , with whom Euler was connected not only by personal friendship but also by common interests in the field of applied mathematics; the versatile scholar Christian Goldbach , with whom Euler discussed numerous problems of analysis and the theory of numbers; F Maier, working in trigonometry; and the astronomer and geographer J-N Delisle.
Euler served as a medical lieutenant in the Russian navy from to In St Petersburg he lived with Daniel Bernoulli who, already unhappy in Russia, had requested that Euler bring him tea, coffee, brandy and other delicacies from Switzerland. Euler became professor of physics at the Academy in and, since this allowed him to become a full member of the Academy, he was able to give up his Russian navy post.
Daniel Bernoulli held the senior chair in mathematics at the Academy but when he left St Petersburg to return to Basel in it was Euler who was appointed to this senior chair of mathematics. The financial improvement which came from this appointment allowed Euler to marry which he did on 7 January , marrying Katharina Gsell, the daughter of a painter from the St Petersburg Gymnasium. Katharina, like Euler, was from a Swiss family. They had 13 children altogether although only five survived their infancy.
Euler claimed that he made some of his greatest mathematical discoveries while holding a baby in his arms with other children playing round his feet. We will examine Euler's mathematical achievements later in this article but at this stage it is worth summarising Euler's work in this period of his career. This is done in [ 24 ] as follows The core of his research program was now set in place: number theory ; infinitary analysis including its emerging branches, differential equations and the calculus of variations ; and rational mechanics.
He viewed these three fields as intimately interconnected. Studies of number theory were vital to the foundations of calculus, and special functions and differential equations were essential to rational mechanics, which supplied concrete problems.
The publication of many articles and his book Mechanica - 37 , which extensively presented Newtonian dynamics in the form of mathematical analysis for the first time, started Euler on the way to major mathematical work. Euler's health problems began in when he had a severe fever and almost lost his life. However, he kept this news from his parents and members of the Bernoulli family back in Basel until he had recovered.
In his autobiographical writings Euler says that his eyesight problems began in with overstrain due to his cartographic work and that by he had [ 24 ] However, Calinger in [ 24 ] argues that Euler's eyesight problems almost certainly started earlier and that the severe fever of was a symptom of the eyestrain. He also argues that a portrait of Euler from suggests that by that stage the sight of his left eye was still good while that of his right eye was poor but not completely blind.
Calinger suggests that Euler's left eye became blind from a later cataract rather than eyestrain. By Euler had a very high reputation, having won the Grand Prize of the Paris Academy in and On both occasions he shared the first prize with others.
Euler's reputation was to bring an offer to go to Berlin, but at first he preferred to remain in St Petersburg. However political turmoil in Russia made the position of foreigners particularly difficult and contributed to Euler changing his mind.
Accepting an improved offer Euler, at the invitation of Frederick the Great, went to Berlin where an Academy of Science was planned to replace the Society of Sciences. In a letter to a friend Euler wrote:- I can do just what I wish [ in my research ] The king calls me his professor, and I think I am the happiest man in the world.
Even while in Berlin Euler continued to receive part of his salary from Russia. For this remuneration he bought books and instruments for the St Petersburg Academy , he continued to write scientific reports for them, and he educated young Russians.
Maupertuis was the president of the Berlin Academy when it was founded in with Euler as director of mathematics. He deputised for Maupertuis in his absence and the two became great friends. Euler undertook an unbelievable amount of work for the Academy [ 1 ] The king also charged Euler with practical problems, such as the project in of correcting the level of the Finow Canal At that time he also supervised the work on pumps and pipes of the hydraulic system at Sans Souci, the royal summer residence.
This was not the limit of his duties by any means. He served on the committee of the Academy dealing with the library and of scientific publications. He served as an advisor to the government on state lotteries, insurance, annuities and pensions and artillery. On top of this his scientific output during this period was phenomenal. During the twenty-five years spent in Berlin, Euler wrote around articles.
He wrote books on the calculus of variations; on the calculation of planetary orbits; on artillery and ballistics extending the book by Robins ; on analysis; on shipbuilding and navigation; on the motion of the moon; lectures on the differential calculus; and a popular scientific publication Letters to a Princess of Germany 3 vols. In Maupertuis died and Euler assumed the leadership of the Berlin Academy , although not the title of President. The king was in overall charge and Euler was not now on good terms with Frederick despite the early good favour.
Euler, who had argued with d'Alembert on scientific matters, was disturbed when Frederick offered d'Alembert the presidency of the Academy in However d'Alembert refused to move to Berlin but Frederick's continued interference with the running of the Academy made Euler decide that the time had come to leave.
In Euler returned to St Petersburg and Frederick was greatly angered at his departure. Soon after his return to Russia, Euler became almost entirely blind after an illness. In his home was destroyed by fire and he was able to save only himself and his mathematical manuscripts. A cataract operation shortly after the fire, still in , restored his sight for a few days but Euler seems to have failed to take the necessary care of himself and he became totally blind.
Because of his remarkable memory he was able to continue with his work on optics, algebra, and lunar motion.
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