Monday, December 7, 2015
Leonard Euler the Mathematician 1841
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THERE are but few chapters in Biography more strikingly illustrative of the ardent love of knowledge, and its pursuit under circumstances of pain and difficulty, than that supplied by the life of Leonard Euler the mathematician.
This great man was born at Basle, in Switzerland, on the 15th of April, 1707. His father was minister of the village of Riechen, where Euler passed his earliest years. After receiving a good education from his father, he was sent to the university of Basle, where he soon became distinguished for his extraordinary memory and the uncommon celerity with which he accomplished his academical tasks. He devoted all his leisure to geometry, which was his favourite pastime. His progress in this noble department of science, gained for him the notice of John Bernoulli, then the first mathematician in Europe, as also the friendship of Daniel and Nicholas Bernoulli who were already emulous of the fame of their illustrious father. In 1723 Euler delivered a discourse in Latin on the occasion of taking his degree as Master of Arts, and the subject of his theme was the philosophy of Newton in comparison with the Cartesian system. This effort gained its author great applause. He afterwards applied himself to the study of theology and the oriental languages with considerable success; but as his ruling taste led him to prefer geometry to all other pursuits, he obtained his father's consent to adopt this in preference to any other. He continued on terms of friendly intimacy with the Bernoullis, and one consequence of this connection was his subsequent removal to the Academy of Petersburg, an institution projected by Peter the Great, and executed by Catherine the First. The two young Bernoullis being invited to Petersburg in 1725, promised Euler, who was anxious to accompany them, to exert themselves to obtain for him a settlement in that city. In the mean time he adopted their advice, and applied himself with ardour to the study of physiology and several branches of physical science. He also wrote a memoir on the propagation of sound; and an essay in answer to a prize question concerning the masting of ships, to which the Academy of Sciences, in 1727, adjudged the second rank.
The splendid talents of Euler would easily have procured for him an honourable preferment in his native city, had it not been that both civil and academical honours were distributed there by lot. Having failed in his attempt to obtain a certain situation at Basle, he went to Petersburg, where he became joint professor with his countrymen, Hermann and Daniel Bernoulli, in the university of that city. He soon added many valuable memoirs to the academical collection; and this excited a noble emulation between him and the Bernoullis, which always continued without the least interference of envy or the disturbance of their friendship. In 1730 he became professor of natural philosophy; and in 1733 succeeded Daniel Bernoulli in the mathematical chair: about this time also he married a Swiss lady named Gsell. In 1735 the academy proposed a problem, to which a speedy solution was required, but for which several eminent mathematicians had required several months. To the astonishment of every one, Euler solved it in three days; but the effort produced a fever which deprived him of the use of his right eye and nearly of his life. The Academy of Sciences at Paris, in 1738, awarded the prize to Euler, for his memoir on the nature aud properties of fire; and proposed for the year 1740 the important subject of the tides; a problem the solution of which required the most arduous calculations, and included the theory of the solar system.
Euler's discourse on this question was considered as a master-piece of analysis and geometry; and it was more honourable for him to share the academical prize with such illustrious competitors as Colin Maclaurin, and Daniel Bernoulli, than to have carried it away from rivals of inferior reputation. Rarely, if ever, did such a brilliant competition adorn the annals of the academy; and no subject, perhaps, proposed by that learned body, was ever treated with such accuracy of investigation and force of genius as that which here displayed the philosophical powers of these three extraordinary men.
In 1741 Euler received an invitation from the king of Prussia to visit Berlin; and being anxious to escape from the scene of those political intrigues which under a suspicious and tyrannical government then agitated Russia, he gladly accepted it. When he was introduced to the Queen Dowager she was so surprised at his taciturnity, that she required an explanation of it, and he told her that he had just come from a country where those who spoke were hanged. He contributed five memoirs to the “Berlin Miscellanies,” and a large number on important subjects to the transactions of the Prussian Academy on the deepest parts of mathematical science, always containing new views, often sublime truths, and frequently important discoveries. At the same time he did not neglect to contribute largely to the memoirs of the Academy of Petersburg, which in 1742 granted him a pension. He also acceded to the request of the princess of Anhalt Dessau, to write for her own use a work on Natural Philosophy. On his return to Petersburg in 1766, he published his celebrated Letters to a German Princess, in which he discusses with clearness the most important principles of Mechanics, Optics, Sound, and Astronomy.
In the midst of all these absorbing pursuits, Euler did not neglect the ties of kindred, nor cease to be a dutiful son as well as an affectionate husband. On the death of his father he went to Frankfort, in 1750, and returned with his widowed mother to Berlin, where she lived until 1761, enjoying, with the feelings of a parent, the high distinctions which her son had attained by his genius and untiring activity. In 1760 a circumstance occurred which shows how greatly Euler was esteemed The Russians having entered Brandenburg, proceeded to Charlottenburg, where they plundered a farm belonging to Euler. When General Tottleben was informed of the name of the owner, he ordered immediate reparation to be made to an amount far above the injury sustained, to which the Empress Elizabeth added the additional sum of 4000 florins.
In 1766 Euler accepted the invitation of the Empress to return to Petersburg; but he experienced no small difficulty in obtaining permission from the king of Prussia to quit his territory, so much was he esteemed by that sovereign, who, although he spoke of Euler as being “only a mathematician,” yet had sufficient discrimination to perceive that he added lustre to a court which aspired to science and literature. On his return to Petersburg, Euler was afflicted with a severe illness which terminated in the total loss of his sight. A cataract formed in his left eye which he had injured by too severe mental application. In this distressing situation he dictated to his servant, a tailor's apprentice and quite ignorant of mathematics, his Elements of Algebra, a work as admirable for clearness and method, as for the distressing circumstances under which it was composed. The amanuensis is said to have acquired a good knowledge of Algebra, in the course of merely taking down what Euler spoke.
The Academy of Sciences of Paris elected Euler to the honourable post of foreign member of their body, and adjudged the prize to three of his memoirs, “Concerning the Inequalities in the Motions of the Planets.” The two prize questions proposed by that academy for 1770 and 1772 were designed to obtain from astronomy a more complete theory of the moon. With the assistance of his son, Euler competed for these prizes, and obtained both. In his last memoir he reserved for further consideration several inequalities of the moon's motion, which he could not determine in his first theory, on account of the laborious calculations in which his method had involved him. But, with the assistance of his son and two other gentlemen, he carefully revised his theory, constructed tables, and published the whole in 1772.
All these means of investigation, employed with such art and dexterity as could only be expected from analytical genius of the first order, were attended with the greatest success; and it is impossible to observe without admiration such immense calculations on the one hand, and on the other the ingenious methods employed by this great man to abridge them, and to facilitate their application to the real motion of the moon. But this admiration will become astonishment when we consider at what period, and in what circumstances, all this was effected. It was when he was totally blind, and, consequently, obliged to arrange all his computations by the sole powers of his memory and his genius; when he was embarrassed in his domestic circumstances by a dreadful fire, which had consumed the greater part of his substance, and forced him to quit a ruined house, every corner of which was known to him by a habit that in some measure supplied the place of sight;—it was in these circumstances, and under these privations, that Euler composed a work, which alone is sufficient to render his name immortal. The heroic patience and tranquillity of mind which he displayed need no eulogy here: and he derived them not only from the love of science, but from the power of religion. His philosophy was too genuine and sublime to stop its analysis at mechanical causes; it led him to that divine philosophy of religion which ennobles human nature, and is alone capable of forming a habit of true magnanimity and patience under suffering.
After this great work was completed, Euler was couched by the celebrated oculist Wenzell, and restored to sight; but the delight occasioned by this successful operation did not long continue. Partly by the neglect of his medical attendants, and partly by his own impatience to exercise his re-acquired powers he again became totally blind, and the relapse was accompanied by intense pain. This misfortune, however, did not check the ardour of his genius. He had engaged to supply the academy of Petersburgh with a sufficient number of memoirs to complete its Transactions for twenty years after his death, and, accordingly, with the assistance of his son and two other gentlemen, he sent to the academy seventy memoirs within the space of seven years, and left above two hundred more, which were revised and completed by the biographer of Euler, from whom we have just quoted.
If we consider the great extent to which Euler carried his researches in mathematics and astronomy, we shall be surprised to find that he was also skilled in the sciences of medicine, botany, and chemistry; that he was moreover a good classical scholar, and had read with attention and taste not only the principal Latin authors, but had made himself familiar with the civil and literary history of all ages and all nations. We learn also that intellectual foreigners, who had previously become acquainted with his mathematical and physical researches and discoveries, were astonished on visiting him to find that he also possessed an extensive acquaintance with the most interesting branches of literature. This wonderful memory doubtless made the acquisition of every kind of knowledge easy to him: as an example of the powers of his memory it is stated that he could repeat the Aeneid of Virgil without hesitation from the beginning to the end, and even name the first and last line of every page of the edition which he used.
In September, 1783, he made some calculations on the motions of balloons, then newly invented. On the 7th day of that month he dined with Lexell and conversed on the subject of the newly discovered planet Herschell, and while his grandchild was at tea, he began to play with it, when he was struck with apoplexy, and died without pain.
Condorcet has left an eloquent and just summary of the character of Euler, which is thus quoted in the article before referred to:
Euler was one of those men whose genius was equally capable of the greatest efforts, and of the most continued labour; who multiplied his productions beyond what might have been expected from human strength, and who, notwithstanding, was original in each; whose head was always occupied, and whose mind was always calm. The nature of his pursuits, by withdrawing him from the world, preserved that simplicity of manners for which he was originally indebted to his character and his education; and he employed none of those means to which men of real merit have sometimes recourse, in order to enhance the importance of their discoveries. It is true that fecundity such as his renders unnecessary all the little calculations of self-love; but still great lucidity of mind, and uprightness of character, are necessary to trace, as he has done, the history of his thoughts, even when his investigations have proved fruitless, or the results disappointed the expectations which he had formed. Euler's constitution was uncommonly vigorous; his health was good; and the evening of his long life was serene, being sweetened by the fame which follows genius, the public esteem and respect which are never withheld from exemplary virtue, and several domestic comforts, which he was capable of feeling, and therefore deserved to enjoy.
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