Leonhard Euler was born in Basel, Switzerland, in 1707. After an essay into the field of theology, Euler found his true vocation in mathematics. Here his father, a Calvinist pastor with an interest in mathematics, helped his son by teaching the basis of the subject. The father had studied mathematics under Jakob Bernoulli, and it was arranged for his son to study under Johann Bernoulli.

In 1727, when Euler was only twenty years old, his two friends, Daniel and Nicholas Bernoulli, who were connected with the new St. Peterburg Academy formed by Peter the Great, secured a position for Euler at the Russian  academy. Daniel left Russia soon after to occupy the chair of mathematics at Basel, and Euler became the Academy’s chief mathematician.

After gracing the St. Peterburg Academy for fourteen years, Euler accepted an invitation from Frederick the Great to go to Berlin to head the Prussian Academy. Euler remained at the Prussian Academy for twenty-five years, but his unsophisticated character did not harmonize with the more scintillating type admired by Frederick, and he suffered many years of petty unpleasantness. The Russian had held Euler in high respect and even after he left for Prussian, they continued to advanced him some salary.

The warmth of the Russian feeling toward him as contrasted with the coolness of the court of Frederick the Great, led Euler in 1766 to accept an invitation from Catherine the Great to return to the St. Petersburg Academy. There he stayed for the remaining seventeen years of his life. He died very suddenly in 1783 when he was seventy-six years old.
Euler was a voluminous writer on mathematics, indeed, far and away the most prolific writer in the history of the subject; his name is attached to every branch of the study. It is of interest that his amazing productivity was not in the least impaired when, shortly after his return to the St. Petersburg Academy, he had the misfortune to become totally blind. He had already, since 1735, been blind in his right eye, accounting for the poses assumed in his portraits. Blindness would seem to be an insurmountable barrier to a mathematician, but like Beethoven’s loss of hearing, Euler’s loss of sight in no way impaired is amazing productivity. Aided by a phenomenal memory and an ability to concentrate even amidst loud disturbances, he continued his creative work by dictating to a secretary and by writing formulas in chalk on a large slate for his secretary to copy down. Euler published five hundred and thirty books and papers during his lifetime, and at death left enough manuscripts to enrich the Proceedings of the St. Petersburg Academy for another forty-seven years. A monumental edition f Euler’s complete works, containing 886 books and papers, was initiated in 1909 by the Swiss Society of Natural Science and is planned to run to seventy-three large quarto volumes.

Euler investigates orbiform curves , which was like the circle, are convex ovals of constant width. Several of his works are devoted to mathematical recreations, such as unicursal and multicursal graphs (inspired by the seven bridges of Konigsberg), and the re-entrance of knight’s path on a chessboard, and Graeco-Latin squares. Of course his chief field of publication was in the areas of applied mathematics, especially the lunar theory, tides, the three-body problem of celestial mechanics, the attraction of ellipsoids, hydraulics, ship-building, artillery and a theory of music. The device of Euler diagrams, used to test the validity of deductive arguments was given by Euler in one of his letters to Princess Phillipine von Schwepps, niece of Frederick the Great. During the Seven Years’ War (1756-1763), the entire Berlin court sojourned in Magdeburg, and Euler tutored the Princess by letters written from his home in Berlin.

Euler was a master writer of textbooks, in which he presented his materials with great clarity, detail and completeness. Among these texts are his prestigious two-volume Introductio in analysin infinitorium of 1748 and the exceeding rich Institutiones calculi differentialis of 1755 and the three-volume Institutiones calculi integralis of 1768-74. These books, along with others on mechanics and algebra, served more than any other writings as models in style, scope, and notation for many college textbooks today. Euler’s texts enjoyed a marked and a long popularity, and to do this day, make very interesting and profitable reading. One cannot but be surprised of Euler’s enormous fertility of ideas and it is no wonder that so many of the great mathematicians coming after him have admitted their indebtedness to him.

It is perhaps only fair to point out that some of Euler’s works represent outstanding examples of eighteenth-century formalism, or the manipulation, without proper attention to matters of convergence and mathematical existence, of formulas involving infinite processes. He was incautious in his use of infinite series, often applying to them laws valid only for finite sums. Regarding power series as polynomials of infinite degree, he heedlessly extended to them well known properties of finite polynomials. Frequently, by such careless approaches, he luckily obtained truly profound results.

Euler’s knowledge and interest were by no means confined to just mathematics and physics. He was an excellent scholar, with extensive knowledge of astronomy, medicine, botany, chemistry, theology and oriental languages. He attentively read the eminent Roman writers, was well informed on both the civil and the literary history of all ages and nations, and showed a wide acquaintance with languages and with many branches of literature. Undoubtedly he was greatly aided in these diverse fields by his uncommon memory.

Many glowing tributes have been paid to Euler, such as the following two made by the physicist and astronomer Francois Arago (1786-1853): “Euler could have been called, almost without metaphor, and certainly without hyperbole, analysis incarnate.” “Euler calculated without any apparent effort, just as men breathe and as eagles sustain themselves in the air.”

Euler had thirteen children ( another matter of productivity). His first son, Johann Albrecht Euler (1734-1800) attained some fame in the field of physics.