Euler

Leonard Euler

Euler was a voluminous writer on mathematics, indeed, the most prolific writer in the history of the subject. His name is attached to every branch of the study. It is of interest to note that his amazing productivity was not in the least impaired when, about 1766, he had the misfortune to become totally blind.

In addition to being a great research writer for some of the journals of his time, Euler was also a masterful writer of textbooks, in which he presented his material with great clarity, detail, and completeness. These texts enjoyed a marked and a long popularity, and to this day make very interesting and profitable reading. One cannot but be surprised at 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.

Euler was helped and encouraged by his father in the choice of mathematics as a vocation. His father was a Calvinist pastor with an interest in mathematics, having studied the subject under Jakob Bernoulli. The religious training of Euler's childhood remained with him throughout his life. His simple, unquestioning faith enabled him to accept blindness with courage, and also made it difficult for him to harmonize with such men as Voltaire and Frederick the Great. Euler married twice and had a total of thirteen children, all but five of whom died when young. His first son, Johann Albrecht Euler (1734-1800), attained some fame in the field of physics.

Tributes to Euler. Many glowing tributes have been paid to Euler, such as the following three, the first two of which were made by F. Arago, physicist and astronomer, and the third one by F. Rudio, historian of mathematics.

" 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."

" We may safely say that the whole form of modern mathematical thinking was created by Euler. It is only with the greatest difficulty that one is able to follow the writings of any author immediately preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first one to teach."

Euler's blindness. In 1735, the year after his wedding and when he was in Russia, Euler received a problem in celestial mechanics from the French Academy. Though other mathematicians had required several months to solve this problem, Euler, using improved methods of his own and by devoting intense concentration to it, solved it in three days and the better part of the two intervening nights. (Later, with still superior methods, Gauss solved the same problem within an hour!) The strain of the effort induced a fever from which Euler finally recovered, but with the loss of the sight of his right eye. Stoically accepting the misfortune, he commented, "Now I will have less distraction. "

Thirty-one years later, in 1766, when he was again in Russia, Euler developed a cataract in his remaining eye and went completely blind. Now 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 his amazing productivity. 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.

In 1771, after five years in darkness, Euler underwent an operation to remove the cataract from his left eye, and for a brief period he was able to see again. But within a few weeks a very painful infection set in, and when it was over Euler was once again totally blind—so to continue for the remaining twelve years of his life.

Euler's memory. Euler possessed a phenomenal memory. He seems to have been one of those very rare people who almost perfectly retain in their minds anything that they have once read or heard. This great memory served Euler in good stead during his years of blindness. He calculated long and difficult problems on the blackboard of his mind, sometimes carrying out arithmetical operations to over fifty decimal places. It is said that he once memorized the Aeneid and was ever after able to recite the entire Latin work word for word, remarking where each page of his copy ended and the next one began.

Euler's death. Euler retained vigor and power of mind up to the moment of his death, which occurred in his seventy-seventh year, on September 18, 1783. He had amused himselfin the afternoon calculating the laws of ascent of balloons. He then dined with Lexell and his family, and outlined the calculation of the orbit of the recently discovered planet Uranus. A short time later he begged that his grandson be brought in. While playing with the youngster and sipping some tea, he suffered a stroke. His pipe fell from his hand and he uttered, "I die." At that instant, in the words of Condorcet, "Euler ceased to live and calculate."