Leonhard Euler


by David F. Coppedge

Here is the true story of a very interesting individual, one whose name will ring a bell for anyone who has studied higher mathematics, because his name is associated with dozens of theorems, proofs, algorithms, constants and laws.  Though not a scientist by training, he contributed immeasurably to science by advancing its language (mathematics) and its toolkit of operations.  According to math professor Howard Anton, he “made major contributions to virtually every branch of mathematics as well as to the theory of optics, planetary motion, electricity, magnetism, and general mechanics.”  His name was Leonhard Euler (pronounced oiler), a true genius who was also a committed Christian all his life.

Euler was so smart it’s almost scary.  In his thick textbook Calculus, Howard Anton includes brief biographies of famous mathematicians; his entry on Euler sounds like an episode from Ripley’s “Believe It or Not” –

Euler was probably the most prolific mathematician who ever lived.  It has been said that, “Euler wrote mathematics as effortlessly as most men breathe.” …. Euler’s energy and capacity for work were virtually boundless.  His collected works form about 60 to 80 quarto sized volumes and it is believed that much of his work has been lost.  What is particularly astonishing is that Euler was blind for the last 17 years of his life, and this was one of his most productive periods!  Euler’s flawless memory was phenomenal.  Early in his life he memorized the entire Aeneid by Virgil and at age 70 could not only recite the entire work, but could also state the first and last sentence on each page of the book from which he memorized the work.  His ability to solve problems in his head was beyond belief.  He worked out in his head major problems of lunar motion that baffled Isaac Newton and once did a complicated calculation in his head to settle an argument between two students whose computations differed in the fiftieth decimal place.

This gives us cause to ponder the possibilities inherent in the human brain.  It makes us wonder what initial abilities the Creator gave to man that have been degenerating since the creation, only to surface occasionally to above-average levels in rare geniuses like Euler.  It also makes us wonder how any theory of evolution could ever produce such a superabundance of potential, far more than needed for mere survival.  The ability to perform abstract, symbolic reasoning in the human mind, unknown in the animal kingdom, provides strong evidence for the special creation of man.  Nothing comes from nothing.  A mind as gifted as Euler’s could only come from a bigger Mind, one that is all-knowing and infinite in wisdom and knowledge.

Did Euler’s genius make him an aloof braggart or freakish savant?  Not at all.  He was a gracious and unselfish person, a loving father of a large family, a teacher, a diplomatic gentleman and a man of deep faith and conviction.  People loved and respected him.  He was a hard worker and a lover of the truth.  There are no indications he thought highly of himself, but that he pursued his area of expertise in the desire to advance knowledge and aid the sciences.  But when it came time to defend his faith, he was prepared, like Pascal, to take up the challenge.

Leonhard’s father was a pastor who also enjoyed mathematics.  After home- schooling the boy for his elementary years, Paul Euler sent his son to the University of Basel, Switzerland (their home town), hoping he would follow in his theological footsteps.  Though faithful to his Calvinistic upbringing all his life, Leonhard’s interest and proficiency in geometry convinced his father a change of career was warranted.  Tutored under Johann Bernoulli, Leonhard by age 16 had a Bachelor of Arts and a Masters in philosophy, and by 18 was doing mathematical research and producing original work that continued unabated for the next six decades.  His career took him beyond the University of Basel to the St. Petersburg Academy of Sciences in Russia, and for 25 years to the Berlin Academy of Sciences, then back to Russia.  In this brief biography, we are more interested in the beliefs and personal life of this amazing individual, who singlehandedly was responsible for about a third of all mathematical output of the 18th century.

Christian living was a practical reality, not a Sunday formality, to Euler.  Dan Graves, in his excellent chapter on Euler in Scientists of Faith says, “Despite his turn to math, Euler retained his firm Calvinist beliefs throughout life, holding daily prayer and worship in his home and sometimes preaching.”  Unable to find work in Switzerland, Leonhard moved to St. Petersburg, Russia where, at age 26, he met and married another Swiss emigrant, Katharina Gsell, his bride for 40 years. Graves describes their family life: “Katharina bore him thirteen children, whom he loved dearly.  He often carried on his work with children sitting on his lap or clinging to his back.”  But Dan Graves also illustrates a theme we have seen often in these biographies, that the individuals we know primarily for their intellectual achievements were real human beings who often had to overcome severe trials and misfortunes.

Not only did Euler lose sight in one eye at age 28 while straining on a particularly difficult problem, he lost sight of his other eye at age 59 in great pain, as Graves describes: “An operation to restore the better of the two was successful, but infection invaded both eyes.  After horrible agony he permanently lost his sight.  He later said that only his faith in God enabled him to bear those days of torment.”  As stated earlier, however, some of his greatest work was yet to come, fully half his lifetime output, as Euler wrote out his complex derivations on “the black slate of his mind.”  Taking this disability in stride, he said, “Now I will have less distraction.”

Additional trials came from political and philosophical enemies.  In his thirties, Euler moved from an unstable political situation in Russia, when spies were everywhere and purges were the rule, and worked under the Prussian emperor Frederick the Great.  There he served 25 years and added immensely to the prestige of the Berlin Academy of Sciences.  But his patron Frederick, an Enlightenment skeptic, sneered at the Christian faith of his niece’s tutor.  In response, Euler wrote Letters to a German Princess, in which he gently combined piety with the sciences.  The book became a best-seller in seven languages, but Frederick was not impressed.  Voltaire, the French Enlightenment anti-Christian deist, joined in mocking Euler’s Biblical world view.  Euler corresponded with apologetic works defending Christian doctrine against Voltaire, Leibniz, Wolff and other Enlightenment skeptics, until the interference and opposition by Frederick became intolerable and he had to uproot again.  At age 59, he moved back to St. Petersburg to accept a position under Catherine II (the Great).  The Russians welcomed him as a returning hero.  But that was the year, 1766, when he became totally blind.  In 1771, his house burned down and he escaped with his life and his manuscripts.  Two years later, his wife died.

Undeterred by misfortune, upheaval and disability, Euler continued his work. With only his mind’s eye, he worked through detailed algorithms and dictated them to his sons.  Dan Graves said that his work actually became clearer and more concise.  An online biography at Ryerson Polytechnic Institute states that “He was apparently able to do extensive and complex calculations in his head, remembering every step so that he could recite them for his sons to record. … he published more than 500 books and papers during his lifetime, with another 400 appearing posthumously”.  Another online biography claims that his death in 1783 left a vast backlog of articles that the St. Petersburg Academy continued to publish for nearly 50 more years.  Dan Graves tallies his publications at 886, which he claims have only recently been brought together, and constitute the size of a large set of encyclopedias.  The Encyclopedia Britannica says the compilations began in 1911 and are still continuing!  That’s an incredible volume of writing for anyone, let alone technical writing, especially for a blind man!

What is contained in all this prodigious output?  Just about anything and everything dealing with mathematics.  Euler’s work transformed the look of homework around the world: the convention of using the letter pi for the ratio of the circumference to the diameter of a circle, the letter e for the base of the natural logarithm, the Greek letter sigma for the sum of a series of numbers, and the letter i for the unit of imaginary numbers.  The theory of infinities and continuity.  Important work on our present understanding of functions, including the highly-used f notation such as y = f(x).  Greater perfection in differential and integral calculus, including many new techniques for solving indefinite integrals and the introduction of the well-known integral sign.  More simplicity in analytical operations.  Advances in the theory of linear differential equations.  The properties of integers and the theory of numbers, leading to the foundations of pure mathematics.  Euler’s criterion.  Euler’s constant.  Euler numbers.  The list goes on.

In addition, Euler tackled numerous theoretical and practical physical problems, including work on the basic principles of mechanics, optics, acoustics and astronomy.  The Encyclopedia Britannica says,

Euler devoted considerable attention to developing a more perfect theory of lunar motion, which was particularly troublesome, since it involved the so- called three-body problem–the interactions of Sun, Moon and Earth.  (The problem is still unsolved.)  His partial solution, published in 1753, assisted the British Admiralty in calculating lunar tables, of importance then in attempting to determine longitude at sea.  One of the feats of his blind years was to perform all the elaborate calculations in his head for his second theory of lunar motion in 1772. … Euler and Lagrange together are regarded as the greatest mathematicians of the 18th century; but Euler has never been excelled either in productivity or in the skillful and imaginative use of algorithmic devices (i.e., computational procedures) for solving problems.

Phenomenal as his intellectual achievements were, we should see beyond them the heart of a faithful Christian, strong enough to defend his faith against the most powerful skeptics of his day, yet humble enough to depend totally on the Lord for comfort in the midst of suffering.  We should see in his popular writings and textbooks for elementary schools a desire to help the young.  We should see in his Letters to a German Princessa belief in the unity of knowledge and virtue.  We should see a loving father taking time to play with his children, the fruit of such love being evidenced years later in his sons’ willingness to help transcribe his mental output during his 17 years of total blindness.  We should see an active senior working tirelessly till the day of his death at age 76.  We should be reminded that steadfast faith in the Word of God is not a hindrance, but rather a stimulus, to the advance of knowledge.  We should see that a mind in touch with its Creator, whether its physical windows are open or shut, can be a beautiful and powerful thing.

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