Leonhard Euler: God Reveals Himself in Mathematics

5 min

On April 15, 1707, a boy was born in Basel, Switzerland. His father was a pastor in a city that had once been a stronghold of the Reformation. Now, the cause of Christianity was on the decline in Europe.

Just two centuries after the days when Swiss preachers such as Zwingli, Farel, and Calvin had proclaimed Biblical truth in Switzerland, God’s wisdom as revealed in Scripture was being eroded by the wisdom of men. Enlightenment thinking had battered the foundations of the Reformation, and faith was being assaulted by intellectual skepticism.

This little Swiss baby, named Leonhard, was destined to challenge one future day the skepticism of human reason. The father of the little boy prayed that God would use his son to turn the tide of rationalism and point the world instead to the eternal truth of God’s Word.

Everyone assumed that Leonhard would follow his father in the pulpit. At an early age, Leonhard learned Greek and Hebrew, and became a master of Scripture. A family friend, Johann Bernoulli, was a skilled mathematician; he began to teach Leonhard mathematics on Saturday afternoons. The young boy was fascinated by the world of mathematics! In a realm where most see meaningless series of dry, boring numbers, Leonhard found a world of satisfying and perfect orderliness—a world of perfection where eternal and absolute truth was a sure guide to knowledge.

Leonhard quickly became a mathematical prodigy. At age sixteen, Leonhard was awarded a Master of Philosophy degree for his dissertation in which he compared the philosophies of Newton and Descartes. His father wanted him to enter the pulpit, but Leonhard believed that he could serve the Lord and advance the cause of truth in the science of mathematics, using the unusual ability God had given him.

While still in his late teens, Leonhard Euler was launched to international fame! He won second prize in a contest sponsored by the Paris Academy. The contest question asked where to place masts on a ship for maximum stability and speed. This complex problem involved many mathematical disciplines, including advanced calculus. Although Leonhard did not win first place, he did take second prize, and all scientific men in Europe took note of the young mathematician who showed such promise.

When Euler was twenty, he was invited to Saint Petersburg in Russia to assume a professorship in the Imperial Russian Academy of Sciences. While there, he married a young lady named Katharina, and together they started a home on the banks of the Neva River. The couple would eventually have thirteen children, although only five of these children would reach adulthood.

Euler loved his home and family; he spent his most delightful hours in their presence. Instead of seeking a quiet study in which to work, Euler loved to do his most intricate and complicated calculations with his children about him: crawling on him, sitting on his lap, and clinging to his arms.

Whenever the Academy of Paris sponsored another international contest for the consideration of scholars, Euler would enter the contest. During his lifetime, he would win first place twelve times. Scholars across Europe were astonished at his brilliant contributions to mathematics, physics, music theory, engineering, astronomy, magnetism, navigation, optics, fluid dynamics, and economics.

Leonhard Euler was at the height of his powers when he was thirty-one years old. At that point, he contracted a fever that rendered him almost completely blind in his right eye. His detractors called him “Cyclops,” but Euler paid them no attention. He had better things to do than joke with scholars.

In 1741, he was invited to the Berlin Academy under the patronage of Frederick the Great of Prussia. There, Euler spent the most productive years of his life, writing, calculating, teaching, and solving mathematical problems.

Euler challenged the current intellectual skepticism. He debated many of the skeptics of his time, including Descartes, Diderot, and Voltaire. An oft-repeated story records a time when Euler was asked by Catherine the Great of Russia to debate Diderot, a French philosopher who advocated atheism. The great mathematician is said to have announced firmly to the astonished Diderot:

“Sir, a+bn/n = x. Hence, God exists. Your reply?”

Confronted by this perfect statement of an orderly God Who presided over an absolute world, the atheistic philosopher was left speechless!

Euler was the world’s leading expert in differential calculus. He described the cause and the nature of tidal motion, explaining the rise and fall of tides as a result of the gravitational pull of the moon. He described music in mathematical terms, terms that were too mathematical for musicians but too musical for mathematicians. His research in music theory showed the perfect order that God built, and that music has absolute rules of beauty and orderliness.

Meanwhile, Euler’s eyesight continued to deteriorate. Already blind in his right eye, he developed a cataract in his left eye. By the time he was fifty-nine years old, the brilliant mathematician was rendered completely blind. When informed that his sight was gone forever, he calmly commented, “Now I will have fewer distractions.”

Blindness did not diminish at all Leonhard Euler’s productivity. His mind, sharpened early by the memorization of Scripture while in his father’s home and honed to keen usefulness through diligent study, continued to calculate. His memory was so sharp that he could remember what he had read, down to the details of the first and last lines on each page. Using scribes, he dictated his remaining work, and his productivity actually increased after he became blind!

When his home was ransacked by soldiers during the Seven Years’ War in 1760, Euler was recalled to Russia by Catherine the Great. She offered him a generous salary. There he would spend the remainder of his life, defending to his last the truth of God. Although his final years were spent in total blindness, he continued to write, debate, calculate, teach, and demonstrate to the world the wonderful order of mathematical perfection.

The closing act of his life was to calculate the orbit of the newly discovered planet, Uranus. Following dinner with his family one evening, he was discussing Uranus when he suffered a brain hemorrhage. The hemorrhage immediately took his life.

His eulogy included the famous line, “Euler has ceased to calculate.”

Leonhard Euler is widely regarded as the most influential mathematician who has ever lived. The letter e (2.71828) as the base of the natural logarithm is sometimes called Euler’s number because he is the one who introduced it to the world. Also, he is the only man who has two numbers named after him. Euler’s constant is represented by the Greek letter gamma γ and is approximately 0.57721. Euler also popularized the use of π to express the ratio of a circle’s circumference to its diameter. He also introduced i to express an irrational unit. Furthermore, he was the man that popularized the modern expression of trigonometric functions.

The other number named after Euler, Euler’s identity, is e+ 1 = 0, and it has been called by modern mathematicians “the most remarkable formula in mathematics.” To Leonhard Euler, this formula was not extraordinary; it was merely the expression of an orderly God. How can irrational, unrelated, and irreducibly complex numbers have a relationship that can be described so neatly? Mathematician Euler would say that this is because God is a God of order. Jesus Christ is the self-existent Author of the universe and “without him was not anything made that was made.”

Sources and Further Reference:

Nickel, James. Mathematics: Is God Silent? Vallecito, CA: Ross House Books, 2012.

This article is from our Matters of Life & Death teaching series.

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