The Life of Leonhard Euler (1707-1783)

Leonhard Euler
Artist Jakob Emanuel Handmann’s rendition of Leonhard Euler. Found on Wikipedia.

I’ve started the algebra section in the math curriculum I’m writing–which meant the time had finally come to cover Euler’s life. Leonard Euler has to be one of my favorite mathematicians. This short extract from the curriculum highlights some important lessons his life teaches. – Katherine

It’s fitting that we end our first week looking at algebra by exploring the life of a man God gifted with an amazing mathematical mind. Leonhard Euler (pronounced “oiler”) has been called “the leading mathematician and theoretical physicist of the eighteenth century.”[1] He left his mark on nearly every branch of math. He wrote an enormous amount of mathematical papers—one resource I read estimated that, while working, he wrote around 800 pages a year,[2] and another called him “the most prolific mathematician in history.” [3] In addition to numerous other works, Euler wrote math textbooks, and his presentations of many concepts are still those we use today. We can think of Euler as the man who went back and “polished” the various branches of mathematics, making them easier to use and understand.

Beyond being a brilliant mathematician, however, Euler’s life provides a beautiful illustration of a famous mathematician who truly viewed math as a testimony to God’s faithfulness and served the Lord despite tremendous challenges.

Euler’s father had been a preacher, and Euler himself, wanting to please his father, had studied to become a minister as well. Fortunately, his father eventually realized that God had clearly designed his son to be a mathematician instead of a preacher. I think the lesson Euler’s father had to learn was critical for us all: God made us all different, and that’s a good thing!

After Euler was allowed to pursue mathematics instead of his seminary studies, the Lord opened up a position for Euler in Russia. Although originally hired to conduct medical research for the government-sponsored academy, Euler was quickly able to switch his focus to mathematics.

During his first stay in Russia, the country underwent a period of turmoil. Euler feared speaking much in public for fear of the spies who literally were everywhere. So, unable to do much else, Euler applied himself with all the more diligence to his mathematical pursuits. God used the upheaval to help Euler complete the tasks before him.

Euler’s life had its fair share of trials. While still fairly young (probably his early 30s),[4] Euler lost sight in one eye. Later, he lost sight in his other eye too. But Euler didn’t waste time in self-pity. God had blessed Euler with an amazing capacity to calculate mentally and remember things, so he kept on solving math problems despite not having good eyesight. As one biographer comments,

He was able to do difficult calculations mentally, some of these requiring him to retain in his head up to 50 places of accuracy![5]

Euler was definitely a man with a remarkable intellect. Yet unlike many of the French philosophers of his time, Euler recognized that his intellect needed submitted to God’s authority. One time, a French philosopher named Diderot came to Russia and began spreading his skepticism about God’s existence. The queen asked Euler to combat him.

“Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it before all the Court, if he [Diderot] desired to hear it. Diderot gladly consented…Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: ‘Sir, a+bn/n = x, hence God exists; reply!’”[6]

Diderot was embarrassed and immediately went back to France. Euler’s simple faith, which recognized that math’s very ability to work depends on a faithful, consistent Creator, had baffled the French philosopher.

May we, like Euler, view math’s very ability to work as a testimony to God’s faithfulness and existence and use our intellects for His glory.

[1] Stuart Hollingdale, Makers of Mathematics (New York: Penguin Books, 1994), 275.

[2] Ibid.

[3] E..T. Bell, Men of Mathematics (New York: Simon and Schuster, 1965), 139.

[5] William DunHam, Journey Through Genius: The Great Theorems of Mathematics (New York: John Wiley and Sons, 1990), 210.

[6] E.T. Bell, Men of Mathematics (New York: Simon and Schuster, 1965), 147.

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Resource Week – Free Practical Math Lessons

It’s resource week!

SCORE Mathematics Lessons – Check this site for some free, practical lesson ideas for grades K-12. Many of these lessons offer ideas on how to have children apply math for a specific real-life project, such as planning a trip or buying a car. Although written for a classroom setting, most of the lessons could easily be adapted to the home. It’s a site you may wish to bookmark and consult when you’re not sure how a specific concept serves as a useful tool or need an idea on how to actually have your child apply a concept. Please use your own discernment, as many of the lessons include Internet usage.

REMINDER! Next week is request week. Does anyone have a specific concept or question you’d like discussed?

Lessons from the Life of Johannes Kepler

Johannes KeplerKnown as the discoverer of the laws of planetary motion, Johannes Kepler was the first to propose that the planets circle the sun in elliptical shapes rather than in circular shapes as previously thought. Although often thought of as a scientist, Kepler was also a mathematician. In his study of planetary motion, Kepler used extensive math, including definitions, geometry, trigonometry, algebra, and other math concepts.

This mathematician’s life both provides an example of math in action and is resplendent with lessons! Join me in taking a brief look.

God’s Plans Are Not Always Ours
Johannes Kepler’s life illustrates the important truth that God’s plans are much better than are own–and sometimes they surprise us! Johannes Kepler did not plan on becoming a mathematician–he set out to become a minister. But toward the end of his university studies, his professors recommended him for a math position.

The young minister-to-be didn’t like the idea of giving up his divinity studies. Although he eventually agreed to take the position, Kepler still planned on becoming a minister one day. But God had something very different in mind for Kepler, as Kepler himself later recognized. [1]

Kepler had always been interested in the movement of the heavens and had admired Copernicus and his sun-centered theory. As a professor, Kepler now had more time to investigate these matters. He spent years developing a theory to explain the movements of the heavens, only to later discover his theory was insufficient. Undaunted, Kepler kept trying. His belief in the universe as an orderly creation of God made him certain the movement of the heavens could be explained by geometry. [2]

In 1600, Kepler’s teaching career at the school came to an abrupt halt. Along with others who refused to convert to Catholicism, Kepler was told to leave the country! Yet although Kepler probably could not see it at the time, God had a plan to transform persecution and exile into a tremendous blessing.

BraheExiled from his own country, Kepler soon found himself assisting (and depending on the generosity of) the famous astronomer Tycho Brahe (pictured to the left)–that is, until Brahe died in 1601. After Brahe’s death, Kepler inherited Brahe’s position and records. Because he had been exiled from his own land and forced to take shelter under Tycho Brahe, Kepler now had the records he needed to discover the laws by which God caused the planets to orbit the sun. Who would have thought God would use a persecution and forced exile to help Kepler accomplish his life work?

Perseverance in the Face of Obstacles
One of the biggest lessons we can learn from Kepler is that of perseverance. Discovering the planetary laws did not prove an easy task. From a collection of numbers Brahe had made over a period of many years chronicling where in the sky Mars had appeared, Kepler tried to find some sort of orderly law that could express the way God caused Mars to orbit the sun.

Just how hard was this task? According to Robert Wilson, “It took Kepler eight years and nearly a thousand pages of closely written calculations before he cracked the problem and discovered his first two laws of planetary motion (the third was to wait another nine years).”[3] Can you imagine spending eight years on a geometry problem you are not even sure can be solved, then another nine years to finish the task?

Confidence God Created an Orderly Universe and Math Could Describe It
Kepler’s willingness to persevere came from his deep faith that God had created an orderly universe. Kepler longed to uncover that order so he might bring glory to His Creator and know Him better.

Kepler was unwilling to accept the “close” results obtained from the prevailing Greek cosmology of the universe, in which planets circled the sun in circles. Instead, he searched for a better model.

Questioning the Greeks was a huge step. For centuries, the Greek philosophers’ teachings had been taught as fact. To question them was equivalent to questioning proven fact. Kepler could only be so daring because he believed in God as the source of truth, not the Greeks’ human reasoning. [4]

Kepler’s Beliefs – The Good and Bad
No one reading through Kepler’s Harmonies of the World can doubt Kepler’s belief in God. He often paused in the middle of an explanation to mention his Creator, and sometimes even broke off into a hymn of praise. It seems almost as if Kepler still viewed himself as a minister, trying to uncover the glory of God throughout creation. His book on planetary motion ends with this tribute to God:

Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number: praise Him, ye heavens, praise Him, ye sun, moon, and planets, use every sense for perceiving, every tongue for declaring your Creator…To Him be praise, honour, and glory, wourld without end. Amen. [5]

We can learn a lot from Kepler’s use of math as a tool to uncover God’s handiwork.

At the same time, though, Kepler’s theology and outlook on math were far from perfect. He carried over a lot of Greek mysticism into his beliefs about God and the universe. Forgetting that creation and our minds are both fallen, Kepler often drew unbiblical spiritual parallels and inferences about God. Kepler also dabbled in astrology (although he admitted it held no weight) and brought a good deal of mystical thinking into his astronomy.

Lesson? We need to be on guard against falsehoods and lies from our culture that try to creep into our hearts.

Within Kepler’s life, we see God’s sovereignty at work, using even an exile to accomplish His purposes. We also find a challenge to persevere–and to view the universe as God’s handiwork and worship Him while using math to explore it. At the same time, we find a warning to be careful about falsehoods that threaten to rob us of living in the completeness of God’s truth.

[1] Max Casper, one of Kepler’s biographers, says, “Looking back later when, through the discovery of his planet laws, he had become aware of his ability, he recognized the voice of God in the call which had come to him. It is God who by a combination of circumstances secretly guides man to the various arts and sciences and endows him with the sure consciousness that he is not only a part of the creation but also partakes in the divine providence.” Max Caspar, Kepler, trans./ed. by C. Doris Hellman (New York: Dover Publications, 1993), p. 51.

[2] Kepler believed God was geometry’s creator. “For the Creator, who is the very source of geometry and, as Plato wrote, ‘practices eternal geometry,’ does not stray from his own archetype.” Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy ed. Stephen Hawking (Philadelphia: Running Press Book Publishers, 2002), p. 645. The Bible, however, never tells us God “practices eternal geometry.” We should not be surprised to find that parts of God’s creation are even more complex than geometry can describe. Nonetheless, Kepler was right in his general belief that God created an orderly universe, and that math records that order.

[3] Robert Wilson, Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe (Princeton, NJ: Princeton University Press,   1997), p. 69. For more details about the obstacles Kepler faced, see Max Caspar’s Kepler or Robert Wilson’s Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe.

[4] See Chapter 6 of Beyond Numbers for a basic overview of the switch from Greek thinking to biblical thinking that paved the way for the Scientific Reformation.

[5] Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy ed. Stephen Hawking (Philadelphia: Running Press Book Publishers, 2002), p. 723.

Resources Consulted

Caspar, Max. Kepler. Trans./ed. by C. Doris Hellman. New York: Dover Publications, 1993.

Kepler, Johannes, Harmonies of the World, in On the Shoulders of Giants: The Great Works of Physics and Astronomy. Ed. Stephen Hawking. Philadelphia: Running Press Book Publishers, 2002.

Newman, James R., ed. The World of Mathematics. Vol. 1. New York: Simon and Schuster, 1956.

Nickel, James D. Mathematics: Is God Silent? Rev. ed. Vallecito, CA: Ross House Books, 2001.

Tiner, John Hudson. Champions of Mathematics. Green Forest, AR: Master Books, 2000.

Wilson, Robert. Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. Princeton, NJ: Princeton University Press, 1997.