My publisher, Master Books, recently interviewed me for their podcast about the Big Book of Math. Check it out to learn more about the resource and how to use it–you might pick up a few nuggets from math’s history along the way!
Did you know that math helps us explore outer space, learning more about the vastness of God’s creation–and how perfectly designed earth is for life?
Have you ever tried to count the stars? We can’t possibly count them all, but we can use math to estimate the number of stars. While there are different ways to do this, one way is to estimate the total mass of a galaxy (which in itself takes a lot of math) and then divide that total mass by the average mass of a star (which again takes math to estimate). So how many stars are there? Well, there’s an estimated 100 to 400 billion stars in our galaxy alone, which would then need multiplied by the number of galaxies (currently estimated to be in the trillions). That’s a lot of stars! Notice we just used math to approximate the stars in our galaxy, but we can’t fully count them all!
Yet God calls each star by name–and it’s because of His power that they continue.
He determines the number of the stars; he gives to all of them their names. Psalm 147:4
Lift up your eyes on high and see: who created these? He who brings out their host by number, calling them all by name; by the greatness of his might and because he is strong in power, not one is missing. Isaiah 40:26
Think about how much greater God is than we are! We can’t even count the stars, and He calls them by name and keeps them in their places. He is greater than we can even imagine.
Have you ever wondered how we know how far it is to the moon, sun, and stars? We can’t just stretch a tape measurer across these distances! Instead, we make the measurements that we can from earth and then use geometry to figure out the distances. When we do, we see that the earth is just the right distance from the sun. If it were closer to the sun, we’d burn up…if further away, we’d freeze.
Now, the earth and the other planets don’t just sit in space; they orbit around the sun in elliptical orbits. How do we know that? Again, men used math! Johannes Kepler used data that had been recorded about Mars to figure out what orbit around the sun would result in those readings. He discovered that planets orbit in ellipses, and that no matter where they are on the ellipse, if you were to go back the same amount of time and look at the resulting area formed between those two locations and the sun, it’d always be the same. So that means God governs creation so consistently that we can mathematically describe how a planet will orbit.
When Kepler shared some of his findings, he paused to praise the Creator.
"Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number…To Him be praise, honour, and glory, wourld without end. Amen." [Stephen Hawking, ed. On the Shoulders of Giants: The Great Works of Physics and Astronomy. Philadelphia: Running Press Book Publishers, 2002, pg. 1157.]
Well, I hope that gives you a little glimpse into how math helps us explore outer space and how as we do, we see that truly, the Heavens declare God’s praises.
Discover more about how we use math to explore the heavens–along with lots of other historical and present-day applications of math in Kate’s new Math History Timeline!
I’m excited to have just finished the draft of a full-color, 8.5 in by 14 in by 15 ft math timeline, on which students will be able to watch math in action throughout history—and see how math points us to the Creator in the process. Below is a sneak peek into just a few of the facts students will learn. Stay tuned for publication information!
Electricity—we take it for granted and use it countless times a day. Turning on lights, using a computer, microwaving those leftovers, looking at a digital clock, cranking down the AC, opening the refrigerator, doing a tub of wash—the list of daily uses of electricity or electrical devices could go on and on.
But did you know it’s math that helps us explore electricity and design devices like lights and computers? A glance back at history reveals a lot of math—and points us to the Creator.
Back in 1785, A man named Charles-Augustin de Coulomb discovered a mathematical relationship between the force and distance between electric charged particles by doing experiments. His result can be expressed algebraically like shown below.
In other words, the force produced by electricity can be described mathematically!
Later, many other men would do experiments and discover more of the ways electricity works. One key discoverer was a man named Michael Faraday, who realized that magnets can generate electricity and invented the first electric generator. Once again, math was used in this design. In fact, the relationship between the electrical voltage, the number of coils of wire, the change in something called magnetic flux, and the time can be described like shown below.
Faraday, like many other great scientists/inventors, saw creation (which math helped them explore) as pointing to God. Faraday wrote,
“The book of nature which we have to read is written by the finger of God.”
Sit back and think about it for a minute. Even at the microscopic level, electricity (which later scientists would realize is the flow of electrons) operates in a consistent enough fashion to describe it with formulas that we can rely on to work to such a degree that devices like light bulbs and computers can be built around it. Why is creation that consistent? Because a faithful, consistent Creator governs all things.
March 14, or 3/14, was both Einstein’s birthday and is also known as Pi Day, as the irrational number Pi (π) starts 3.14.
There are a lot of different ways you can use the day to build a biblical worldview of math in your upper elementary (or students who’ve learned about decimals) through high school students.
Make a circular pie and talk about how π is the ratio between the circumference (distance around the pie) and the diameter (the distance across), or π = C/d . (Note that this is just rearranging the formula for the circumference you may be more familiar with of C = πd to solve for π.) This ratio is one we can’t even calculate all the digits of! There are parts of God’s creation we can’t even fully describe. You could also explore more applications of π and discuss it further; see the ideas and links in this previous Pi Day post.
Explore (or have your students explore and give you a report on) the life and work of Albert Einstein and talk about his view of God. Here are a few fascinating highlights from his life and work:
Sadly, Einstein was not a Christian, although he acknowledged that there had to be a God.[3]
I’m not an atheist and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages.…The child dimly suspects a mysterious order in the arrangement of the books but doesn’t know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God.[4]
Einstein realized that creation proclaims that there has to be a Creator, or at least, according to the quote below, something miraculous. He recognized an order throughout creation and acknowledged that it doesn’t make sense why men can develop theories that end up tying so beautifully with that order—something that makes perfect sense if the same God created both us and creation.
You find it surprising that I think of the comprehensibility of the world . . . as a miracle or an eternal mystery. But surely, a priori, one should expect the world to be chaotic, not to be grasped by thought in any way. One might (indeed one should) expect that the world evidence itself as lawful only so far as we grasp it in an orderly fashion. This would be a sort of order like the alphabetical order of words in a language. On the other hand, the kind of order created, for example, by Newton’s gravitational theory is a very different character. Even if the axioms of the theory are posited by man, the success of such a procedure supposes in the objective world a high degree of order which we are in no special way entitled to expect a priori. Therein lies the “miracle” which becomes more and more evident as our knowledge develops. . . . And here is the weak point of positivists and of professional atheists, who feel happy because they think that they have not only pre-empted the world of the divine, but also of the miraculous. Curiously, we have to be resigned to recognize the “miracle” without having any legitimate way of getting any further. I have to add the past point explicitly, lest you think that, weakened by age, I have fallen into the hands of priests.[5]
We know from Romans 1 that deep down, we all know there’s a God. Creation, as Einstein recognized, proclaims God’s existence.
For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and creeping things. Romans 1:20-23 (ESV)
But while Einstein’s exact views varied some throughout his life,[6] rather than heading God’s revelation to us in the Bible,[7] Einstein made up a god he was comfortable with, essentially worshiping the creation (his own intellect) instead of the Creator. Einstein didn’t want a God who would hold him responsible. He recognized something miraculous about creation, just like Romans 1 says we all do, but decided to worship a god of his own shaping instead.
The God Spinoza revered is my God, too: I meet Him everyday in the harmonious laws which govern the universe. My religion is cosmic, and my God is too universal to concern himself with the intentions of every human being. I do not accept a religion of fear; My God will not hold me responsible for the actions that necessity imposes. My God speaks to me through laws.[8]
Einstein’s birthday provides a great opportunity to point out to your students how creation declares God’s praises. There is a God—and we need to acknowledge Him and recognize that we’ve all broken His holy Law and need a Savior, Jesus Christ. Otherwise, no matter how smart we may be, we’ve become foolish in what matters most.
As you remember both Pi Day and Einstein’s birthday, remind your students to lift their eyes from God’s amazing Creation to the Creator of it all. Encourage them that creation’s very complexity/order and our ability to explore it scream out His existence.
If you enjoyed these ideas, please share with others so they can too.
[1] Kaku, M.. “Albert Einstein.” Encyclopedia Britannica, Invalid Date. https://www.britannica.com/biography/Albert-Einstein and “Albert Einstein,” Star Child Team, https://starchild.gsfc.nasa.gov/docs/StarChild/whos_who_level2/einstein.html
[2] “Albert Einstein,” History.com, May 16, 2019 update, https://www.history.com/topics/inventions/albert-einstein
[3] You can view some more quotes about his view of God here: https://libquotes.com/albert-einstein/quotes/god
[4] Kaku, M.. “Albert Einstein.” Encyclopedia Britannica, Invalid Date. https://www.britannica.com/biography/Albert-Einstein.
[5] Albert Einstein, Lettres À Maurice Solovine (Paris: Gauthier-Villars, 1956), pp. 114-115; quoted in Nickel, p. 210, quoted on http://www.christianciv.com/Atheists_Confess.htm.
[6] John Brooke, referenced in “Einstein Letters Show Views on the Bible and Christianity,” Answers in Genesis, May 17, 2008, https://answersingenesis.org/theistic-evolution/einstein-letters-show-views-on-bible-and-christianity/.
[7] “Einstein Letters Show Views on the Bible and Christianity,” Answers in Genesis, May 17, 2008, https://answersingenesis.org/theistic-evolution/einstein-letters-show-views-on-bible-and-christianity/.
[8] Einstein and the Poet (1983), p. 89. Found on https://libquotes.com/albert-einstein/quote/lbs0n1m
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.
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?
Known 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.
Exiled 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.
Conclusion
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.
I’m a sinner saved by grace through Jesus Christ. I’m also a writer—I’ve been writing ever since I could hold a pen. I… Meet Katherine [Loop] Hannon.
