The King of Every Subject – Even Math

This article first appeared on www.desiringGod.org.

(@LeslieSchmucker) retired from public school teaching to create a special education program at Dayspring Christian Academy in Lancaster, Pennsylvania. She and her husband Steve have three grown children and two grandchildren. She blogs at leslieschmucker.com.

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Two weeks ago was my first day of school, for the fiftieth time — my thirty-second as an educator. Twenty-eight of those years I spent teaching in public school, and the last three in the Christian school where my husband and I sent our children.

Unlike many Christian schools, this particular one goes beyond tacking a few Bible classes onto their classical curriculum. Here, the Bible is the heart of the curriculum. Every day, in every subject, in every class, the students are taught that God is the Creator of every bit of information. Teaching at this school goes past merely imparting knowledge. The goal is to use the subjects as vehicles to behold the glory of Christ.

Of course, this is not revolutionary. Martin Luther asserted,

I am much afraid that schools will prove to be great gates of hell unless they diligently labor in explaining the Holy Scriptures, engraving them in the hearts of youth. I advise no one to place his child where the Scriptures do not reign paramount.

A century later, on September 26, 1642, the founders of Harvard College in the Rules and Precepts at Harvard stated,

Let every student be plainly instructed, and earnestly pressed to consider well, the main end of his life and studies is to know God and Jesus Christ which is eternal life (John 17:3) and therefore to lay Christ in the bottom, as the only foundation of all sound knowledge and learning. And seeing the Lord only giveth wisdom, let every one seriously set himself by prayer in secret to seek it of him (Proverbs 2, 3).

America’s Schoolmaster

Even in our more recent American history, education’s goal was to foster a biblical worldview in its citizens, not only to lay biblical foundations for civic duty, but to educate biblically as a compass to lead children to the true north, Christ.

Noah Webster was named the Founding Father of American Scholarship and Education and “America’s Schoolmaster.” His famous Blue Back Speller was the fundamental reading book used by Colonial American children, along with the Bible, which was the primary textbook. Webster went on to write the incredible American Dictionary of the English Language, which was published in 1828. Webster’s 1828 is a massive and thorough volume of comprehensive definitions of English words and pervaded with Scripture. In it, he defines education this way:

The bringing up, as of a child; instruction; formation of manners. Education comprehends all that series of instruction and discipline which is intended to enlighten the understanding, correct the temper, and form the manners and habits of youth, and fit them for usefulness in their future stations. To give children a good education in manners, arts and science, is important; to give them a religious education is indispensable; and immense responsibility rests on parents and guardians who neglect these duties.

Luther, Harvard’s founders, and Noah Webster could be so boldly Christ-centered because they knew the sciences existed to display the wonder, majesty, grandeur, minutiae, vastness, intricacy, opulence, and sublimity of creation, and the genius of the Creator. They recognized that history outlines God’s providence throughout the expanse of time. Nothing escapes his notice or his hand. Spurgeon said, “When we read human history, we should read it to see the finger of God in it.” Webster especially understood that studying language scrutinizes God’s primary way of communicating with humans, words (Hebrews 1:1–2). Teaching it should point students to the Word, who is Christ.

What Does Math Say About God?

But what about math? Until my children went to Christian school, I had long declared a profound devotion to the hatred of math. But I have come to see that math is part of God’s character. There is no getting around it. Nothing you can see or think about is separate from math. God is a God of order, and math is the essence of that order. The day my second-grade daughter brought home an assignment to find a Bible verse pertaining to math was the day I rescinded that lifelong devotion to hating it.

To obtain knowledge of the world around us is to obtain knowledge of the character of God (Romans 1:19–20). To teach is to point our students to God and to lead them to give him the glory he deserves. Why do you think Jesus said that if his disciples kept quiet, even the rocks would cry out (Luke 19:40)? He knew that God’s creation is so spectacular that every inch of it declares his glory. We must show this to our children!

Parents Are Teachers Too

Noah Webster contended that this responsibility falls on the shoulders of parents, and, by extension, teachers. Even parents who send their children to public school are primarily responsible for making sure Christ is exalted in the things their children are learning.

So how do we do it when the amount of images and information that compete for our children’s attention is so staggering? It is practically incomprehensible to my generation. And as a teacher, it is a daunting task to teach my students anything new. There has been an added paradigm to the imparting of new knowledge. We now must teach students how to access and apply the knowledge that is at their fingertips every second. And much of that knowledge has been distorted, perverting the purity and beauty of God’s good creation.

As Christian teachers and parents, we are charged with the formidable task of showing our children that God is infinitely more beautiful than anything of the world. By our own strength — because of the enemy’s insidious, albeit God-sanctioned, rule in the carnal realm — this task is impossible. But as Jeremiah pointed out, nothing is too hard for God (Jeremiah 32:17).

We must pray with intention and deliberation for our children. We must get creative in our teaching, showing them Elohim, the Creator God. We must compel our students to see God’s glory in everything from a bumblebee to a tree to a skyscraper. We must lead them to an understanding of the quintessence of the old hymn,

All things bright and beautiful, all creatures great and small;
all things wise and wonderful, the Lord God made them all!

We must never stop teaching them to give God the glory in all created things.

The Final Exam

John Piper says, “The redeemed cosmos will reach its final purpose when the saints enjoy God in it, and through it, and above it, with white-hot admiration.”

So teachers and parents, while your heads swirl with technology woes, scope and sequence charts, lesson plan rubrics, faculty or co-op meetings, state standards, IEPs, differentiated instruction, outcomes-based learning, curriculum changes, seating charts, lunch duty, schedules, standardized testing, and wondering when you’ll get a minute to use the restroom, pause to pray. Ask God to help you cut through the noise of regulations and procedures to the ultimate desired outcome of our teaching: God’s glory.

Pray that God would compel you to be perpetually cognizant of the beauty in his creation and to give you a soul-saturated appreciation of the majesty of the world around you. Then ask him to show you how to teach in such a way that by June your children will have seen the wonder in the knowledge you’ve imparted.

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A Short Post on Infinity

I was recently asked to write a few paragraphs on the mathematical concept of infinity for a school news letter. I have copied it below. It is indeed brief for the subject that it deals with. I encourage those interested to do additional reading. I especially encourage reading the chapter on infinity in Math through the Eyes of Faith.

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Infinity is a difficult concept to grasp. We often misuse the term “infinity” to mean “something really, REALLY, big.” When Buzz Lightyear exclaims, “To infinity, and beyond!” the implication is “Let’s go really, really far… and then past that… I guess.” However, when we say that we worship an infinite God, we must be saying more than simply, “God is really, REALLY, big.” So then what are we saying? We can find some insight in mathematics.

To get an idea of infinity in mathematics we have to first be clear on some basic terms and definitions. We can count the numbers in a set by comparing them to the natural numbers (whole, positive numbers). {3,5,7,9} has 4 numbers because we can match each number in this set to the natural numbers 1 through 4: {1->3,2->5,3->7,4->9}. We say this set has size 4. A finite set is any set that can match to the numbers {1,2,3,…,n} where n is some number. An infinite set is a set that is not finite. In other words, there is no stopping point. The natural numbers themselves are infinite: {1,2,3,…}. They just keep going.

Now for some fun.

Consider the even numbers {2,4,6,8,…}. Also infinite. Half as big as the natural numbers right? Wrong. The set of even numbers, which is the set of natural numbers minus the odd numbers, is actually the SAME SIZE as the natural numbers!!! This seems counterintuitive, but we can match each even to the natural numbers {1->2, 2->4, 3->6, 4->8…}. For any even number you can think of, I can give you the natural number it pairs with. We can also prove that the set of all fractions {1/1, 1/2, 1/3, 1/4, …, 2/1, 2/2, 2/3, ….} which intuitively seems much bigger than the set of natural numbers, is also the SAME SIZE as the natural numbers.

So is every infinite set the same size? Nope. The set of all real numbers (every decimal expansion) is infinite, but LARGER than the set of natural numbers. This was proven by George Cantor in the late 1800’s. In fact, it has been proven there are infinitely many different sizes of infinity! Try wrapping your brain around that. Cantor spent his whole life working with concepts of infinity… and he went insane… seriously.

So when we say that we worship an infinite God, what are we saying? From a math perspective there are some familiar aspects about infinity, but it is also wholly different than anything we have ever encountered. It seems to follow rules of logic, yet it is surprising and mysterious. A lot of the characteristics of God that may seem paradoxical on the surface (transcendent yet immanent, perfectly just and yet perfectly gracious, one and three) may not be so paradoxical when you are talking about the infinite.

I’m not proposing any answers to questions of faith based on mathematics. It is my hope that you will see how studying math may give us just as much opportunity to reflect on the wonder of God as does a beautiful painting, song, or piece of poetry.

Enjoy pondering the infinite!

[After my initial post, I received another great comment from Scott Eberle that I thought would be worth including in the post itself]

Infinity is such a great subject for exploring the impact of our faith on mathematics!

Yes, Cantor suffered from depression and had multiple mental breakdowns, partly because of the intense opposition to his ideas. But what is really interesting to me is the whole reason he pursued the study of infinity to begin with.

Up until Cantor’s time, Aristotle’s idea that “actual infinity” does not exist was generally accepted by everyone. This was Aristotle’s way of avoiding the seeming paradoxes associated with infinity. Aristotle taught that we could accept “potential infinity”—that we could always keep going out as far as we needed—but that a real, “actual infinity” does not exist; we can never “get there.” And because mathematicians could not figure out how to deal with infinite paradoxes (like there being as many even numbers as whole numbers), Aristotle’s ideas were accepted. A few mathematicians, like Bolzano and Galileo, toyed with attempts to study actual infinity, but without modern set theory, they did not get very far.

Cantor, on the other hand, was a devout believer. He knew that God was infinite and that “actual infinity” must really exist. And because of this deep-seated conviction, he passionately pursued the study of infinity and developed set theory to describe infinite sets in the face of much opposition, especially from Kronecker, one of his teachers. Cantor insisted that his pursuit of infinity was founded on the theological premise that infinity was an attribute of God and that it was right for us to study it. Studying infinity, for Cantor, was a call of God.

At the time, many mathematicians rejected Cantor’s work and there was quite a lot of opposition. Today, virtually all mathematicians accept it, and the set theory he developed is today considered the very foundation for all mathematics. A real story of faith.

Christ is Risen

Christ is risen from the dead
Trampling over death by death
Come awake, come awake!
Come and rise up from the grave

Christ is risen from the dead
We are one with him again
Come awake, come awake!
Come and rise up from the grave

Oh death! Where is your sting?
Oh hell! Where is your victory?
Oh Church! Come stand in the light!
The glory of God has defeated the night!

Oh death! Where is your sting?
Oh hell! Where is your victory?
Oh Church! Come stand in the light!
Our God is not dead, he’s alive! he’s alive!