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[2] Mathematics in a Christian Context

by Robert Craigen, Associate Professor of Mathematics, University of Manitoba, Canada

1. Mathematics and Christianity

My principal thesis in this essay is basically quite simple:  In the Gospel of John, Jesus responds to Pilate’s questioning, “So, you are a king?” by saying that he is indeed a king, but that his kingdom is not of this world — it consists of truth, and his subjects are those who follow the truth.  In another place, he says “I am the Way, the Truth and the Life”.  In another, “You shall know the truth and the truth will set you free”; elsewhere, “the true worshipers will worship the Father in spirit and in truth”.  Math and Christianity meet in focusing on the primal nature of truth.

Now, the truth of which Jesus speaks in the passages to which I refer above (and many others) is not a synonym for mathematics, by any means, but it means first of all one thing to me–that a Christian is one whose first allegiance is to the “kingdom” that consists of truth.  While many Christians may seem very dogmatic, one who is true to his roots as a Christian is committed to what is true, whether or not it happens to coincide with what he has believed thus far.  We should refuse to follow lies, and we must insist on carving our way along paths of established truths, insofar as we are given light, and to the extent that we are able; when we act with only partial light, we do not act in direct violation of known truth.  We cannot dogmatically hold to beliefs in the face of clear, verifiable facts to the contrary.  I take this as to apply to the very tenets of the faith itself (including, paradoxically, the truth doctrine I am espousing here).  Indeed, if beliefs fail to stand up to rigorous analysis, they fail to provide an adequate foundation for life, and are not worth adhering to.

Mathematics, at least the variety of math (more on this later) with which I deal, concerns itself with propositions known, or accepted, as true.  It has been said that math is the science of “if…then”, that is, there are no conclusions in math other than those arising from some assumptions, and so there is no universal truth in mathematics.  There is some truth in this statement, but it contains a fatal flaw — “if…then” is itself a form of truth; either the relationship between the antecedent and the conclusion is “true” or it is not.  If this relationship founders, so does all truth, so we had better be careful how eager we are to knock out this foundation stone.  As you will see, with my definition of mathematics, this relationship itself falls within the realm of mathematics, and so there is
no difficulty imposed by accepting that mathematics (at least as we practice it) begins with initial assertions (axioms, etc.) and proceeds by logical deductions from there.

Rightly viewed, mathematics is a gold standard for truth.  It is one way of establishing unassailable truths.  I usually get one of two main responses to this claim:  i) either an outright denial of it (I believe this response is badly misguided–in sheer ignorance of the facts, or with great articulation and quasi-clarity of thought in one of the great mind-bending exercises of “postmodern” deconstructionism,); or ii) an acceptance that mathematics indeed can establish unassailable truths, but that such truths as it deals in are largely irrelevant to the issues that form the meat-and-potatoes of daily human existence and certainly not to the larger issues such as Love, Eternity, Divinity, Morality and Purpose in life (this response seems much more reasonable than the first, and I do not blame those who respond in this way at all, but I shall argue that it is based on a fundamental misunderstanding of the nature of Mathematics.

In any case, even if you don’t accept my above statements about mathematics, clearly mathematics is about truth, of a sort, and it is about establishing the validity of that truth, whether effective in doing so or not.  That, and my preceding statements about the nature of Christianity, is all one needs in order to understand my claim that there is some interplay between the two, at least in the life and mind of an evangelical Christian who is also a mathematician.  I will attempt to show here that this interplay is not trivial, that it has some significance.

2. What is Mathematics?

Mathematicians are sticklers for proper definitions.  Without proper definitions, everything that follows is made of jell-o.

Have you ever heard a mathematician define “mathematics”?  Most don’t try, but I have heard several; the result is often laughable.

The boldest definition of mathematics by a mathematician that I have heard is that of Reuben Hersch:  “Mathematics is what mathematicians do”.  This definition carries the unacceptable implication that mathematics is no more, and no less, than an arbitrary collection of human activities.  The reader of Hersh’s extended articulation of this idea — his book “What is Mathematics, Really?”–will find, after hundreds of exhausting pages of philosophical mumbo-jumbo, that he eventually reaches the natural conclusion that math is a cultural artifact, and mathematical truth is arbitrary, a mere consensus, subject to change and revision over time and at the whims of those forming the consensus.

The definition I shall give, in contrast, does not refer to mathematicians, or to any other group of humans at all — humans are quite irrelevant to the question of what mathematics is.  Indeed, so is the earth, and the very cosmos.  In this sense, mathematics is transcendent.  By “transcendent”, I simply mean “beyond”; mathematics is not dependent on any particular material or temporal manifestation, its truths go beyond these things.

Chemistry, biology, physics–each branch of science delves into what can be known about a particular aspect of the world that is open to our exploration and yields information to our means of exploration, and whose truths can be resolved by appropriate tests of validity.  Yet it is defined not by the activities of the practitioners of the discipline but by the objects of study toward which those activities are directed.

I contend that the word “science” is a bit unfortunate because it tends to denote only those things which can be known.  But a physicist, for example, does not generally mean this when he speaks of physics.  What the physicist really means by “physics” is the set of facts about physical systems that completely describe how they operate and what they are.  Perhaps these facts can all be known; perhaps not.

Similarly, mathematics is a science–not in the limited sense of “what can be known”, but in the broader sense of “the facts, whether they be knowable or not”.  By this I mean also whether they can be expressed through mathematical symbols or not.  This understanding of the word “science” is important to my definition.  Moreover, mathematics is more than just a science.  It is also an art, and it is also a humanity.  In these cases, however, one focuses not on mathematics proper, but on mathematical activity, or on human appreciation of, or ability in, mathematics.  The main shortfall of most definitions of mathematics is that they limit the scope of “mathematics” to some subset of human endeavor, I will treat mathematics primarily as a science, with “science” taken in the above sense.

With all of the above understood, here is my definition of mathematics: Mathematics is the science of structure, form and relationship.

Mathematics, unlike the three physical sciences mentioned above, does not study any one particular aspect of the physical world–it studies that which lays behind and undergirds all physical manifestations of all phenomena–structure.  I mention form and relationship, because it is necessary to properly delineate the scope of the subject and to avoid potential misunderstanding as to the intended uses of the definition.

This definition explains why all scientists use mathematics in their discipline.  It is indispensable because one cannot do science without establishing patterns and facts that deal with structure, form and relationship.  It is, in a way, what science is about.  At the very least, this is why mathematics provides the “language of science.”

There is nothing without structure, form, or relationship that we know.  If we know something it has a relationship, first to our conscious thoughts, and second to the symbols in terms of which we are able to think of it.  If it “exists”, then it has some relationship to some realm in which it “exists”.  If it is something, then it has some form, be it abstract, or material, or spatial, temporal, conceptual, and so on.

Suppose something is “formless, and void,” as the world is said to be in first chapter of Genesis.  This is a form as much as 0 is a number and the empty set is a set, and thinking about nothing is thinking about something.  To think that formlessness lends that thing the property of not having any form is a mistake.  For “formlessness” means to us “lack of identifiable form”.  If there is such a thing as “identifiable form”, then this can be defined and delineated.   Deliberately try to conceive something with no form and you are still required to ask and answer questions about form, or the lack thereof–both of which qualify as the “science” of form.  Form cannot be escaped.

Keith Devlin defines mathematics as “the science of patterns”.  Then, one objects, what about things that have no patterns?  “Patternlessness” is itself a pattern, of a higher sort, in the same sense as formlessness is a form.  So this property and our knowledge (if it is knowable) of it, falls squarely within considerations native to the science of patterns.

Although I prefer Devlin’s definition to Hersh’s, by “pattern”, he means “humanly perceived pattern”, which is a step in the direction of Hersch.  Structure cannot be escaped.  What about a random structure?  As long as you give “random” a precise meaning, then it indeed has a structure, which can be defined in terms of this avoidance, as with “formlessness” and “patternlessness” above.

One could argue that this definition is so general that it no longer has any meaning — it is as bad as Hersch’s definition, but for the opposite reason — it is not connected to any particulars at all!

The “disconnection from particulars” in my definition is its strength; it reveals precisely what it is that makes mathematics unique among the sciences, for mathematics is not about any particular instance of any particular object, material or otherwise.  It is about those characteristics shared by all things.

Incidentally, it is this very generality that makes mathematics so useful.  Solve one equation, say the quadratic equation x2+3x+2=0, and you have solved the essential part of myriad problems in economics, biology, chemistry, physics, epidemiology, quantum mechanics, general relativity, and problems not yet thought of.  As everyone with experience doing word problems knows, the hard part is usually not the mathematics, it is finding the mathematics — putting the words about some specific situation into its most general context, keeping only that information relevant to the actual problem.  When the problem is boiled down into these terms, it magically becomes mathematics.  That is because mathematics is the bare bones of reality.  It is what is left when all the particulars are erased.  The process of stripping the words away to reveal the essential core has been called abstraction.

In spite of the dictionary meaning of the word, I shall use the term abstraction to refer to such things as have no physical or material particulars, though they may (or may not) be taken as categories into which particular phenomena and objects fall, such as: number, measure, sphere, line, tesseract, continuity, connectedness, consistency, matrix, variable, set, ordered lattice, interval, loyalty, goodness, computability, and so on.  Here’s another, inadequate, attempt: Abstraction is “possibility before (or in the absence of) realization.”

Mathematics is abstraction (not the verb, the noun)–merely “abstraction” as a pre-existent state, a mold into which all specific things must fit.  This is what we study when we study mathematics, the skeleton on which all other things hang.

So is mathematics a branch of philosophy?  NO.  Mathematicians don’t need to concern themselves with the nature of the field of mathematics, but can go ahead and study the subject, even in blissful ignorance of its boundaries of the philosophical category into which it fits.

3.  What does this have to do with Christianity?

Here are some thoughts regarding this question.   I will refer to my identification of the central tenet of Christianity, not an orthodox way to define Christianity, but one which sees “truth” in some direct way, associated with who Christ  I will take truth as an atomic concept, and instead give a couple of personal anecdotes that relate to truth as a concept that intersects the two worlds of an evangelical Christian who studies mathematics.

Scene I — An isolated Christian mathematician

Several years ago, I had a chance meeting with the web page of a fellow Christian mathematician who was struggling with the relationship between these two areas of his life.  I should not say that he saw a conflict himself, but that he had some difficulty explaining his Christianity to his mathematical friends, and his enthusiasm for mathematics to his Christian friends.  Some extracts from his correspondence with me:

There were at least four difficulties evident in his thinking: i) one is that there is a fear of mathematics, and more generally, of science, among many evangelicals; ii) there is a sense that mathematics is a frivolous endeavor, wasteful of one’s resources for doing good in the world; and on the other side iii) there is a sense (by the “mathematical side”) that a mathematician ought to be too rational to believe in such things as God–particularly in the Christian formulation of God.  Finally, iv) there is a feeling that the job of the mathematician is to reduce all human activity to the level of axioms and thus rationalize one’s life.  My friend discovered, to do this from a purely formalist perspective leaves one with no definite answers—any one axiom system is as good as any other (consistent set of axioms), and one is led, at best, to relativism along this road.

I take up each of these briefly.  As for i), Many evangelicals simply do not understand mathematics and/or science, and there is a great fear of the unknown.  There is a fear that, if math or science was allowed free reign, they might do serious damage to one of the foundations of our faith and it will come crumbling down.  Like most fears, it is based not on the known, but on the unknown.

I have a simple twofold answer.  The first part is that all truth is God’s truth, or at least consistent with the doctrine of God if Christ’s statements about his relationship to truth are taken as foundational.  The second part is Christ’s declaration that, not only has he come that we may know the truth, but that the truth will set us free.  So, a Christian should not be afraid to face truth, no matter what form it comes in.

The second problem is more profound.  Is mathematics a frivolous activity?  If I play all day with equations and symbols in my mathematician’s paradise, at the end of the day, whom have I helped?  To this I answer that the pursuit of truth is inherently a good end in and of itself.  That I thoroughly enjoy the pursuit does not detract from its value.  From the outside it is easy to dismiss the truths of mathematics as frivolous pursuits and of less value than, say, the pursuit of truth in a criminal court or relating to some justice issue.  But it is precisely there that the aspiring critic reveals his or her misunderstanding of mathematics.  A review of my definition of mathematics will reveal that mathematics is the underlying structure for all phenomena found in the universe, and beyond.  This includes all such human activity, and more.

The problem is in bringing that significance, in the broadness of its generality, down to a level we can understand and appreciate.  This is the problem of Applied Mathematics—to show how mathematical truths and methods can be used to solve problems in the real world.  It is a great study to follow the path of mathematical discoveries from a recreational tinkering in someone’s head to some important application.

Minkowski space is an exotic space conceived only as a solution to a rather esoteric problem:  is it necessary to admit the parallel postulate among Eulid’s axioms of geometry?  Minkowski (and others) discovered that, if the parallel postulate is replaced with other statements, one can obtain interesting and surprisingly beautiful alternate geometries that become fascinating playthings for the mathematician.  But are these geometries of any use?  In the case of Minkowski space, the answer came when Einstein formulated his Theory of General Relativity.  He discovered some laws that dictated how the universe would evolve but there was one problem—the laws say that the universe violates the flat geometry of Euclid.

Einstein learned, perhaps by chance, of Minkowski space, and thereby found a setting in which his laws work.  And today, broadly speaking, we treat the shape of the universe, not as a manifestation of Euclidean space, but (approximately, and locally) as Minkowski space.  A frivolity becomes the framework of the universe, and it’s all in a day’s work in mathematics.  When one grasps the enormous consequences of each tiny advance in mathematics, it is hard not to be awed by the great significance of mathematical work, whether one is a pure or applied mathematician.  To work in this field is a tremendous privilege, and we deal in a currency of unfathomable worth.

What about problem iii)?  Should a mathematician be too rational to believe in God?  This question presupposes, of course, that there is something irrational about belief in God.  On what basis must we say this?  You might say that it does not follow from the axioms, and I would ask, “What axioms do you have in mind”?  For relativism cuts both ways.

When Laplace finished his great Celestial Mechanics, a treatise on the working of the heavens, none other than Napoleon challenged him by asking how he could write a great work about the mechanisms of creation without ever once mentioning the creator.  Laplace responded, ” “Sir, I have no need of that hypothesis”.  One may argue along Laplace’s line that, for sure, there is no obvious harm to science in having a God-axiom, but it is completely unnecessary in order to have a complete conception of the universe—it is therefore an irrelevant hypothesis.

Whether or not one grants the second half of this line of reasoning, one must ask whether the point of having a belief in God is to fill in gaps in one’s scientific knowledge.   If so, then one has fallen into the old line of the “God of the Gaps”—the God who exists mainly as an explanation for otherwise unexplainable phenomena.  This is an uncomfortable position in a civilization in which knowledge of the world increases.  For this god will find himself continually retreating from the light of human discovery, always seeking the shadows and hiding in dim corner beyond the latest advance of science.  Followers of such a god find themselves continually in need of revisions of their beliefs.  Or they are thrust by necessity into debates to defend the “unknowabilty” of fields even as they fall increasingly under the scrutiny of science.  Much of the so-called creation/evolution debate strikes me of having this kind of character—that is, the better half of the debate does (the other half comes when proposals are made for “scientific” theories designed to support a god-hypothesis, and with no support that goes beyond attacking competing explanations; this is the more degenerate side of the debate, but it is a problem entirely separate from the one I am currently addressing.)

I hold this perspective partly to blame for the negative response of some evangelicals to scientific advances (my point i) above).

The main difficulty with the God of the Gaps, from a Christian perspective, is simply that it is foreign to God as he is presented in the bible.  The God of the bible does not hide in shadows delineated by man’s ignorance—quite the opposite, he declares that all that is hidden will be made known (e.g., Lk 8:17), and that in him there is no darkness (meaning, in context, ignorance).  He broadly invites mankind to explore his truths, to come and reason, to pursue knowledge and wisdom.

This is not a timid god, but one who openly declares himself and walks among us.  As the apostle John put it, “The light shines in the darkness, but the darkness has not understood it…the true light that gives light to every man was coming into the world.  He was in the world, and though the world was made through him, the world did not recognize him.”  (Jn 1:4-10, NIV) The God portrayed in the bible has very much the opposite character one expects of the God of the Gaps—he offers truth, light, knowledge and insight, and meets us in person to present it.  From this perspective a christian who pursues the sciences, such as mathematics, is working in concert with God, part of whose business is revealing truth to mankind.

Here is an exciting realization—the Christian scientist or mathematician is not in the business of avoiding intersections between his field and “ultimate question”, but that he is participating with God in bringing light to bear in realms once dominated by the darkness of.

Finally, we have question iv):  should we not limit our lives to that which can be derived “mathematically” from some set of fixed laws, or axioms?  In a sense, the answer to this question is “yes”—presupposing we have full knowledge of such axioms and full power to carry out the requisite mathematical derivations.  But there are many reasons why, operationally, the answer must be “no”; I list four:

1.  We do not, in fact, possess knowledge of all the “axioms” of life.

2.  We certainly do not have the mathematical power to work these axioms out into imperatives concerning daily choices in our lives.

3.  Ask whether this requirement is true for the routine choices of daily life, and you will see the absurdity of it.  Must the Christian mathematician have mathematical certainty whether to wear the red socks or the blue each day, or whether to take the stairs or the elevator to his office?  It is not necessary to attempt to resolve every question of life as if it were a quadratic equation—even if such a thing were possible, in principle.

4. There is a very good reason to doubt that axiomatics are sufficient to resolve all truths in the pure realm of mathematics (namely Godel’s incompleteness theorem, which I shall perhaps address later).  How much less the truths of life.  This is not to deny the ability of mathematics to address such questions.  It is merely a denial of the centrality of the axiomatic method to the global domain of mathematics.  It is now understood how limited axiomatics are in this regard and even tightly minded formalists and those of the constructivist school have now to admit that math pushes beyond the chains imposed by any measly set of axioms.

So problem iv) is not really a problem at all, it is an illusion.

Scene II — A (non-Christian) deist/theist mathematician

I will call this person James — not his real name.  One day James gave me a paper he had written.  I was particularly struck by the Acknowledgement he gave at the end of the paper.  He wrote something like, “The author wishes to acknowledge God, who knew all these things first.”

As a Christian I was impressed with the boldness of such a declaration.  Although it was exactly the right thing to say, one does not offer such boldfaced declarations as part of serious published work because the inevitable ridicule will detract from the work itself and ultimately not serve either the cause of God or promote the value of the academic work.  Scholarship ought to stand on its own merit.  This is the principle of not “casting pearls before swine”.  There is simply no point in offering such acknowledgement in an arena in which it would only invite ridicule.

I was impressed with James’ acknowledgement and mentioned to him that it was refreshing to see a reflection of this sort in an academic work.  He responded by telling me of his background was not a Christian, but had come to the conclusion, after many sorts of deliberations, that there must be a God, that he is creator of all that there is, and that this god is transcendent, omniscient, and either benevolent, or in the very least, not evil.

He saw God as unlikely to have any particular kind of personality; he was more like a force that pervades the universe.  God, being creator, was not equated with the universe, and was not contained within it.  Those familiar with the distinction between Theism (belief in a personal god) and Deism (belief in a supreme being devoid of personality) will recognize that James fell slightly on the Deist side of the fence.

One day I asked James if he thought God had any particular characteristics that defined him as a God.   James considered the question, but not for very long.  He said that he didn’t think that God had anything that would qualify as a personality.  The things that delineated God from elements of the creation were some abstract and very general properties.

So I asked James how he came to the conclusion that God must be the creator of the universe.  Because it is self-evident, he says, that the universe must have a cause—something cannot come from nothing, and there must be a reason why there is something rather than nothing.  So I asked, “Why?  If God has no passions, no sentiments, no motivations, then why did God create the universe?”  If one appeals to God as a first cause then one must attribute something to God that acts as motive, that explains, in terms of the characteristics of God, why he would do such an extravagant thing—or one is again left with the problem of an absent first cause, but a worse one, in which a God frivolously, or for no good reason, creates the universe, with no interest in it and for no purpose.

James clearly had not ever considered that question.  He asked what my answer to the question was.  I responded that God is a person, and has definite personality traits.  For example, he is good; he identifies with the lowly and the oppressed.  He actively promotes justice, promises to ultimately avenge all wrongdoing and reward all good.  He calls a people to be his own and identifies himself with them — and more.  Although God is far beyond our comprehension there are some basic traits that allow us to understand some of what motivates him. Although our thinking about these things is imperfect, we can examine the better parts of our own souls and use them, by way of analogy, as a window into his eternal being.

So why did God create the universe?  I think it is because he was lonely.  Although that may sound as if God has a weakness, the God who makes himself weak and vulnerable for the sake of others is very much part of the Christian story. Though “lonely” is surely not exactly right, it may be the only way we can humanly conceive of his motivation.

God is lonely, and he desires relationships.  He desires a relationship with you.

The more I think of the lonely God, the more I think it fits the Christian worldview because it is consistent with the God who seeks out relationships with men and women, and who sacrifices to guarantee these relationship.  It explains why God is our friend, and why he desires to adopt us into a family relationship.  The thought that God created the entire universe, in its immensity, just to commune with humankind, seems too wonderful to accept, but the christian conviction is that God loves the “world”, not only in the grand scale, not only by the countless millions, but right down to the individual scale — he knows my name, and he knows yours; he knows us deeply, intimately, better than we know ourselves.  The psalmist wrote, “O Lord, you have searched me and you know me.  You see me when I sit and when I rise; you perceive my thoughts from afar.  You discern my going out and my lying down; you are familiar with all my ways.  Before a word is on my tongue you know it completely, O Lord…you created my inmost being; you knit me together in my mother’s womb.  I praise you because I am fearfully and wonderfully made…My frame was not hidden from you when I was made in the secret place.  When I was woven together in the depths of the earth, your eyes saw my unformed body.  All the days ordained for me were written in your book before one of them came to be…”  (Ps. 139, selections).

I sometimes wonder—what was there about our conversation that was peculiar to an interchange between mathematicians?  I’m not sure, but I do know that it was in the context of a presentation of mathematical ideas.  How we both thought through these questions is a reflection of the way we think of things.  My question about God concerned structure, form and relationship (suitably interpreted).  Yet our thoughts are basic to those of people of almost any background who engage in such a discussion.  There was little new in our thoughts by way of content, but perhaps they were articulated in a helpful way because of our mathematical way of thinking…I don’t know.

But I like to think so.

Dr. Craigen is a much published author and professor.  He is a winner of the Kirkman Medal for his work in Combinatorics.  This essay–published with his permission–is adapted from his article on  http://home.cc.umanitoba.ca/~craigenr/PWP/mathchrist.html.

[1] God’s Language is Mathematics

by Mark Eckel, Dean of Undergraduate Studies, Crossroads Bible College

“I’m not a math person.”  For years this had been my response to any question involving numbers, equations, or solutions.   But I had wrongly given up responsibility for a crucial characteristic of God’s creation.  I began to realize my answer was a wrong approach to math or, for that matter, anything else in life.

In the summer of 2003 I was asked to do a Christian school in-service on biblical integration including three hours on elementary math.  I asked for and received the table of contents along with sample lessons from each textbook.  As I pondered God’s natural revelation of arithmetic The Spirit began to open my eyes to at least twelve major concepts directly dependent upon Scriptural truth.

I used to believe that math was the most difficult subject for biblical integration.  Indeed, it seems immediately plain that math is the essential core of God’s world.  As I understand it now, math could well be described as “God’s language.”  For instance, John D. Barrow’s book The Constants of Nature: From Alpha to Omega–the Numbers That Encode the Deepest Secrets of the Universe seems to mirror Scriptural injunctions concerning “the works of God’s hands” that endure “from age to age.”  The stability of creation is consistently used as the measuring rod for God’s interaction with people.  Why?  The Creator’s truthful rule over this world and this life marks his dependability for the next world and afterlife (see examples in Psalms 35, 71, 73, 80, 88, 92, 95, 103, 118, 120, 146, and 148).  Numerical order is essential for life and central to “the whole truth” of God’s creation.

Here is a sample of biblically integrative lesson plan goals from the first of twelve mathematical concepts entitled “systems and roles.”  Each aim is premised upon observations from Genesis one and two.  [I have created 12 lesson plans which include goals, objectives, anticipatory sets, readings, discussion, methods, and questions.]

1. To prove God’s world is interrelated–each part working within the whole.

2. To express how God brought various systems together in complemenary equilibrium.

3.  To state that creation’s organization is based on the plans and decrees of God.

4.  To explain how something is “unique”–each thing assigned its place, given a role by God.

5.  To appreciate mathematics as a system by which God runs the world.

After describing God’s numerical ordering of His creation Job cries, “And these are but the outer fringe of his works!” (26:14). Never again will I say, “I’m not a math person.”  Since The Personal Eternal Creator binds His world with numbers, I am bound to discover more about math.  Discovering more of God’s world helps us to know more of our God.

 Mark Eckel is a frequent contributor to this site.  He believes God spoke creation into existence with numbers.  You can enjoy his excellent and insightful book and movie reviews on this site.

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