Finding God in Mathematics
Date: April 26, 2012
Presenter: Brett Edwards
Contact: bedwards@accak12.org
Blog: brettedwards.com
In my 11 years of teaching mathematics, the most difficult thing for me has been how to
communicate to my students a distinctly Christian worldview of mathematics.
This is not to say I haven’t struggled with how to teach a particular concept or idea or
how to control a wild class, etc.
By far the thing I have spent the most time blankly staring at a blank lesson plan is how to help
students see how what we do in the math class relates to their lives as Christians.
Why is it so difficult for the Christian math teacher to know how to inculcate a Christian
worldview of mathematics?
1. We were not taught to think this way ourselves when we were students.
o I am a product of a secular school system that taught me God had nothing
to do with academics and especially not mathematics
o I think arguably the most dangerous thing today about secular education is
not what they DO say but what they DON’T say in the classroom
 When a student goes through 13 years of mathematics
instruction without ever hearing the name of God, they logically
think God has NO place within the walls of science
 We as Christian math teachers are to provide a sanctuary where
God is welcome in the math class
2. We have a misconception about what teaching a Christian worldview constitutes.
o Teaching a student in Bible class who the author of Romans is is not
inculcating a Christian worldview
o Chapel once a week does very little if the child is not immersed in the gospel
the rest of the week
o A daily Bible verse or prayer before math class may help but is NOT
sufficient in inculcating a Christian worldview
o Teaching the students to think of the cross every time they see an addition
sign is NOT teaching Biblical worldview
o There are many Bible teachers that are communicating a lot of Biblical
information to there students but they are not giving their students an
ability to analyze the world through a Christ centered perspective
o
The point is that Christian worldview is difficult in EVERY class because most
of us were not trained to do so
3. Our students have not been prepared by their own parents, their own churches and
even their authorities within the school to think of mathematics as an area where
God applies
o I was told by a teaching friend of mine who is a Bible teacher and also
teaches at a Christian school. He said that once when having a conversation
with this principal, the principal told him how sorry he felt for the science
and math teachers at the school. My friend asked why and the principal of
a conservative Christian school said that math and science teachers don’t
get to teach about the “important” matters of life. It’s the Bible teachers
that get to teach the important things while math teachers teach the
subjects unrelated to spiritual things!
o This is not helped when week after week, chapel messages emphasize that
“while math, science and history are important… the most important thing
they can do is give their life to Jesus” please don’t hear what I am not
saying
 Sure if I had a choice, I would rather my students understand the
gospel than the Pythagorean theorem but I don’t think it’s
appropriate to phrase it this way
 It’s like saying “while being nice to your neighbor, loving the orphan,
and respecting your elders are important things… the most
important thing you can do is give your life to Jesus”
4. We want to believe there is a magic formula, a 3 step process to teaching Christian
worldview in mathematics
o I naively thought that I just needed to get my hands on the right book, go to
the right math conference and then employ a few nifty techniques and
within 6 weeks my students would be seeing Jesus in every equation the
worked out
o We have to retrain our minds and see how we can find the Lord in the math
class room
So, here we are, we have established that it is a difficult task. I now embark on a the daunting
task of trying my best to tell you what I have learned in my short 11 years of teaching
mathematics how we can communicate a Christian worldview of mathematics.
How do we communicate a Christian worldview in mathematics?
1. Emphasize the presuppositional aspect of math
2. Explore the mysteries of mathematics
3. Help students see math as a quest to find the order and harmony of God in nature
4. Instill a passion for truth, beauty and goodness in our students
5. Teach students that math class is an important training ground for the mind
I.
Emphasize the presuppositional aspect of math
a. Students must see through the lie that mathematics and science are purely founded
upon observable and provable fact alone
o It is critical for them to understand this because the modern world tells
them from day one that math and science does not accept anything on faith
which couldn’t be farther from the truth
o All math performed is based on presuppositions, things assumed to be true
o Only when things are assumed to be true without proof can math begin to
make sense of the marvelous world in which we live
a. Foundations of Geometry with Euclid
o
o
Greek geometry, as exemplified with Euclid’s classic textbook Elements,
offer us a great example of how even the mathematician must grant some
things as true without proof.
 The foundational textbook for Western mathematics is Euclid’s
Elements, 467 propositions proven with a rigorous logic still
respected by virtually all mathematicians today
 Bertrand Russell eloquently describes the value of Euclid saying “At
the age of eleven, I began Euclid, with my brother as my tutor. This
was one of the great events of my life, as dazzling as first love. I had
not imagined that there was anything so delicious in the world.”
To even start the textbook, Euclid grants that he is unable to prove anything
unless he assumes certain things to be true
 these assumptions include definitions, 5 postulates and 5 common
notions… he was unable to prove them but he would not be able to
make mathematical sense of the world if he didn’t first assume
them to be true.
 This is where students must see the connection to their faith in the
Christian God. Even the geometer must have “faith” in these 5
postulates if he wants to make sense of the physical world.
 Obviously points and lines are fundamental to geometry and listen
to how he defines a point
Point - “that which has no part”
Line - “a line has breadthless length”
 this is what greek geometry stands upon, “no part” and “lengths of
0 width”…

o
o
o
o
o
o
o
Euclid’s controversial 5th postulate or Parallel Postulate is in essence
that two lines parallel to one another will never intersect
 This can not be mathematically proven!!!
 Show me the deductive proof for this
Christians must admit their inability to prove mathematically or scientifically
the existence of God
 But if our students can see that only when they accept God as true,
the same way Euclid accepted his 5 postulates as true, his
definitions and so one then they then make sense of the world…
they will then be armed with the reasoning skills to attack an
unbelieving world
 Looking at our world with an atheistic worldview does not give the
foundation, the necessary presuppositions, to understand good and
evil, what is beautiful, what is true, the inherent value of man, etc.
Greek Geometry begins with fundamental assumptions and then proves 467
propositions
In like manner, the Christian begins with fundamental assumptions and view
the world on the basis of these assumptions
 The Christian faith is built upon things we are unable to prove
 But when we accept these things to be true, they give supremely
satisfying answers to why man has any inherent value… why man
should seek to do good to his neighbor… what is true, good and
beautiful
I do not think that defending Christianity should look like a Euclidean proof
but I think our students need to see the connection between
presuppositional thinking in the math class and such thinking in defending
the Christian faith
The great European mathematicians of the 16th- 18th centuries founded
their mathematical studies on a belief in a God that would create a rational
world
“To Descartes this result, God’s existence, was more important for
science than for theology, for it afforded the possibility of solving the
central problem of the existence of an objective world.” - Math
Historian Morris Kline (Mathematics and the Search for Knowledge)
Unbelief mocks the Christian’s dependence on faith and then welcomes and
depends upon it in mathematics and science
Faith is fundamental to every thing in this world… there is no knowledge
outside of God
“For with you is the fountain of life;
in your light do we see light.” – Psalm 36:9
o
Conclusion - Our students need to learn in the higher levels of mathematics
that all understanding (even in the sciences) is presuppositional, based on
things assumed to be true with no ability to prove them. Yet, it is only when
these things, Euclid’s postulates or the existence of God, when accepted as
true that we can then make sense of the world around us.
b. Foundations of Calculus with Newton
“If we lift the veil and look underneath… we shall discover much emptiness,
darkness, and confusion; nay, if I mistake not, direct impossibilities and
contradictions… they are neither finite quantities, nor quantities infinitely small, nor
yet nothing… May we not call them the ghosts of departed quantities?” – Bishop
George Berkeley, The Analyst
- the initial discovery of what we know as Calculus was made by the great Isaac
Newton
o Calculus, for students that are able, is the crowning achievement to
their mathematical journey
o If learning mathematics is thought of as climbing a monumental
mountain, I think it could be said that Calculus is the final steep ascent
 When the peak is reached, a marvelous view is given to give
you context to the work you have done
- Calculus is the language of nature
- BUT the very foundation of Calculus is wrought with contradiction
o As Berkeley says “emptiness, darkness, and confusion… direct
impossibilities and contradictions…”
- Why is Calculus built upon apparent contradiction?
o In Calculus we have this mystical union between infinity and zero known
as the infinitesimal
o This is central to the foundation of Calculus
o Let us examine how Isaac Newton initially manipulated this little
anomaly in his version of differentiation known as fluxions
o Let’s look at the equation
y = x2 + x + 1
o Newton assumes y and x are changing (flowing) as time continues so he
o
o
denotes their rates of change as… and respectively
But he lets them change “infinitesimally” which means in essence… no
time! Zero time!
Now let’s look at his algebraic manipulation illustration his method of
differentiation
(y + o ) = (x + o )2 + (x + o ) + 1
Add the infinitesimal change in x ( )
and y ( ) to each x and y
y + o = x2 + 2x(o ) + (o )2 + x + o + 1
Square (x + o )
y + o = (x2 + x + 1) + 2x(o ) + 1(o ) + (o )2
Rearrange the terms
o = 2x(o ) + 1(o ) + (o )
o = 2x(o ) + 1(o )
2
y = x2 + x + 1 so we subtract from both
sides
Fuzziness begins… because (o ) is
infinitesimally small, we can assume
this value squared is virtually nothing so
we eliminate it… New mathematical
property called the elimination
property of equality 
o / o = 2x + 1
We now divide every thing by o which
is the real math sin, Why? We are
essentially dividing by 0, breaking a
cardinal rule of mathematics
- We break a fundamental rule of math when we divide by o , we just allowed it
to vanish as a zero and then we act as if it is not zero when we divide
What’s the dilemma?
- Newton and Leibniz break fundamental rules of mathematics to create a
remarkably powerful method in explaining the nature of the world
- Only when we have faith that such operations can be done will we be able to
use the power of Calculus
- Our faith in the reality of Calculus is synonymous to our faith of the reality of the
Christian God
o Both contain inconsistencies in the human mind (infinitesimals, the
Trinity, etc.)
o But when we take these things to be true, they have an awesome ability
to make sense of the world around us
“Nobody could explain how these infinitesimals disappeared when squared; they
just accepted the fact because making them vanish at the right time gave the
correct answer. Nobody worried about dividing by zero when conveniently
ignoring the rules of mathematics explained everything from the fall of an apple
to the orbits of the planets in the sky. Though it gave the right answer using
calculus was as much an act of faith as declaring a belief in God.” – Charles
Seife, Zero: The Biography of a Dangerous Idea
-
-
Seife believes the answer to this quandary is provided in recognizing the idea of
a limit… reading his justification is like the Christian trying to explain away the
mystery of the trinity
I think Berkeley better grasps the complexities embedded in the discipline of
calculus
“He who can digest a second or third fluxion, a second or third difference, need
not, methinks, be squeamish about any point in divinity.” Bishop George
Berkeley
II. Explore the mysteries of mathematics
-
There are many complex corners of mathematics that will continue to confuse and
challenge the finite human mind
Unbelief responds in one of two ways:
1. Denies the existence of any mystical aspect to mathematics
2. Acknowledges the unknown but believes that as man evolves he will be able to
rationally solve all mathematical dilemmas
- The believer does not ignore mysteries of mathematics nor do they not make an
effort to attain a rational understanding
o But ultimately the Christian does understand that in creating the world
God left his unfathomable fingerprints and finite man will not ever be
able to understand all the ways of God
- Connect this lack of understanding with the only solution of an infinite God
“Oh, the depth of the riches both of the wisdom and knowledge of God! How
unsearchable are His judgments and unfathomable His ways!” – Romans 11:33
- The more we learn in the arena of mathematics, the more we find out how much
we truly don’t know.
- I suggest that the Christian math teacher should not avoid the mysteries of
mathematics but ignite the curiosity of the student and help them confront the
limits of human knowledge
“Great is our Lord, and abundant in power; his understanding is beyond
measure.” – Psalm 147:5
a. Mystery of Infinity
-
Whenever mathematics approaches the concept of infinity, things begin to get a
little fuzzy.
Set theory, originally investigated by Georg Cantor, seeks to study the nature and
behavior of various sets of numbers.
One attractive area within set theory is comparing sets of infinite numbers.
-
-
-
-
-
-
-
-
There is much to say but I just want to share a great illustration given in David Foster
Wallace’s book Everything and More: A Compact History of Infinity.
The big question; is the number of points between 0 and 1 equal to the infinite
points on the real number line?
o Contrary to the most basic sense of logic, the answer is YES!
o Let’s look at the illustration given by Wallace to see how this can be
shown
To start, our goal is to set up a one-to-one correspondence between the points on
the real number line and the points between 0 and 1.
For example, if we wanted to know if the number of people in a classroom was
equal to the number of desks, we would simply ask all people to find a desk to sit
in.
If when everyone was seated, there were no empty desks nor any people without a
desk we would consider the “set” of people in the room equal to the “set” of desks
in the room.
Using this analogy, if the points between 0 and 1 are seats, we are trying to find one
seat for every single real number on the real number line. That is a lot of seats!
Let’s see how the illustration proves this bizarre truth. We begin by taking the
portion of the real number line between 0 and 1 and raising it above the number
line as illustrated below.
We describe a circle about the middle point (1/2) of segment AB.
Let’s now start picking points on the real number line and finding “seats” for them
between 0 and 1. Let’s begin with 1/4. We join ¼ to the center point of AB. Where
this blue line intersects the circle, we draw a line (green) perpendicular to AB. Thus,
¼ has found its seat in the 0 to 1 classroom at p1.
We proceed by taking a second point at 2. We follow the same process as before
connecting this point to the center of the circle. Where the second blue line
intersects the circle we draw a second green line perpendicular to AB. Thus, 2 has
its corresponding “seat” at p2.
Hopefully the light bulb is going off at this moment. We pick a third point at -3 to
find its corresponding point at p3. Our fourth point will be -1,000,000 which has its
corresponding point at p4. As you can see, we can continue this ad infinitum to
show that every real number has a seat in the 0 to 1 classroom (a one-to-one
correspondence).
Thus, the number of points on the real number line is equal to the number of points
between 0 and 1. Such an assertion seems like saying the length of my house (not
very long) is equal to the distance from the earth to the Alpha Centauri star system.
Sounds like good fodder for Zeno’s dichotomy paradox. At this point, one might
conclude that all infinite sets, by similar reasoning, would be equal to one another
but this is not correct. Such exercises should direct the student towards humility
and reverence to the great God of Creation.
b. Mystery of Numbers
-
-
-
-
-
There are an infinite supply of curiosities with numbers including the wonders of:
Prime Numbers
Fibonnaci Sequence
Perfect Numbers
Amicable Numbers
I thought it would be interesting to take a look at what is caked Euler’s Identity as
we look at the mysterious nature of numbers
Euler’s identity is the following
What is so significant about Euler’s Identity?
o There is probably no better illustration of mathematical beauty (would be
appropriately placed in my point number 4)
o What is so beautiful about this identity?
 Contains three fundamental operations of addition, multiplication
and exponentiation
 It also possesses the five greatest mathematical constants: 0, 1, e, i
and π
o A poll of readers conducted by the Mathematical Intelligencer awarded
Euler’s Identity the most beautiful theorem in mathematics
Carl Gauss reportedly said that if a student did not immediately grasp the equation
when looking upon it, he would not be able to become a first class mathematician…
me!!
A 19th century mathematician and Harvard Professor, Benjamin Peirce, proved the
theorem in a lecture and then noted the following:
"It is absolutely paradoxical; we cannot understand it, and we don't know what
it means, but we have proved it, and therefore we know it must be the truth."
The question is “Why Christian worldview in math class?” Many Christian math
teachers might think, sure it is necessary in Bible or History but math is math
o Our modern Christian culture has bought into this destructive distinction
between the sacred and secular
o Francis Schaeffer relates it to two stories in a house…. Where in the bottom
story is the realm of reason, science and mathematics… if you want to think
of spiritual things you must climb the stairs to the second story, go to
church, Bible class, but this is to be done outside of the public square and
definitely not in any scientific capacity
o Students fragment their lives believing that only a small portion of their
daily life has any relationship to their identity in Christ
o We aim to train our students to recognize that they are to understand all
things, history and mathematics through a Biblical perspective
o
-
Think of going into an art museum enjoying a magnificent piece of art and
then denying an artist created it…
o In math class, we observe things like Euler’s identity and recognize the
remarkable order and harmony of such an equation which points us to a
Creator
Take your students on number journeys where the ultimate goal is to create wonder
in the minds of the student, to spark their curiosity and then connect it to the
unfathomable ways of the God in which we believe
III. Help students see math as a quest to find the order and harmony of God in nature
“For since the creation of the world His invisible attributes, His eternal power and
divine nature, have been clearly seen, being understood through what has been
made, so that they are without excuse.” – Romans 1:20
-
The explorations in math give us a greater understanding of the nature of God
I want to look at two illustrations where we see a discovery of the order and
harmony of God in nature.
a. Pythagoras and Musical Harmony
-
The first was by Pythagoras, an unbeliever, who still believed the world to have
been created in an orderly fashion with mathematics at its foundation.
o Legend has it that one day on his way to work, Pythagoras was passing a
blacksmith when he heard beautiful and harmonious sounds coming from
the anvils being used by the blacksmith.
o He was convinced that there was a scientific law creating such harmonious
sounds.
o He investigated the anvils and found out that harmonious sounds were
created by hammers that were simple ratios or fractions of each other.
o Thus, the hammer that was ½ another or 2/3 would create a harmonious
sound while a hammer that was not a simple ratio of the other would create
disharmony.
o Why is the world designed like this? Why the order? Why the beauty? This
is the question before unbelief…
o In his book Why Beauty is Truth, secular mathematician Ian Stewart says the
following in response to the order and harmony of the world…
“Why does the universe seem to be so mathematical? Various answers
have been proposed, but I find none of them very convincing. The
symmetrical relation between mathematical ideas and the physical
world, like the symmetry between our sense of beauty and the most
profoundly important mathematical forms, is a deep and possibly
o
o
unsolvable mystery. None of us can say why beauty is truth, and truth
beauty. We can only contemplate the infinite complexity of the
relationship.” – Ian Stewart
None can say… there is no answer according to Stewart
I argue against this notion and provide the answer that the infinite and
beautiful God of order leaves his fingerprints on the world
b. Kepler and his Three Laws of Planetary Motion
-
-
-
-
In the second illustration we see how a scientist explored the laws of nature in an
effort to learn more about the Creator is in the man Johannes Kepler.
Kepler, lived from (1571-1630), and is best known for his work as an astronomer .
I want to guess that if Kepler had a favorite Bible verse it was:
“The heavens declare the glory of God, and the sky above proclaims his
handiwork.” – Psalm 19:1
Kepler believed the world was designed by God in accordance with a mathematical
plan. In similar fashion to Psalm 19:1, Kepler said;
“Thus God himself was too kind to remain idle, and began to play the game of
signatures, signifying his likeness into the world; therefore I chance to think that
all nature and the graceful sky are symbolized in the art of geometry.” - Kepler
It was the relentless goal of Kepler to find these signatures. One of these signatures
he postulated was that the orbits of the six known planets of the time had a
relationship to the 5 Platonic solids (the cube, tetrahedron, etc.)
o After great efforts to make this connection, Kepler abandoned the effort
seeing that the data did not match his hypotheses
However, Kepler continued in his quest to discover God’s handwriting on the
universe and did so in his most famous contribution to astronomy with his three
laws of planetary motion.
1. The first law was revolutionary. It confirmed the Copernican idea that the
Earth revolved around the sun but departed from Copernicus and rightly
stated that the Earth does not rotate in a circle but in an ellipse.
 Both Ptolemy and Copernicus resorted to what are called epicycles
to explain a certain “unexplainable” phenomena that was seen
 Kepler, convinced their was a more beautiful answer to the
question, abandoned the idea of epicycles and this directed him to
the idea of ellipses which was true
 He also noted in the first law that the Sun was at one “focus” of the
elliptical paths and the other point is merely a mathematical point
with nothing there
-
2. His second law also departed from a long held belief in constant velocities of
the planets when Kepler stated that Earth revolved on an ellipse but at
varying velocities.
 Faster when nearer to the sun and slower as the Earth went away
from the Sun.
 Included in his second law is the understanding that the area of
sectors covered by the Earth were equal for equal time periods. See
illustration.
 This finding overjoyed Kepler and reaffirmed his belief that God had
used mathematical principles to design the universe.
3. Kepler’s third law states that T2 = kD3 in other words “the period of
revolution squared is equal to the product of a constant (same for all
planets) and the cube of a planet’s mean distance from the sun”
 After stating this Third Law in his book The Harmony of the World,
Kepler broke forth in praise of God saying (picture one of your
students saying this after successfully find the roots of a quadratic
equation);
“Sun, moon, and planets glorify Him in your ineffable language!
Celestial harmonies, all ye who comprehend His marvelous
works, praise Him. And thou, my soul, praise thy Creator! It is
Him and in Him that all exists. That which we know best is
comprised in Him, as well as in our vain science.” – Kepler
I want to encourage little Kepler’s in the classroom seeking truth and beauty
knowing that harmony exists in the Universe because they know God has created it
according to His nature. His nature being that of truth, beauty, harmony and order.
IV. Instill a passion for truth, beauty and goodness in our students
a. Value of finding truth in every discipline
-
-
All truth is God’s truth and worthy of pursuit by all
o “Great are the works of the LORD, studied by all who delight in them.” Psalm 111:2
the emphasis today in our schools is on vocational training
in the coming months, the presidential candidates will discuss why education is so
important
o the number one reason they will give is a pragmatic work force type of
answer
o “If we want to compete in the 21st century global economy we need
students that excel in mathematics…” keep the machine going
o
-
-
I remember asking when I was in school… asking my teachers… “what’s the
purpose of it all?” (I was that kid) And the only reasons provided to me
were pragmatic, job oriented, college, pass the class… supremely
unsatisfying answers
o another brick in the wall
I am not opposed to helping train my students to be a great engineer, architect or
actuary but this is not the purpose or end goal of my job as a math teacher
I am teaching them truth of God’s world as He has created it
I don’t think it helps our students as Christians to train them to think their
motivation in the math class is to get a good grade, which gets them into a good
college which gets them a good job which makes them a lot of money which inherits
them a great retirement playing lots of golf
We want to create life long learners that love to learn… enjoy learning about God’s
world through the discipline of mathematics
b. Seeking truth and beauty regardless of its practical use
-
Students need to see the value in finding truth without regard for its practical use
o The great Greek mathematician Euclid, when asked by a student the
purpose for what he was learning looked at his slave and said
“Give the boy a penny since he desires to profit from all that he learns.”
o Euclid is saying, truth is worth learning regardless of what it profits you.
o We should seek to eliminate, as best we can, the “why do I need to learn
this?” attitude in the math class.
o We should long to find the source of beauty, the source of truth, the source
of goodness….
"It was when I was happiest that I longed most...The sweetest thing in
all my life has been the longing...to find the place where all the beauty
came from." – C.S. Lewis
c. Gauss and the Heptadecagon
-
Greek mathematicians were absorbed in a variety of geometrical pursuits
o Central to their understanding of mathematics was using only a straight
edge and compass for their constructions
o The Greeks, as exemplified in Euclid and his Elements took special interest in
constructing regular polygons (among other constructions
o They were able to complete constructions for regular polygons with sides
 3, 4, 5, 6, 8, 10, 12, 15, 16, 20
o we know today that the following cannot be constructed
 7, 9, 11, 13, 14, 18, 19
o
-
-
-
what is missing between 3 and 20?
 17-gon or the heptadecagon
between the Greeks before Christ and March 30, 1796, no real progress had been
made in determining the constructability of the 17-gon
o enter stage right, the brilliant Carl Gauss
o Carl Gauss, at the age of 19, found a Euclidean construction for the regular
heptadecagon
o The brilliant part is he was able to determine its constructability without
ever actually constructing it with a straight edge and compass
Its constructability is based on two properties of the number 17
1. Prime #
2. One greater than a power of 2… 2n + 1
o These numbers are known as Fermat Primes as he was the first to
investigate them
o The only known Fermat primes are 3, 5, 17, 257 and 65,537
o Whether there are more is yet to be proven
o But if they do exist, the next Fermat Prime is at least 233,554,432 + 1
Gauss’s proof is based on the fact that the solutions of the equation x17 – 1 = 0 form
the vertices of a regular 17-gon in the complex plane
o One obvious root is x = 1, the other 16 are roots of a polynomial of degree
16 which can be shown to be x16 + x15 + x14 + … x2 + x + 1 = 0
o a series of quadratic equations can be solved at this point because 16 is a
power of 2
o Although he did not describe how to construct the 17-gon, he did determine
that the main point is to construct a line of length
o
o
-
-
-
What beauty!
Being square roots are always constructible, we can conclude with out ever
picking up compass and straight edge that the heptadecagon is
constructible
In 1832, F.J. Richelot published papers explaining the constructability of the 257-gon
o The title was “De resolutione algebraica aequationis x257 = 1 sive divisione
circuli per bisectionem anguli septies repetitam in partes 257 inter se
aequales commentatio coronata.”
In 1894, J. Hermes of the U. of Lintgen devoted 10 years to the construction of the
65,537-gon
o His unpublished work is preserved at the U. of Gottingen
o Present day mathematician John Conway, maybe the only one to have ever
looked at the papers, doubts that it is correct
Is this beautiful like a Monet painting? No.
-
Beauty can be attributed to many different areas
It is a balance or harmony within nature… the idea of symmetry is often connected
to the idea of beauty
That Gauss was able to determine the constructability of such an elegant polygon
using the rules of mathematics is in my opinion both true and beautiful
d. The place of goodness in the math class
-
Mathematics is an effective tool for accomplishing good in the world
In essence it gives man a very practical means to love his neighbor
Mathematics applies in the world and allows man to generate technologies improve
our life, these technologies are able to bring much good in the world
I spend little time here because we can easily see the application of this as new
technologies, developed upon a foundation of our increased understanding of
mathematics, spread around the world
V. Teach students that math class is an important training ground for the mind
“And do not be conformed to this world, but be transformed by the renewing of
your mind, so that you may prove what the will of God is, that which is good an
acceptable and perfect.” – Romans 12:2
-
I have had many a student argue to the nth degree why math is worthless yet I still
have yet to hear a student argue that thinking is a worthless endeavor
Not a single student of mine has ever expressed a sincere desire for ignorance
Mathematics is mental weight lifting preparing them mentally for every area of life
a. Teaching students to be patient Christian problem solvers
-
We are teaching them to be Christian problem solvers in the math class
Do not allow your students to think the problem solving in the math class does not
apply to other areas of their life
b. Problem solving in the math class applies to every area of life
-
The student that creatively finds solutions in the math class will be the same
creative problem solver in family disputes, the same person that finds a solution to a
business dilemma, that finds a creative method to finding justice in the court room,
that brings peace to a church in turmoil… The determination, the will to find a
solution that a teacher can cultivate in a classroom can not help but over flow into
other areas of the student’s life
-
-
-
I still have a hard time understanding how a student can fail at understanding how
to develop a proof in the geometry class yet develop a strong logical argument in an
English paper.
Even Lincoln understood the value benefits of mathematical reasoning skills when
he said in an autobiographical sketch the following;
“I said, “Lincoln, you can never make a lawyer if you do not understand what
demonstrate means”; and I left my situation in Springfield, went home to my
father’s house, and stayed there till I could give any proposition in the six books
of Euclid at sight. I then found out what “demonstrate” means, and went back
to my law studies.” – Abraham Lincoln
The first six books of the Elements contain 173 propositions, it’s hard to believe but
who would doubt honest Abe
Mastery in the math classroom can only help our students in whatever area they
will venture in the future.
Conclusion
-
“Mathematics is the language in which God has written the universe.” - Galileo
Mathematics is understanding in greater detail the handiwork of God. It is learning
how our Lord has created all things.
We can help our students find the Christian God in the math class if we can
1) Emphasize the presuppositional aspect of math
2) Explore the mysteries of mathematics
3) Help students see math as a quest to find the order and harmony of God in
nature
4) Instill a passion for truth, beauty and goodness in our students
5) Teach students that math class is an important training ground for the mind
Resources
Dunham, William. Journey Through Genius. John Wiley & Sons, Inc. 1990.
Dunham, William. The Mathematical Universe. John Wiley & Sons, Inc. 1997.
Kline, Morris. Mathematics and the Search for Knowledge. New York: Oxford University
Press, 1985.
Nickel, James. Mathematics: Is God Silent. Ross House Books, 2001.
Seife, Charles. Zero: The Biography of a Dangerous Idea. Penguin Books, 2000.
Singh, Simon. Fermat’s Enigma. Walker Publishing Company, 1997.
Stewart, Ian. Why Beauty is Truth. Basic Books. 2007.