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MY TESTIMONY IN RELATION TO MY SCHOLARSHIP

INTRODUCTION

Regarding my testimony and its interaction with my professional life, I will present three major segments. First, I will give my personal testimony of the gospel of Jesus Christ—essentially why I believe what I believe. The second segment details how my experiences as a teacher are related to my testimony. Finally, the last segment is an argument against those who believe that science can disprove religious beliefs.

MY PERSONAL TESTIMONY OF THE GOSPEL OF JESUS CHRIST

My testimony is simple. I know that there is a supreme being, a God, or our Heavenly Father. I know that his son, Jesus Christ, is the Savior of the world. I know that his Atonement happened and is vital for each of us. The Atonement is a comprehensive word for his suffering in the Garden of Gethsemane and on the cross and his subsequent resurrection. This Atonement is the key to our overcoming physical death and overcoming the spiritual death or our own separation from God due to our choices, attitudes, and actions. These two barriers that keep us from God are impenetrable for each of us without the Savior. I know that God is the same yesterday, today, and tomorrow. I know that, as in ages past, He has spoken and speaks to men in our days. One such man was the Prophet Joseph Smith. Another such man is a current prophet, a man named Thomas S. Monson. I know that both of these men are prophets of God. I also know that both the Bible and the Book of Mormon are true scriptures written by other prophets of God throughout the ages. Knowing that Joseph Smith and Thomas S. Monson are prophets also lets me know that the Church of Jesus Christ of Latter Day Saints is indeed God’s church on earth. Two very natural questions arising from these statements are “How do you know these things?” and “How can you be sure?”

HOW I KNOW

The answer here is also simple, but many, I fear, will look beyond the mark or think that it’s just too simple. However, just as in mathematics, the more simple the solution, often the more elegant and profound it really is. In religious matters too, the more simple the answers, the more profound they often really are. I took only a few simple steps which have led me to this knowledge. These steps are (1) faith, (2) prayer, (3) listening, (4) living it, and finally (5) observing.

Several years ago, I realized I had a desire to find out more about God and religion. At that point I had (1) faith in a supreme being. This belief was almost a decision, but also it was a feeling. Looking back now, I know it was based on faith. I felt that there was a God. I had learned that if one prayed to God (see James 1:5 or, in the Book of Mormon, Moroni 10:3-5) that he would answer your prayers. So when I decided to find out if Jesus Christ was the Son of God and our Savior, I (2) prayed and, when doing so, I felt calm, peace, happy, assured,… feelings that I have come to recognize as coming from the Holy Ghost (or the Spirit, see Galatians 3:5). I have had similar experiences praying about whether the Book of Mormon and the Bible were the words of God and whether Joseph Smith and Thomas S. Monson are indeed prophets of God.

I (3) listened to these feelings and believed that they were an answer from God. But more than this, I (4) started living the Christian principles taught in the scriptures and by the prophets. As I have tried to live these principles (with varying degrees of success—I am by no means perfect), I (5) observed what happened (see John 7:17). The results of my living these principles solidified my belief, and it grew to knowledge (see, in the Book of Mormon, Alma chapter 32). As I have lived the principles of the gospel of Jesus Christ taught in the Book of Mormon, in the Bible, and by modern prophets such as Thomas S. Monson and Joseph Smith, I have come to know that this gospel is the doctrine of God.

MY EXPERIENCES AS A TEACHER AND MY TESTIMONY

How have my years of teaching experience and my higher learning about education interacted with my testimony? (1) Faith is closely related to hope. Both provide a focus or an end in sight. Successful teachers know that they often need to give their students a reason for why they are learning a particular topic. When I give my students good reasons (or if they have already acquired these good reasons from other sources), they usually succeed. They (3) listen to their brain’s reasoning, saying “(4) Engage in the material,” and pretty soon they start to engage in the material. That is, they (4) start to live the principles of the discipline that the teacher is teaching. Once they engage in these principles of this discipline, they (5) begin to observe what has happened and they see the power of the discipline. These realizations strengthen their initial faith in the discipline.

For example, I teach math to future elementary teachers (some of whom struggle at math). One principle about learning mathematics is engaging in the material. If you engage in the material enough, you might fail at times but, overall, you will learn. Many students who struggle at math just give up way too soon.

I have seen students who “struggle at math” suddenly start succeeding. Why? Well, these pre-service elementary teachers already have a reason to try. They know they need to understand math to teach it effectively later. But, many doubt their ability to learn math. So their faith is shaken. Yet, time and time again I have seen these students suddenly start having success in my classes.

The key to my method is that I attack their belief that they can’t succeed. When they start having (1) hope and faith that they can succeed, good things happen. Based on this hope and faith, (3) they begin to believe in themselves just enough to (4) actually start studying differently. Now, with this new attitude, when they miss a part here and there, they (4) start sticking to it, they persevere rather than give up. The eventual result is . . . learning mathematics. As my students start having success, they (5) observe what is happening and are shocked. Their whole mindset of how they think of themselves and mathematics has been fundamentally shifted. Now they realize that they can learn mathematics. Their faith and hope has been made sure and solidified. Faith and hope have morphed into knowledge and confidence. Of course, what often happens in these situations is that these students also start to like mathematics. That is, they begin to see the power that mathematics has in changing their power of reasoning (the essence of mathematics’ power).

A quick side note about education and the gospel.

Another aspect about gospel of Jesus Christ that I have learned over the years, which has been influenced by my educational training, is the importance of the simplicity of the gospel. In education, and in mathematics too, the simpler solutions are the most powerful and when you get down to it, they are the most elegant. Consider these quotes from famous mathematicians.

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. S. Gudder

You know that I write slowly. This is chiefly because I am never satisfied until
I have said as much as possible in a few words, and writing briefly takes far more time than writing at length. Carl Friedrich Gauss

As an educator, I am constantly revamping my lessons to try to deliver the content in a more compact, efficient manner. I am continuously seeking for better ways to teach the concepts. Of course, many of the concepts are complicated, but only until they are understood. Then the simplicity stares out at you and you wonder, “Why didn’t I see that before?” Many times the simplest concepts, once understood, are immensely powerful. They are applicable to many different situations and problems.

Similarly, as I’ve studied the gospel and understood it more and more, I see that it is based on simple principles and standards. They are easy to understand but powerful. In religious aspects, many adults look beyond the mark. We see the simplicity of the gospel and think that we want to see the mysteries of the gospel. We hear a “do this” or “don’t do that” and think “that’s too easy”. We act like Naaman (see 2nd Kings chapter 5). But our Heavenly Father’s gospel is not one of complexity; it is one of simplicity and one of power. “God would indeed be unjust if the gospel were only accessible to an intellectual elite. In His goodness, He has ensured that the truths regarding God are understandable to all His children, whatever their level of education or intellectual faculty.” (Gérald Caussé, “Even a Child Can Understand,” Ensign, Nov 2008, 32–34). Remember, who is greatest in the kingdom of heaven? (See Matthew 18:1, 2-4). For example, consider the power of the very simple concept called faith. It’s a simple concept once understood, but the power of it is huge. Faith can and has moved mountains. I know that it has moved me closer to God and helped make me a better person.

MATHEMATICS AND SCIENTIFIC ARGUMENTS AGAINST GOD

Many claim that truths or well-established theories from science, such as evolution or the increasing understanding of the universe, can disprove that God exists or other issues of religion. As a mathematician, I reject this notion wholeheartedly. On the contrary, I can use what I know of mathematics, one of the necessary bases of all science itself, to prove that this approach is a fallacy. So let me back up this bold claim.

All of mathematics is based on assumptions. This may be a surprise to those who have only common understandings of mathematics, but it is nonetheless true. Ask a mathematician if you don’t believe me. Geometry is a typical part of mathematics where one comes face to face with such assumptions. Postulates are mathematical words for assumptions. The five postulates of Euclid (and the subsequent work by the nineteenth- and twentieth-century geometers to fix them) are a fascinating part of the history of mathematics related to the interplay between assumptions and mathematics. For example, one of Euclid’s base assumptions is logically equivalent to making this statement: “Parallel lines exist.” This seems like a pretty safe statement to make. After all, we all believe this is true. “They must exist. Don’t they?” This is an understandable reaction.

Euclid wanted to make Geometry to be based on as few postulates as possible. He generally succeeded in only using five assumptions. His fifth postulate was one that dealt with parallel lines. While this seems like a nice assumption to make (that parallel lines exist), Euclid was quite disturbed by it and tried unsuccessfully to avoid using it. For hundreds of years after Euclid, mathematicians tried and failed to prove that the fifth postulate was a result of the first four postulates and sheer logic. Finally it was proven that it was impossible to avoid using this fifth postulate.

The average person would still say, “What is the big deal? After all, I can see parallel lines. I understand the concept. I know they exist.” But, unfortunately (or, rather, fortunately, since it leads to my big result), this unwavering faith in the existence of parallel lines is questionable. What is the definition of a parallel line? One definition states that parallel lines are two lines that never intersect. However, can you really draw two such lines? How would you know they won’t ever intersect? Consider two such lines, drawn on the ground outside your house. They are drawn so that they look parallel:

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Yet, if these lines continue on the earth, they will eventually meet! How? Well, if they were longitude lines, they would meet at the North Pole, for instance! Other lines would similarly meet at some point on the earth. Perhaps space is curved too (after all Einstein believed it was). Perhaps even space is really nothing but a huge sphere. In other words, perhaps our universe is nothing but a giant sphere and a pair of lines drawn on its surface might meet at its North Pole equivalent. Other lines drawn inside might even hit the boundary and bend and then meet at the “North Pole”. All lines would meet somewhere!

Why does this matter? When mathematicians realized that that the fifth postulate might indeed be false they started looking at “What if Euclid was wrong” situations. They decided to investigate

(a) Are all the postulates there? Do more exist?

and

(b) What would happen if they assumed any of these postulates were false?

During part (b), for example, they assumed parallel lines didn’t exist and then used sheer logic to investigate what sort of theorems and Geometry emerged. They did this with all five Euclidean postulates and all the combinations of the five postulates (in yes-and-no form). This ends up being 5! or (5x4x3x2x1) or 120 different possible Geometries, only one of which is the Geometry taught and understood as true in high school. What happened? Well, several of the Geometries were complete nonsense, not fitting what we could observe in the real world. Some however, weren’t. In fact, some of the non-Euclidean geometries were internally consistent (coming from careful logic based on the assumptions) and at the same time fit many of our regular world observations. That is, some non-Euclidean Geometries actually seemed to fit the world and might be not only logically valid, but better than what we’ve assumed is the best approach for over three thousand years.

These investigations led mathematicians to a dilemma. These Geometries are logically opposites of each other in the sense that one Geometry might say that Euclid’s third postulate is true, whereas another Geometry may say it is false. Yet other than that one contradiction, the rest of each Geometry could have identical assumptions. These Geometries might end up with different theorems, but because the postulates are assumptions one could never know which Geometry is “true.” That is, belief in a particular Geometry—like, say, the one we usually teach and understand—is based on (1) faith.

Mathematicians cannot tell which of the one hundred and twenty Geometries is true. In a very real sense, all of them are valid. They are all just logical results of the initial assumptions. The famous mathematician Henri Poincare put it this way, “Geometry is not true… it’s advantageous.” So we use the Euclidean Geometry that we use today, not because it will lead us to true conclusions necessarily, but because it seems to work pretty well. We’ve (3) listened to its claims, and (4) lived using it and (5) observed what happened. Since this Geometry has worked out well, we’ve stuck with it.

The moral of this is that mathematicians have to operate on faith to a much greater extent than most people realize. That is, the very foundation of the Geometry accepted by most people is mathematics based on faith. And it is a somewhat shaky faith at that (since it’s possible that one of the other one hundred and twenty Geometries is really the best one or the true one for our world).

This scenario is even more startling in arithmetic. After their successful attempts to uncover all of the Geometry postulates (there were actually more than five postulates eventually found, and thus even more than one hundred and twenty possible Geometries), several other mathematicians tried to uncover the postulates of Arithmetic. This proved to be an extremely challenging task. Several mathematicians and logicians attempted and failed to come up with a good set of postulates. When one group would announce they had finally done it, within a few years, a huge hole in logic would be found and the hunt would begin again.

Then in the 1930s the mathematics world was shocked by the results of one Dr. Gödel. He found the following stunning result: Any set of postulates complex enough to give birth to Arithmetic would either be infinite, or it would have a contradiction built into the postulate system. This was an amazing result! Not only would mathematicians have to trust some statements, they would have to trust an infinite number of statements on sheer faith in order to logically set up the basic Arithmetic that we teach in grade school. It is possible that our understanding of Arithmetic is like Geometry, in the sense that some of these postulates that we intuitively think are true (like the parallel one) might indeed be false. That is, it is possible that an entirely different way of understanding even basic Arithmetic at a very core level is true and what we are doing is actually just false.

The results of all this, to my mind, can be summed up in a few statements. (1) All of science is based to some extent on mathematics—imagine doing science without ever using Arithmetic or Geometry. (2) Our understanding of mathematics is itself based on faith (postulates) and there is substantial reason to at least question whether the postulates we have accepted are even correct, so (3) people who base their disbelief on God on the conclusions of science are basing their disbelief of faith on . . . faith.

CONCLUSION

In conclusion, as I have studied educational theory and mathematics, I have learned how to take ideas apart and look for contradictions in logic. As one does this, one either finds a flaw in the reasoning (a flaw in logic) or eventually gets down to the base assumptions. These base assumptions are undeniably true or not. One must either accept them based on faith, or reject them, also based on faith. In studying the religious ideas of the Church of Jesus Christ of Latter-day Saints, I have similarly taken the ideas apart as I have learned them. While doing so I have never found any contradictions in logic. On the contrary, I have found the simple teachings to be valid and consistent. The crux of my belief is whether I believe the base assumptions: That God and His Son Jesus Christ and the Holy Ghost live, that they speak to prophets today as in times past, that the Bible and Book of Mormon are the word of God. When I have put to the test the promises (see James 1:5 or, in the Book of Mormon, Moroni 10:3-5) found in the Bible and Book of Mormon and started with (1) some faith, (2) prayed for more answers and guidance, (3) listened to the answers that I recognized as coming from God, (4) lived the principles taught to me in these answers and the scriptures, and then (5) observed the results, my faith has become knowledge. I know that God lives. I know his Son is our Savior. I know that the Church has been restored. It is the Church of Jesus Christ of Latter-day Saints and is led by a living prophet, Thomas S. Monson. I know the Book of Mormon and the Bible are the words of God. For the skeptics who are reading, don’t think that this method to spiritual knowledge is too easy. When you get down to it, it is very similar to the method which has been used by teachers and mathematicians for centuries to discover truth. If you do doubt, put your doubts aside for a bit and try. Be like Naaman; give up a bit. Have faith, pray, listen, live, and observe.

Sincerely,

Your brother in Christ,

Michael Matthews

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I am Dr. Michael Matthews, a mathematician/mathematics educator at a large, urban, Midwestern university. After graduating from Brigham Young University in 1997 with a Bachelor of Arts in Mathematics and a teaching certificate, I taught mathematics at a treatment facility for adjudicated youth from 1997-2003. During this time, I acquired a Master of Science in Secondary Education at the University of Nevada. After this, I pursued a Ph.D. full time at the University of Iowa. I received a second Master’s degree in Mathematics while there, and my Ph.D. in Mathematics Education in 2006, after which I acquired my current position at the University of Nebraska at Omaha. I have published some theoretical research articles in teaching and learning mathematics and also some practitioner articles (written for a current-teacher audience instead of fellow researchers). My research focuses are improving content knowledge of pre-service elementary teachers, using Lesson Study in teaching, and appropriate integration of technology in mathematics teaching and learning.

Posted August 2010