Math & Computer Science
http://calledtoscience.org/math-and-cs
enJeffrey Wheeler, PhD, Mathematician
http://calledtoscience.org/node/50
<span class="field field--name-title field--type-string field--label-hidden">Jeffrey Wheeler, PhD, Mathematician</span>
<div class="field field--name-field-profile-portrait field--type-image field--label-hidden field__item"> <img src="http://calledtoscience.org/sites/default/files/styles/medium/public/2018-12/Screen%20Shot%202018-12-02%20at%209.49.26%20PM.png?itok=uz2ENrtg" width="206" height="220" alt="Dr. Wheeler and his wife looking super" typeof="foaf:Image" class="image-style-medium" /></div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="http://calledtoscience.org/user/3" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">curator</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Mon, 12/03/2018 - 12:36</span>
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<div class="field__item">jwheeler@pitt.edu</div>
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<div class="field__label">Discipline</div>
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<div class="field__item"><a href="http://calledtoscience.org/math-and-cs" hreflang="en">Math & Computer Science</a></div>
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<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><ul><li><img alt="Professor Wheeler interacting with Creation and non-linear wave behavior" data-entity-type="file" data-entity-uuid="71788954-29a1-4064-a26c-b9e472c9350a" src="http://calledtoscience.org/sites/default/files/inline-images/Screen%20Shot%202018-12-02%20at%209.53.38%20PM.png" class="align-right" />PhD in Mathematics, University of Memphis</li>
<li>Mathematics Faculty, University of Pittsburgh</li>
<li>Reviewer for the American Mathematics Society</li>
<li>Serves as high school outreach</li>
</ul><p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>I grew up in Wheeling, WV and was fortunate enough to have parents that were willing to sacrifice to send me to a private school. In high school at Linsly, I was one of ten members on the Math Team. We did well in state competitions and my senior year seven of the state’s ten representatives to the national competition were from Linsly, one of them a junior, and none of them me. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>I then went to Miami University in Oxford, Ohio and after three lectures decided I wasn’t cut out for architecture. I’m pretty sure I was a Physics major next, but I don’t remember. What I do remember is that during the second semester my sophomore year I noticed that I only needed four math classes over my last two years to get a math degree, so I declared a math major, took lots of history, philosophy, and religion courses, and earned a minor in social work. Though I wanted to save the world, the only job I could find after graduating was teaching developmental math courses at a local technical college. I loved my work, but the school would not hire me without a graduate degree, so I got myself accepted into a religion PhD program one year and didn’t go, then a history PhD program the next year, and didn’t go, then for good measure another history PhD program the following year, but still didn’t go. Finally, I got into Miami’s graduate math program and this time went, but mostly did that so I could take history classes and go to history talks. They were great, but didn’t help me in my math classes, and the Math Department was paying my bills. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span> I left Miami math because it didn’t have a PhD program to go to the University of Tennesse, Knoxville, then left UT to go to Memphis because my wife got a job at FedEx. At UT, I was in hoping to do a dissertation in algebraic number theory, but ended up leaving writing a master’s thesis in the subject on the abc Conjecture. At Memphis, the one algebraic number theorist in the department agreed to take me as his first student, but then told me we were doing Combinatorics and not Number Theory. That was at the time disappointing because I had taken many algebra and number theory courses, but only one Combinatorics course (It now seems strange that as a fledgling number theorist I was disappointed being asked to consider a subject area primarily concerned with counting… ok, coloring is also involved, but I wasn’t sophisticated enough at that time to see it).</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
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<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>C.S. Lewis wrote it so very well; so I quote the master.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>“Look at the universe we live in. By far the greatest part of it consists of empty space, completely dark and unimaginably cold. The bodies which move in this space are so few and so small in comparison with the space itself that even if every one of them were known to be crowded as full as it could hold with perfectly happy creatures, it would still be difficult to believe that life and happiness were more than a by-product to the power that made the universe.”</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>This absence of meaning troubled me greatly as a youth and though Mathematics does not provide answers to such problems, Mathematics is a spiritual-type of experience for me and in my eyes is a concrete example of a higher power. Mathematics does not obey the scientific method; nor do we search for mathematical truths in nature. She exists outside the physical world but yet the physical world is subject to her authority.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>This meta-meaning to Mathematics is not what motivated me to be her disciple, but yet I believe that in dancing with this fairest of maidens I subconsciously received psychological satisfaction to my troubling adolescent existential concerns. What drew me to Mathematics – and continues to draw me – is her beauty. Using Liouville’s Theorem from Complex Analysis to prove the Fundamental Theorem of Algebra (which, as the joke goes, is neither fundamental nor algebraic); Euler’s Formula and the particular case eiπ+ 1 = 0; the brilliance and technique of Galois; the simplicity of the statement of Fermat’s Last Theorem compared with the incredible effort it took to prove it; that Linear Programming over a bounded feasible region is infinitely simpler to solve over the real numbers (infinitely many possibilities) than when we restrict our answers to the integers (only finitely many possibilities); … this list can go on.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Doing Mathematics is sometimes like mining coal: it’s dirty and it’s rough. But then the light comes on and you find yourself standing in the most beautiful of art galleries.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
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Mon, 03 Dec 2018 17:36:50 +0000curator50 at http://calledtoscience.orgClaire Graber, BS, Mathematics Graduate
http://calledtoscience.org/node/20
<span class="field field--name-title field--type-string field--label-hidden">Claire Graber, BS, Mathematics Graduate</span>
<div class="field field--name-field-profile-portrait field--type-image field--label-hidden field__item"> <img src="http://calledtoscience.org/sites/default/files/styles/medium/public/2018-11/ClaireG.png?itok=zongab2z" width="220" height="146" alt="Mathematician Graber working on a problem" typeof="foaf:Image" class="image-style-medium" /></div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="http://calledtoscience.org/user/3" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">curator</span></span>
<span class="field field--name-created field--type-created field--label-hidden">Fri, 11/02/2018 - 21:05</span>
<div class="field field--name-field-profile-discipline field--type-entity-reference field--label-above field--entity-reference-target-type-taxonomy-term clearfix">
<div class="field__label">Discipline</div>
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<div class="field__item"><a href="http://calledtoscience.org/math-and-cs" hreflang="en">Math & Computer Science</a></div>
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<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><ul><li><span><span><span><span><span><span><span>Graduated from Wheaton College with a B.S. in Mathematics and a minor in Geology</span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><span><span>REU student researcher at Lamont-Doherty Earth Observatory of Columbia University (summer 2016)</span></span></span></span></span></span></span></li>
<li><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Just graduated college</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></li>
</ul><p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>My parents are missionaries in the country of Vanuatu, South Pacific. Although I was not directly involved in the two New Testament translations they worked on, I grew up steeped in theological discussions (and sometimes linguistic puzzles that went right over my head). While at Wheaton, I attended and eventually became a member of Bethel Presbyterian Church, which became my church home.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>I was never the sort to really settle on one particular realm of interest. In many ways, I’m the sort of person who enjoys the humanities more than the sciences, and would gladly spend most of my time reading fiction and listening to history lectures. This stems largely from the fact that I like the mystique and fluidity of no particular right answer. The irony is not lost on me that I then turned around and declared a major in Mathematics. When I began at Wheaton, I majored in physics by default. It may seem like an odd default choice, but given that my siblings had both been physics majors, it seemed natural at the time. However, like many freshmen, I quickly found out that my long-term plans for the study of solar physics were not to be: after one semester as a physics major, I decided it wasn’t quite what I wanted to study, and became a math major. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Of course, in college, one of the first questions you answer in conversation with someone new is “What’s your major?” For me, what followed was the ever-present question: “Do you want to teach?” Yes and no. I enjoy teaching, but that’s not the reason I wanted a degree in pure mathematics. What drew me in is the elegance, simplicity, and boggling infinitude of mathematics. Most people think of math majors as people who sit down and “do problems” all day. But the truth of a math major is that much of your time is spent in staring down the implications of an idea. In many ways, math is philosophy that is bounded by a very particular set of rules. There are two ways to find creative ideas: 1) Think outside the box. What limits can be pushed so that something new can be created? 2) Build a box and get in it. This is mathematics. By limiting your options, you can get somewhere interesting. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>This method of creativity leads to some extraordinary situations. For one thing, it forces everyone to acknowledge the assumptions of every argument. What kind of box have you built? What shape and dimensions did you design your box to be? What materials and methods did you use to build it? That is standard practice in mathematics. But what happens when you reach a disagreement about the assumptions? Then you have a problem! And a fun one, too.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>During my final year at Wheaton, I took a class designed and required for seniors in a mathematics major. Many people in the course were double majoring in something else, or were in athletics or student government. Most apparently had the capacity to work around the clock. I felt a little out of my league. <em>These</em>were the brilliant minds. I needn’t have worried, since everyone was encouraged to speak their mind, everyone else wanted to hear, and I was no exception. As it turns out, even the quietest of these brilliant minds can engage in heated discussion on whether or not numbers do, in fact, exist. These discussions quickly became my favorite component of the course. We all chose material to read independently and bring into discussion, but all of us read the same questions and answers on subjects related to mathematics and faith. The overarching question of the discussion throughout the semester was this: “What <em>does</em>God have to do with mathematics?” </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>At many schools, no one would even think to ask this question, but at Wheaton one of the most prevalent conversations is about the integration of faith and learning. In this discussion, I was not expecting more than an anecdotal explanation of how we can glorify God in mathematics by recognizing his infinitude reflected in the infinities we use in mathematics, or maybe a questionable representation of the Trinity using some geometric figure. I was quite surprised then, to find that there are serious theological implications of more than a few questions in mathematical philosophy. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>One of these questions was the debate which has long been held among mathematicians and which centers around the question “Do numbers exist of themselves, or do we imagine them for our own purposes?” Among a Christian community, this translates to “Did God create numbers?” The simple answers to this question, “yes” and “no” are not so simple when you press them for details. These two views are called the Platonic and Aristotelian perspectives, named (as you might guess) for Plato and Aristotle.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Before we discuss the theological implications of these views, we must acknowledge that the question itself is a little odd. The Platonists argue that numbers exist as “forms” (don’t ask me; ask a philosophy major). But what does it mean for a number to exist? The numeral ‘3’ doesn’t just float around space somewhere, and even if it did, it wouldn’t be the essence of “Threeness”. It would just be a written representation of the idea. The same goes for an instance of three objects. Supposing we have three of the most perfect spheres, all made of the same material, and of exactly the same weight. This is not three itself, but an instance of it. In that way, even though there is no variation between the three, it is no different than if we gathered three cows of different size and color and said “Look, I found three!” In both cases, it is not the idea itself which we see or imagine, but an example of it. (See, I told you math is just philosophy wrapped up in some logic.)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Here the Aristotelians have an advantage, because they don’t have to try to describe where these numbers exist. The Aristotelian point of view can even explain <em>what</em></span></span></span></span><span><span><span><span>numbers are, namely, the most logical invention of necessity. The difficulty then, lies in how people of all different cultures somehow managed to imagine and develop ideas that were, for all their different names, exactly the same. Yes, some cultures found the zero and decimal systems to be useful before others did, but everyone at least can agree that the numbers we count with are standard. No one who is trying to buy four cows will buy three and think he’s gotten the proper deal, even if the transaction happened across multiple languages and cultures. Three is three, no matter the instance, which seems to indicate the existence of the idea before it was named.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>As you can see, making a convincing and thorough argument is difficult for both groups. Most of the math majors I met at Wheaton did still fall into one camp or the other, with some bias towards the Platonists. This is where the fun began! When you have two groups of Christian nerds whose fundamental assumptions about numbers are practically opposite, you get into some intriguing discussions. The Christian Platonists argued that to say humans invented numbers by necessity was claiming that God did not create numbers, and that this was an affront to His nature as Creator. The Christian Aristotelians countered that being made in God’s image, we are creators, too, though of a different sort. To claim that we only discover the numbers and their characteristics is to discount the grueling process of mathematical development and creative efforts. And so on and so forth. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>The point is that regardless of how they viewed the origin of numbers, both camps were arguing for the sake of God’s glory in his creation: the Platonists arguing for God’s having directly created numbers as an idea, and the Aristotelians arguing for God’s having created creative genius in his image-bearers. This is one of the crucial aspects of integrating faith and learning: whatever you argue for, argue for God’s glory. </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p></div>
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Sat, 03 Nov 2018 01:05:30 +0000curator20 at http://calledtoscience.org