If you’re not planning on pursuing a so-called STEM career, do you really need to be good at math? Yes, but not just for the often-stated reason that people encounter math regularly throughout their lives. Being able to handle everyday math is certainly important. For example: If you’ve been offered varying aid packages by different universities, which one makes the most financial sense for your family? If you’re deciding between leasing or buying a car, which is the best deal in the long run? While no one doubts that being better at money arithmetic would benefit individuals and society as a whole, such specific situations require a narrow skill set.
The benefits of being good at math, however, go beyond correctly computing the tip at dinner to a wide array of circumstances that call for abilities prized in virtually every field of employment. For example, people who have learned to think mathematically are better at understanding the structure required to complete a given task. The first step in solving any math problem is sizing up the situation. What do you already know? What information is missing? Can you break the larger problem into more manageable pieces? Having both the skills and confidence to dissect complex problems, including ones that look nothing like what you’ve seen before, is one of the main benefits of becoming good at math.
People who have learned to think mathematically are also better at assembling new ideas. Once you’ve assessed the situation, broken down the problem, and gathered the necessary pieces, how do you put it all together to get from where you are to where you want to be? When faced with a novel situation, can you devise an approach where there wasn’t one before? If you’ve studied mathematics in a way that pushes you to think both logically and creatively, then you will be much better prepared to handle an ever-changing variety of circumstances that call for these skills, no matter what career you choose.
This month, IMACS chats with alumnus Daniel “Danny” Vidaud. Danny started taking IMACS math enrichment classes as an elementary school student and progressed through the introductory computer science class. He went on to earn his B.S.E. in Aerospace Engineering from the University of Michigan. Danny is currently in his third year as an engineer with Boeing.
Tell us about your current position at Boeing. What exactly do you do?
I am an aerodynamics engineer working in technology and product development. In a nut shell, I am part of the team of architects for the external shaping of future commercial jet airplanes. We spend our time sketching up new, outside-the-box ideas and bringing them to life!
What were you like as a kid? What kinds of things interested you?
I was a very intuitive child. Very not normal. Constantly absorbing as much as I could about the world around me. I had a tendency to quickly gain a functional understanding of complex ideas. The downside was that this only applied to topics I found interesting. A repetitive spelling assignment, for example, was as interesting to me as watching paint dry in an empty room with no windows. I needed to actively seek ways to challenge my inspiration or I would inevitably fall into a state of no motivation.
I enjoyed music. The piano, I found, was quite versatile at conveying a variety of musical ideas, but I hated studying it. I couldn’t stand the classical books or the structured process. The musical expression was inspiring; the structured training was not. Instead, I decided that mimicking what I heard on the radio was inspiring enough to practice for hours on end. Free improvisation and jazz composition became the new method of study.
Computer games! Fun! Not so fun when they freeze and get choppy, right? So I decided it would be interesting to develop a theory on what made a computer “fast” or “slow” and subsequently exploit that theory to help others in creating new systems or maintaining their old systems to do what they needed them to do.
Physics and all other things I found interesting went along the same lines of thought. The approach was always the same: Take a complicated problem, gain a general intuitive understanding for how it works, then generate as many permutations or original ideas as possible.
Did you know from a young age that you wanted to be an engineer?
Always. I didn’t always know it was called engineering though. I just knew that I liked asking the “Why not?” question a lot. “Why can’t we do something like this?” Challenging the normal. Being weird. It just seemed like more fun to not do what everyone else was doing.
Given that, rocket science seemed like a viable candidate. No one was doing it, everyone said it was impossible, and it seemed like it might be a good place to start if I wanted to get involved in something really complicated that may have high demand and low supply. So I turned 15, applied with a pre-declared major of Aerospace Engineering to the University of Michigan, a few years later developed a powerful network of friends, and then came to work for Boeing in the heart of its commercial think-tank.
How did your IMACS classes prepare you for college? Your position at Boeing?
The teaching philosophy for computer programming at IMACS is not the classical piano book approach. You will not become an expert at solving any kind of existing, well-defined problem with one specific and popular language. You’ll spend a lot of time not learning the computer language that you will be taught in your first term in college.
Instead, you will gather an understanding of what you might call “computer linguistics”. The ability to communicate an idea through the assembly of conceptual components. The skill of decomposing a multipart task into a simple abstract algorithm. At which point you are then free to cut code in the language that would be most efficient for communicating that idea. IMACS computer science provides you with a different way of thinking, not just an add-on to your résumé about how you can write code in an industry favorite language.
At Boeing, we spend time studying new functional aerodynamic shapes to solve a variety of complex problems while keeping in mind the multidisciplinary nature of every component. With every new idea, you walk through the development process to show that it’s viable, or even patentable. Some of the skills I learned at IMACS allow me to draft up a few quick and dirty scripts in languages I had never coded in before. This allows me to save a significant amount of time repeating similar analytical tasks on multiple candidate solutions or parsing out test data in a useful way. After IMACS, you become more comfortable interacting with the machine and make the most of the computational power you have available at your disposal.
You also have some experience teaching. What do you think the US has to do as a nation to improve math, science and computer science education?
I was a substitute teacher at a high school and subsequently a graduate teaching assistant in a first-year programming course for future engineers at Purdue University.
Successful college students today are very aware of the concept of perceived economic value. Students today are more likely to seek out business-related, social science or history degrees rather than physical science or engineering degrees. It demonstrates a general sentiment that the technical degrees are no longer worth their perceived cost (years and/or intensity of training, accrued financial burden, etc.). Science is not the “cool” thing to do anymore as it once was when scientists were in the limelight of the 60’s. The perceived benefit of being in a technical field was much higher. Marketing happened by default on the news every time a rocket launched at the NASA Kennedy Space Center. Unfortunately, the need for technical degrees is inherently difficult to quantify and isn’t always obvious at a cultural or global economic level anymore.
Today, we’ve come to take for granted the engineering and scientific leaps that have been made in the recent past, such as leaps in wireless data transfer, functional nanotechnology and intuitive human/machine interfaces. Advances in biotechnology research (e.g. replacement organs, spray on skin) have unlocked a new approach for healing the infirm.
Unless the general culture regains an appreciation for scientific exploration by raising the perceived benefits and reducing the perceived cost (as was once shown in the 60’s during the Space Race, or during WWI and WWII in aircraft and military weaponry development, or personal computer development in the late 80’s), we will see a general stagnation in “technological advancement” as it has been traditionally defined.
Traditionally defined innovation and scientific exploration is a high-risk, high-expense endeavor. It will only happen when the global market demands it and demonstrates its true value. When the free market price of oil is allowed to inflate beyond the point of affordability without manipulation, the economy will require immediate and immense creativity in alternative energy and fuel technology. The need for scientists and engineers will be made immediately relevant and the market support will demonstrate the true benefit to all who depend on that which they take for granted.
The traditional ambition within transportation advances, for example, in the past century has repeatedly contained the adjectives “faster, farther, higher”. On the ground we went from conventional rail to high-speed rail (e.g. France’s TGV) to magnetically levitated trains (e.g. Japan’s MLX01). In the air we’ve seen US Air Force-funded demonstrators like the Boeing X-51 flying multiple times the speed of sound over the Pacific Ocean.
It seems the general population is now fairly uninterested in the traditional. We are no longer actively pursuing this long-established goal. In a modern culture that is approaching one of perfect information (made possible, in part, by economically accessible, internet-enabled, naturally intuitive smartphones), we have the ability to make more rational purchasing decisions. Now the market tends to instantly reward those who can make a substitute product for a cheaper price. Engineering and science is being redirected to the practical. For example, after you pick your destination, travel websites will automatically sort by price. The name of the game now isn’t “faster, farther, higher” anymore. The commercial business case is just not there for it.
Social awareness is starting to flow into the demand for science and engineering. Privatized venture philanthropy and private humanitarian and community foundation efforts have created a multi-billion dollar industry in the past 10 years. Modern innovation is making commodities such as digitally-based financial services for the poor or basic health services available to the masses that were previously prohibitively expensive.
Science, Technology, Engineering and Mathematics are here to make the world a better place. How we each define “better” will guide innovation and large private capital into the directions that have highest economical demand and true value. The only thing we can do now is try to show the world what we are capable of accomplishing and what they can do as the culture begins to appreciate, once again, how powerful ideas really are.
This month’s guest blog post comes from Christopher Tiwald. Christopher studied the Elements of Mathematics curriculum from 6th to 9th grade as a student in Lincoln Public Schools in Lincoln, Nebraska. He attended the University of Nebraska-Lincoln where he majored in Political Science. After exploring a diverse series of careers, Christopher became a self-taught software engineer and now works at Conductor, Inc. as a Technical Operations Engineer.
The most common complaint you hear from students in math class is “We won’t use this in the real world.” I’m ten years out of high school and six years out of college. I’ve made sandwiches professionally, waxed floors full-time, went to grad school, dropped out of grad school, and worked in professional politics. I can honestly report, “We were wrong.”
It turns out the real world doesn’t reward education as much as passion, self-starting, and the ability to solve problems. The Elements of Mathematics curriculum, or “Elements” as we called it in school, taught me how to learn. For four years I studied problems that bent my brain and stretched my imagination. They required every last modicum of creativity I could muster and, in truth, I wasn’t terribly good at them. I didn’t graduate top of my class — nowhere close. When I did graduate I vowed, “Never again”, and studied liberal arts instead of science in college.
But I couldn’t escape the Elements of Mathematics. Freshman Philosophy is a breeze when you’ve tackled deductive number theory. Supply and demand are trivial when you recognize their curves as simultaneous equations. College grades are driven less by raw IQ than they are by pattern recognition. Once you know how to solve one class of problems, it’s easier to solve again and again. It’s like the compound interest of education — compound interest, of course, being a concept I first encountered in Elements.
I thought it would stop when I finished college. Surely the real world, crammed full of unqualified positions, internships, and the entry-level, would not echo the Elements of Mathematics?
Did you know that if you have five ingredients to make a sandwich, the number of sandwiches you can make with two ingredients is exactly equal to the number you can make with three? Have you ever canvassed door-to-door for a campaign? The most efficient way to knock doors is often an Euler circuit — a route that takes you down every street exactly once. Here’s a fun one from the economist Thomas Schelling: Ski resorts are a closed mathematical system. The amount of time it takes to sit on the lift and wait in its line are inversely dependent. If you make the lift faster, you make its lines longer, because the time people take to ski down the mountain or warm up in the lodge won’t change.
You don’t need to know these things to run a sub shop, win an election, or enjoy a winter vacation, but knowing them gives you a more thorough, practical understanding of the world, one that is immediately useful to employers and in daily life. You learn new concepts quickly because you learned how to learn. You solve problems more efficiently because you’ve solved thousands of similar problems before. The Elements of Mathematics is a competitive edge without qualification. Bosses love it as much as professors.
As for me, I wouldn’t be who I am without the program. Elements changed the way I interact with the world. After wandering from career to career, I landed comfortably in software engineering, something I taught myself. That says less about me than it does my education. All jobs are strings of solvable problems. Once you’ve learned how to think, the rest is easy.
Milo Gardner may be retired, but he’s not letting his mind rest idle. This amateur code breaker chatted with IMACS about his mathematics background and how it influenced his life. After serving in the United States Army as a cryptanalyst, Milo went on to earn his B.A. in Mathematics with a minor in History of Economic Thought at California State University – Chico. What followed was a career in aerospace engineering and an M.B.A. from CSU – Fullerton. Years later in retirement, Milo’s curious mind, a letter to the editor, and a meeting at a coffee shop led him to his current passion – decoding ancient Egyptian math texts. IMACS blog readers can review his extensive list of online publications on the subject. Now let’s hear from Milo in his own words.
Please tell us about your mathematics background, including what interested you as a child.
Baseball and sports of all types filled my youth. In the 8th grade I was sports editor of our school newspaper. This meant computing box scores and other game statistics for the various teams and writing up short narratives. Several sports teams were enjoyed during high school. Basketball was my favorite. Math was a special high school interest, as well as Spanish, chess and the sciences. Algebra I, Algebra II, Geometry and Trigonometry were studied in the context of set theory. That is, math students determined in advance which number system(s) would solve particular problems.
Right out of high school, the US Army was joined with hopes of spending time in Europe. My high school language skills were tested first. Two entrance exams for the Defense Language Institute at Presidio of Monterey, California, were taken. Luckily, the second exam score was low. The Army’s code-breaking tests followed, which were passed. In a five-month code breaking school, language and number-based patterns were studied. Techniques identified one-to-one, two-for-one, and other substitution systems. Finishing third in a class of 20, Germany was selected as my two-year assignment. Lower ranked students were sent to Africa, Turkey, Korea and Japan. In Germany, ad hoc Russian language projects were assigned to cryptanalyst and linguist teams. A two-month side trip to Lebanon widened my foreign language exposure to include Arabic.
Upon discharge from the Army, a number of my co-workers went to work for the National Security Agency (NSA) in Washington, D.C. I went to college in Northern California and earned a Mathematics degree with a minor in History of Economic Thought, with an intention of applying to the NSA. Computer programming courses were taken, as I was preparing to be a high school math teacher as a back-up career. Upon graduation, wishing to be married and raise a family, a southern California aerospace engineer accepted. The pay was better than teaching. Equally important the location kept me and my wife-to-be close to both of our families.
What kind of work did you do in the aerospace industry?
The first aerospace position was at Vandenberg AFB as a systems analyst. Western missile test range issues input computer-generated data to hand drafted range safety charts. The charts factored in daily wind measurements and drag aspects of missile parts that allowed three-second delays for the missile safety officer to blow up errant missiles. Nearby populations were protected. Subsequently, college programming skills were applied working with a team that automated the hand drafted charts.
The second aerospace job was at Rockwell International in Fullerton, California. Failure patterns of Minuteman I, II and other avionics guidance systems were studied in terms of maintainability issues. While at Rockwell, evening business classes were taken towards an MBA degree. Upon graduation, a career change allowed our family move to northern California to be near our respective families.
You raised a daughter who went on to become a civil engineer. What advice can you offer to parents of mathematically talented girls on how to nurture their talent?
Missy, my CE daughter, was self motivated by the second grade. All three of my children played musical instruments. Parental guidance consisted of coaching youth softball and baseball teams up to age 12 and supporting each child’s active social life. Thereafter, tryouts for competitive teams were arranged. Missy made a traveling team at age 14 in an organization that her older sister played. My wife and I attended most of Missy and her sister’s weekend tournaments. Our children knew their parents were their biggest supporters.
Missy was strong willed and stood up to basketball, softball and volleyball coaches in high school. Her sports experience gave her confidence to confront one engineering professor in college who refused to call on women in the class. After receiving a failing grade at mid-term, she called a conference with the professor and asked why he had not taken even a single question from one woman in the class. Her strong position was understood and respected. Thereafter, in-class questions were answered sufficiently for her and other women to earn passing grades. Today, she is an engineer working for a private firm. Incidentally, she told us this story weeks after the situation had occurred. Missy had the confidence to handle it herself.
In retirement, you now pursue code breaking as a hobby with a specialization in ancient Egyptian math texts. How did you become involved in these pursuits?
In 1962, an upper division college history of math class told a fuzzy history of zero story. Zero, as we know it today, did not reach Germany until 1200 AD, in time for the birth of our base 10 decimal system in 1585 AD (that defined n^0 = 1), an unbelievable assertion. “Some day I’ll research that topic,” I told myself. In 1988, six months were spent studying the topic at two local university libraries. Medieval and older Near East numeration systems including Classical Greeks used zero, a round figure topped by two dots in clear ways. Babylonians and Egyptians used zero as a limit 1,500-2,000 years earlier. Zero was also the value of empty sets in an Egyptian double entry accounting system. The older uses of zero did not use placeholders. Care had to be taken to read the context of mathematical documents and inventories –- issues that I knew well as a military code breaker.
After completing the study of the longer history of zero, an unexpected event took place. Acting on the dehumanization of classroom math topics (e.g., omitting personal stories like how the pre-teen Gauss summed the addition of 1 to 100 by a formula), I wrote a letter to the editor of the Sacramento Bee on the weaknesses of the 1990 California Math Framework. The day after the letter was published a phone call from a retired electrical engineer was received. Noel Braymer asked that we meet at local coffee shop. I said yes, and my retirement world changed for the better.
Noel had worked on 1650 BCE Egyptian text called the Rhind Mathematical Papyrus (RMP) for 15 years. A 50 member RMP 2/n table was encoded. The table took up 1/3 of a papyrus that contained 87 other problems. Noel offered a modern number theory solution to the 2/n table. Number theory stresses prime numbers in ways that ancient and modern mathematicians parse divisors of composite numbers into primes. The ancient 2/7 was recorded as 1/4 + 1/28. What set of ancient rules were used in the entire 2/n table?
The 2/n table encoded 2/3, 2/5, …, 2/101 to concise unit fraction series in ways that scholars hotly debated during the 20th century. Robin-Shute published the Rhind Mathematical Papyrus text in 1987 and suggested one incomplete solution. Noel gifted the book to me, and asked if I would assist in publishing his work. I said yes, provided the ancient scribal methods were also decoded and published.
Ten years later, working with a linguist, a sister document to the RMP, the Egyptian Mathematical Leather Roll (EMLR), was decoded with modern number theory. Attempting to explain connections between the two documents, aspects of the RMP 2/n table construction methods slowly emerged. Another seven years passed. Finally, by considering Egyptian wages paid in commodities, a 2011 paper included a complete solution to the 2/n table problem as an appendix.
In your opinion, what mix of interests and skills makes a person well suited for a career in cryptography? What should kids who are interested in code breaking be doing now to prepare themselves for a career in this field?
Students should enjoy solving all types of puzzles. I have loved crossword and other puzzles since high school. Learn a foreign language and learn about new and old foreign mathematical issues. Enjoy competitive individual and team games. Chess and bowling took up much of my free time. Choose your games and puzzles wisely. To pursue a puzzle solving career, a student should learn to contribute to all sorts of teams. Team membership is an important skill in many aspects of the adult world.
Dan Dugger is a professor in the Department of Mathematics at the University of Oregon. He received his Ph.D. in mathematics from the Massachusetts Institute of Technology and his B.A. in mathematics from the University of Michigan. Professor Dugger is a graduate of Project MEGSSS of Broward County, Florida, which used the mathematics textbooks that underlie the EMF Math online program. As a high school senior, he submitted an original research paper entitled "On the Homomorphisms between Finite Abelian Groups" to the 41st International Science and Engineering Fair, winning–among several other honors–the first place award from the American Mathematical Society.
When did you know that you wanted to be a mathematician? Who or what experiences influenced you in that direction?
When I was in elementary school, there was a class for gifted students run by a remarkable teacher. Her idea was that the students should be in charge of their own education, so she had them each pick a subject they wanted to study. At first I studied space exploration, and then I studied whales. The next year I studied computers for a long while (this was in the days before anyone had a computer in their home!), and the year after that I switched to lasers. One day I was reading an explanation of lasers in a physics book when an older kid came along and in a tone of complete awe asked, "Danny, you're studying physics?" I sheepishly explained otherwise, and he went about his business, but I came away with the idea that physics was a difficult and impressive subject! So the next year, in fifth grade, I was determined to study physics. After that, I was convinced I wanted to go to Caltech and become a physicist.
At that point, I honestly had no idea that there were such things as mathematicians. I liked math, and I liked it when my dad showed me mathematical things he knew that were over my head, but I had no idea a person could make a career of it. Then in middle school I went into Project MEGSSS (the precursor to IMACS) and started learning from the Elements of Mathematics curriculum (the basis for the EMF curriculum). At that point I felt the wonderful beauty and poetry in mathematics. I had great teachers like Burt Kaufman and Ed Martin who were encouraging and really made this material accessible, and thanks to them I was hooked. So pretty much from then on I wanted to be a mathematician.
The important point that I want to get across is this: I remember fairly little of elementary school, but I remember every subject I studied in the four years of that gifted class. That strikes me as remarkable. And in a very direct way I see that class as having put me on a path that led me to my eventual career. It's really hard to overestimate the effect that good, caring teachers have on children.
You attended the University of Michigan at Ann Arbor for your undergraduate degree. At what point did you start looking into grad schools? What were you looking for, and how did you decide on MIT?
As an undergraduate, there were times when I was uncertain that I still wanted to go to graduate school, but I also didn't know what I wanted to do. A kind math professor grabbed me one day after I had taken his class and said "Are you planning to go to graduate school? Because you really should!" At his suggestion I participated in a summer research program at Michigan with another great professor. The next fall this professor sat me down and said, "Okay, here are the places you should apply to graduate school: Harvard, MIT, Princeton…" I was pretty shocked! I had no idea I would be able to get into schools like that.
So I applied for graduate school, although I was still not exactly sure that this was what I wanted to do. For a while I was convinced that I wanted to go to University of Chicago, but when I visited there, it didn't quite click for me. I remember quickly calling up MIT afterwards and asking to arrange a visit! Luckily, during that visit something did click. What I mostly remember was the very pleasant atmosphere among the graduate students at MIT. Seven or eight of them took me out to dinner, and I remember they spent the whole evening gossiping about the professors in the department. That doesn't sound like a good reason to choose a graduate school, but somehow it worked.
I think the real lesson here is that visiting schools is very important. It is quite difficult to know, or to predict, when things are going to click or not click. Every school is different, and different things work for different students.
Tell us about your years at MIT. How did you choose your advisor, or is it the advisor who chooses the student? How do you decide on the topic for your thesis?
I came to MIT determined to study a subject called commutative algebra. But once I was there, I found myself more and more in the company of topologists. There weren't many people studying commutative algebra at MIT, but there were numerous topologists–it was a very active and exciting community. My best friend was a topology student, and I always seemed to be hanging around the topologists and their interesting seminars, so at some point it seemed that I should just become one of them!
Unbeknownst to me at the time, other forces were also at work. During my first semester at MIT I took a seminar in topology run by a retired professor, and he decided that I should become a topologist. (He didn't tell me this at the time.) He somehow set things up so that I started talking regularly with a brilliant topologist named Mike Hopkins, and after a while Mike became my advisor. I never formally asked him to be my advisor, and he never formally invited me to be his student; it somehow just came to be. However, this is somewhat atypical. Most students just choose someone who is in the area in which they want to work, possibly having already taken a class from such a person, and simply ask. It's typical for the student to do some independent reading under the professor's guidance to see if things are a good fit before anything is set in stone.
Concerning choosing a thesis problem, most advisors will assign the student a problem based on the student's interests. Usually it is a problem the advisor has some ideas about, so that he can suggest a plan of attack. Some advisors, however, have the students find their own thesis problem. In some ways the latter is a better, albeit more challenging, technique because eventually in his or her career a student will have to learn to do this anyway. In my own case it was somewhere in between these extremes, but closer to the latter.
Were there challenging times when you just hit a wall with the research? How did you keep yourself motivated?
It is not just that sometimes there is a wall to get past; it would be fair to say that almost all of the graduate school experience is a wall. Let me try to explain. Everyone goes into graduate school assuming that when they write their thesis it's going to be fun and beautiful like the mathematics they fell in love with, but that is an idealized view. When you take mathematics courses as an undergraduate, you are presented with a very beautiful, developed theory. But it's important to realize that what you are seeing in these courses has been refined over hundreds of years–you are almost never seeing "raw mathematics" as it comes out of the ground, so to speak. Instead of polishing a beautiful diamond, a working mathematician spends most of his or her time digging in a mine, carving away at the rock. In addition, when you learn mathematics in a course you are carefully protected from all the false trails that mathematicians took to get there. Actual mathematics research has many false trails, or trails that lead a little ways but then peter out. Someone once described their life as a mathematician this way: "I spend my days writing lots of stuff on the blackboard, most of which turns out to be wrong." This description, although exaggerated for a humorous effect, is not that far off.
So in some sense graduate school ends up being largely about making a transition in how you see mathematics. It is not easy to do. And a challenging factor that accompanies this is that the gulf between working mathematicians and students becomes particularly large here. Working mathematicians made this transition long ago in their careers, and many are not quite aware of it anymore. This can make communication between students and their professors somewhat frustrating.
The question of how to keep motivated in the face of all this is the crucial one. It is very difficult, and that difficulty never goes away. Not many people get PhDs in mathematics, and far fewer are still engaged in research ten years afterwards–and I think this is largely because of the motivation issue.
I don't want to give the impression that this is an impossibly difficult career path; obviously, there are new math PhDs awarded every year. I do think it is important to understand that life as a mathematician is very different from life as a mathematics student. When you are a student doing exercises from a book, the distance between what you know and what you are trying to find out is relatively small. In mathematics research, that gap is multiplied by a hundred. It can seem like you are walking from San Francisco to New York, but with the added twist that there are no roads or maps and that you don't really know that New York is even there! Everyone has to find their own answers for how to keep motivated on a journey like that. You can look at it as an insurmountable feat, or you can look at it as an challenging adventure, or somewhere in between. For what it's worth, I will tell you the answers that have worked for me. For myself, it always comes back to the fact that I like teaching; I like understanding neat things and sharing them with people. This is where my motivation comes from, even for my research. I'm always out to find that next "neat thing" to explain.
How did you know when you were ready for your thesis defense, and what was that like?
In most U.S. mathematics departments the thesis defense is, to some extent, a formality. Basically, you are ready when you have proven a new theorem. As long as you can convince three or four professors that it really is a new theorem, and that your proof is correct, you will get your PhD. The defense consists of you giving a lecture about the topic and about what you've done, and as long as you can do this intelligently and answer a few of the professors' questions, you get your PhD.
In my case, I was ready for my defense much earlier than I realized at the time. I had a new result that would have made a perfectly fine thesis, but it wasn't the result I was after—it wasn't the kind of result I wanted my thesis to be about. But looking back, having seen much more of the mathematical world since then, I realize this was pretty silly. I ended up spending about eight more months working on it until I got a result that I was happier with in the end (although still not really the one I wanted!). It wasn't really wasted effort, but it also wasn't necessary to put myself through the extra struggle.
So you officially become Dan Dugger, PhD. What's next in the process?
This is an important question. The first thing you need to realize is that getting a PhD is just the beginning. Someone once described it to me as a "license to practice mathematics." Getting your license doesn't mean you're ready for the Indy 500, or even rush hour on I-95. In mathematics, recent PhDs do not immediately go on to become full colleagues in a math department somewhere. Usually there is an apprenticeship process called a post-doctoral position that lasts two to three years, and, depending on circumstances, a person might end up doing more than one of these. (I did two of them for a total of five years.) During these years a person needs to establish his or her own research program and prove (by writing several papers) that he or she can do research without having an advisor. Assuming you do this, you can get a tenure-track position in a research department. These are highly competitive jobs, so you go where you are lucky enough to get an offer.
And what interesting research are you working on now?
I'm afraid this would take a very long time to explain. It is the curse of being a mathematician: it is very hard to explain your work to people outside the field, in a short amount of time and space.
Adam Sternberg began his path to engineering as part of Project MEGSSS in Broward County, Florida. (The principal curriculum developers and teachers for the Florida MEGSSS program founded IMACS in 1993 using the same Elements of Mathematics courses.) He went on to earn his B.S. in Electrical Engineering from the University of Maryland College Park and his M.S. in Electrical Engineering with a concentration in Digital Signal Processing from Florida Atlantic University. In his role as a software engineer for innovative companies such as AlliedSignal (now Honeywell) and RadiSys, Adam was responsible for developing software used with flight navigation tools and telecommunications products. He is currently a senior software engineer at Pace Americas. In his spare time, Adam has even been a volunteer teacher, sharing his knowledge of computer programming and university-level logic with elementary school students.
You were part of the first group of students in the Broward County MEGSSS program. What were your thoughts when you started progressing through the curriculum?
The MEGSSS curriculum (which has now evolved into the IMACS curriculum) was different from anything I had seen previously. In the standard honors math class, my friends were mainly doing more of the same material as the regular class at a faster pace. In MEGSSS, we covered the expected topics, but the majority of the time was spent learning concepts that students usually don’t see until college. In most math classes, theorems are stated as fact, and then students are expected to apply them. In MEGSSS, learning how to prove those theorems from principles proven earlier was an essential part of our education and resulted in us having a deep understanding and appreciation of the subject.
What knowledge and perspective did you gain during that time that influenced the career path that you took?
The subject matter from MEGSSS that helped the most was logic (predicate calculus). I found I always had an affinity with logic and the structure of proofs, and that made me comfortable with the process of coding in a high-level language, such as C or Perl. The MEGSSS/IMACS experience in general, with its emphasis on logical proofs building on previous theorems and axioms to explore new topics, evolved into an ordered approach to problem-solving that is the hallmark of a good engineer of any discipline.
Please describe what a software engineer does, big picture and day-to-day.
A software engineer is responsible for the design, implementation, and maintenance of a software product, whether it be a Web site, an app for a smartphone, or the radar on an airplane. This includes designing proper test cases for the product, and identifying and correcting bugs found in the product code. Software engineers are also often called on to make judgment calls in triaging bugs found during a test cycle and determining both the severity and the likelihood of a bug appearing in the field with a released product. As software and the equipment they run on are rapidly evolving, software engineers must also make sure that they are familiar with the latest trends in programming languages, algorithms, tools, and related technology.
In your experience, what kind of personality and/or non-technical skills makes a person well-suited to be a software engineer?
Good communication skills are vital to be able to explain technical details to a non-technical audience (such as customers or the sales team) because software engineers often work in a corporation and not a vacuum. Also, good detective skills (such as observing behavioral patterns) are vital to finding bugs. Finally, no one’s code is perfect, and colleagues and supervisors will find fault with an engineer’s design or code in a review, so a thick skin is also helpful.
What education, skills and training make for success in the job?
A Bachelor’s degree in Computer Science, Computer Engineering, or related field (such as Electrical Engineering) is vital, and a Master’s Degree is often preferred. As an engineer’s career progresses, tasks may become more senior in nature, so leadership, project management, and even mentoring skills are good to have. Structured problem-solving skills, like what students develop at IMACS, and solid design skills are vital.
This week, IMACS catches up with an old friend, Mark Engelberg. Mark was part of the inaugural class of Project MEGSSS students in Broward County, Florida, when that program began in 1983. MEGSSS (Mathematics Education for Gifted Secondary School Students) was an ambitious public school course of study with a curriculum designed specifically for the brightest math students. The Broward program became IMACS in 1993. Like many of his fellow MEGSSS/IMACS alumni, Mark went on to an accomplished career in a STEM-related field. He is known for having designed the bestselling logic game, Chocolate Fix, as well as adding thousands of new challenges to the popular Rush Hour game.
How did Chocolate Fix evolve from an idea to a bestselling game to the basis for a new logic curriculum?
Chocolate Fix started out as a product called Gridworks. Gridworks was my first collaboration with ThinkFun, and its creation was very much a team effort. Bill Ritchie, the CEO of ThinkFun, had the initial inspiration to build a visual logic puzzle system. I proposed the pattern-matching framework for the clues and made the case that such a system would be simple, elegant, and expressive. Two very brilliant and prolific puzzle designers, Serhiy Grabarchuk Jr. and Scott Kim, ran with the idea and came up with the initial book of 60 puzzles. And of course, ThinkFun’s excellent artists and graphic designers came up with the product’s look and feel. It was a real thrill to work with so many talented individuals.
The funny thing, looking back, is that at the time, we weren’t entirely certain whether such a clue system would be rich enough to create challenging and interesting puzzles. Yet nearly a decade later, we haven’t even come close to exhausting Chocolate Fix’s potential; we’re constantly discovering clever new types of puzzles that can be expressed within the system.
Meanwhile, Chocolate Fix received the Parents’ Choice Gold Award in 2008, and in 2010, the Bunge Lab at UC Berkeley published a study that named Chocolate Fix as one of a handful of puzzle games that were shown to increase IQ. We know of at least one geometry teacher who has successfully used Chocolate Fix to teach his students the skill of constructing mathematical proofs. This is all exciting stuff, and it looks like Chocolate Fix has a bright future. Right now, we’re looking at ways to combine all the things we’ve learned about Chocolate Fix and turn it into an actual curriculum for teaching logic, problem solving, and mathematical proof skills.
You were also instrumental in using technology to develop thousands of new challenges for the Rush Hour app when the initial thought was that all the “good” challenges were gone. What are your thoughts on how technology continues to affect how we play games?
Technology touches every facet of our lives, and games are no exception. Computer games, for example, now form one of the largest segments of the entertainment industry. Even when it comes to non-electronic games and puzzles, computers play an important role behind the scenes. Nearly every crossword puzzle and sudoku are created these days with the assistance of computers. Artificial intelligence programs continue to shed new light on strategies for the world’s deepest games, including Chess, Go, and Poker. So to me, it seemed perfectly natural to apply my programming skills to the task of creating fresh new Rush Hour challenges.
You are the inventor of two other games – Animalogic and Snorkels. Tell us about them.
Animalogic received the Parents’ Choice Gold Award in 2009. Like Chocolate Fix, it is a solitaire puzzle system that comes with a book of challenges. The premise is that you have to successfully get 16 colored animals across a river, but the animals will only line up behind other animals that match in type or color. It’s a nice spatial, attribute-matching puzzle system with simple rules that even the youngest of kids can understand, but the puzzle book has a full range of difficulty levels, including expert challenges that will give adults a mental workout.
Snorkels is a two-player strategy game where each player controls a team of cute, colorful aliens with the goal of being the first to capture one of your opponent’s aliens. The capturing mechanism in Snorkels comes directly from the ancient Asian strategy game Go, which is widely regarded as the deepest strategy game ever devised (even deeper than Chess!). In fact, I created Snorkels primarily to be a “gateway game” to Go, which happens to be my favorite game. Snorkels is satisfying in its own right, but once you master Snorkels, you’ll find it a snap to learn and enjoy Go.
You recently said that the MEGSSS program, which is now part of the IMACS curriculum, gave you the logical thinking skills that enabled you to develop Chocolate Fix. Can you elaborate on that?
When creating the clue system for Chocolate Fix, I was heavily inspired by my experience with Book 1 of the Elements of Mathematics series, “Introductory Logic.” [Editor’s note: This material now forms the Logic for Mathematics I (LM1) curriculum at IMACS.] In a strong sense, each proof challenge in EM Book 1 is a kind of puzzle, and I wanted to capture that kind of thinking in Chocolate Fix. The partial grid clues are a form of disjunction, and the ability to put multiple constraints within one pattern are a kind of conjunction. (Gridworks also featured negative clues. We removed them from Chocolate Fix to simplify the system, but we hope to bring them back as part of the curriculum we’re developing.) When solving a challenging Chocolate Fix puzzle, you can expect to use Inference by Cases, Indirect Inference, and other techniques now taught in the LM1 course at IMACS.
Describe your career path from when you graduated from MEGSSS to your current work in puzzles and games and curriculum development. Who or what experiences influenced you along the way?
After MEGSSS, I went to Rice University, where I double-majored in Computer Science and Cognitive Sciences. From there, I programmed virtual reality simulations at NASA, and then got into the computer game industry, working at Sierra On-line and Rad Game Tools. These days, I’m primarily a stay-at-home dad, but I continue to dabble in puzzles and games when I have spare time.
With respect to puzzles and games, my biggest influence is my own childhood. I logged a lot of hours playing computer adventure games, solving puzzles in GAMES Magazine, and playing boardgames with friends. I was fortunate in college to find a group of friends with similar interests, and I ended up learning a lot about puzzle construction through our many conversations and brainstorming sessions about what worked and what didn’t. I try to create the kinds of things I would have enjoyed when I was in middle school.
If someone reading this thinks he or she has the next brilliant idea for a game or puzzle, what should he or she do next?
The beauty of the Internet age is that it is so easy to get your idea out there. Learn how to program so you can put together a mobile or Web app to showcase your idea.
IMACS chats with Thomas Rutkowski, Assistant Professor in the Department of Anatomy and Cell Biology at the University of Iowa Carver College of Medicine. Prof. Rutkowski received his Ph.D. in cell biology from UC San Francisco and his B.S. in biotechnology with a minor in chemistry from the University of Delaware. He completed his post-doctoral fellowship at the Howard Hughes Medical Institute/University of Michigan. Prof. Rutkowski is also an alumnus of Project MEGSSS of St. Louis, Missouri, the sister program to Project MEGSSS of Broward County, Florida. The latter became IMACS in 1993. All three programs share a common curriculum that teaches students how to think critically using logic and reasoning.
Tell us what you’re currently working on in the lab.
My lab studies how cells respond to perturbation (“stress”) in the endoplasmic reticulum (ER). Sensing ER stress and responding appropriately is essential for the development and normal function of many different cell types, and dysregulation of the response contributes to a number of human diseases. We have two main interests. The first is understanding how ER stress contributes to fatty liver disease (FLD), which is the most common liver disease in the western world. FLD is latent and reversible in most people, but can progress to hepatitis, cirrhosis, or liver cancer, which are all irreversible. We have evidence that the ER stress response fundamentally alters how fat is metabolized in the liver, and that these alterations might contribute to FLD.
Our other interest is in understanding how the ER stress response senses the nature, strength, and persistence of the stresses that activate it, and then alters cell physiology to generate the appropriate response. For example, the ER stress response is activated both in immune cells when they are stimulated to produce antibodies, and in the liver after a mealÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âtwo very obviously different stimuli. What makes the ER stress response in the liver cell different from the response in the immune cell? This project actually has a significant mathematical component, and we are collaborating with a professor in the department of mathematics to build a mathematical model of the ER stress response. We will use the model to predict how the cell will respond to stresses of different types, thereby (hopefully) understanding how the signaling networks of the response are wired.
What are some of the potential applications of your research?
The simple answer to this question is that if we understand how cellular stress responses alter fat metabolism in the liver, then we will better understand how conditions like obesity, alcoholism, and hepatitis C infection lead to liver dysfunction and liver cancer, and ideally be able to prevent these problems. With the number of obese adults in the U.S. rapidly approaching one in three (not to mention the comparatively smaller but still significant numbers of alcoholics and hepatitis C patients), understanding and treating fatty liver disease and its downstream consequences is a huge challenge.
Of course, the larger reality is that basic research often comes with substantial but unforeseen rewards. By understanding basic cell biology we ultimately gain insight into many diseases, as well as normal human biology. A classic example I like to give is the MutS geneÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âwhich was first identified by a group studying DNA repair in bacteria, which would seem to most to be a highly esoteric topic with little practical value. However, the human equivalent of this gene later turned out to be involved in hereditary colon cancer. The rewards that come from simply asking how cells work, while perhaps harder to pin down, are probably far greater in the long run than anyone can imagine.
How did your experience in Project MEGSSS studying what is also the IMACS curriculum influence your path from high school to your present career?
I think in two ways, one somewhat abstract and the other fairly concrete. I think the abstract influence was in helping me to realize that my intellectual potential was far greater than IÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢d appreciated. In fact, I think most people never have a moment where they realize how limitless their own potential is, and that is a shame. When you go from being bored to death by long division in a traditional elementary school curriculum to learning college-level logicÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âand realizing that you are in fact learning itÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âit suddenly seems more reasonable to think big: big ideas and big aspirations. In this kind of curriculum, you are also exposed to other students who have already hit upon this realization. Then, as now, I think it stimulates my own thinking to be exposed to those who think about things on a wholly different plane, with incredible depth and creativity. Being a scientist, it is clear that big ideas are what move progress forward. MEGSSS was really my first exposure to the world of big ideas and creative thinkers that has (hopefully) shaped my initial inclinations toward science and how IÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢ve approached it since IÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢ve become a practicing scientist.
The other more concrete influence is in how we are using mathematics to inform our understanding of biology. In our quest to understand how cellular stress pathways work, one of the approaches we are taking is to develop a mathematical model of the stress pathway. By that I mean that each of the steps in the process is replaced by a differential equation that (ideally) accurately describes it. The point of this process is to develop a dynamic mathematical representation of the response that allows us to do computational experiments that we cannot do in real life, and so learn more about how the stress response works as a complex unit. Many biologists shy away from this kind of investigation, because they donÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢t intuitively appreciate how broadly applicable math is to problems in other areas and they arenÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢t comfortable with the language. Admittedly, we are collaborating with a mathematician to help us with our modeling, but I think that programs like MEGSSS and IMACS makes students much more aware of how diverse a field mathematics is, and also makes them so much more comfortable with the language, and willing to apply it elsewhere.
You’re a parent with a mathematically precocious child. What are some of the activities you engage in as a family to help foster that talent?
We ultimately try to expose our children to new ideas (mathematical and otherwise) and challenge them to reason through problems they donÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢t understand without pushing so hard as to turn them off. As my mother used to say, ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦“Use what you know to figure out what you donÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢t know.ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â Math has to be fun; learning has to be fun. Opportunities present themselves if you just look around. For example, we used the weather changes to illustrate the concept of rate of change. Here in Iowa we are blessed, or perhaps cursed, with four very distinct seasons. In the summer and winter months, the temperature doesnÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢t change much over time, but it changes quite rapidly from early fall to late fall, or early spring to late spring. Notice how the temperature might be warmest in the summer and coldest in the winter, but it changes the most in the spring and fall? Differential calculus at work, and hopefully introduced in a low-key way. Our primary goal as parents is to do whatever we can to keep them interested in math (and learning in general); if we can successfully do that, I hope theyÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢ll naturally take to whatever curricula they are exposed to. Of course now that our oldest is entering third grade, and getting to the point where boredom with his regular math curriculum is starting to be a problem, we have had to look more actively for ways to foster his interest. I vividly remembered my exposure to logic and number theory in my first summer with MEGSSS (after fifth grade) and have since ordered those beginning books for him.
There is a lot of talk about the challenges the US faces in math and science education. From your point of view as a professor and a parent, what actions need to be taken to help US students become competitive again in the new global environment?
The U.S. is far and away the world leader in scientific research, which makes the mathematical and scientific illiteracy of the general population all the more discordant and alarming. We absolutely cannot sustain our technological edge in this environmentÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âpartly because we will no longer continue to produce talented scientists and mathematicians; and partly because a population that does not understand math and science will not support them intellectually or financially. A majority of Americans do not accept the idea of evolutionÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âthat all life arose by descent with modification from a common ancestorÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬Ãƒâ€šÃ‚Âdespite the fact that it is the central organizing principle in biology, paleontology, and, importantly, medicine, and is one of the best supported scientific theories ever devised. A large minority of Americans do not accept that human activity is warming the planet, despite this too being an extremely well-supported theory and having reflected the consensus scientific view for nearly 20 years.
Where does this illiteracy come from? I think it ultimately arises from the fact that science (and math) represent fundamentally unique ways of thinking about the world that are simply not well-taught in schools. Science is not knowing the difference between igneous rock, sedimentary rock, and metamorphic rock. It is not repeating some ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦“experimentÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â thatÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¾Ãƒâ€šÃ‚Â¢s been done thousands of times over by millions of students with a prescribed result. Science is inquiry. It is observing the world, asking a question, forming a hypothesis, testing the hypothesis, and discarding the hypothesis if the test falsifies it, or moving forward with it if the test supports it. Every student learns this as ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦“the scientific method,ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â but how many get to put it into practice, to address a question to which the answer is unknown? How many science teachers make this kind of investigation the centerpiece of their curriculum, versus simply presenting a series of facts that must be memorized and ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦“labsÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢”Ãƒâ€¦Ã‚Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â that must be suffered? Knowing that, as a scientist I am learning the answers to questions that have never been answered before, however big or small, is one of the true excitements of my vocation.
The same applies to math as well; math is not a worksheet full of arithmetic problems. It is a language that can be applied to real world problems, and requires its own way of thinking. There are teachers who approach science and math in this way, but I am convinced they are few and far between, and many others who want to probably feel they cannot, lest their students perform poorly on standardized tests. That people are not generally trained to think this way is evident from our national discourses. Debates are driven by ideology, with every viewpoint given equal weight. Arguments are made by assertion and evidence is cherry picked to support a preformed viewpoint. This is totally antithetical to scientific thinking, where the evidence drives the viewpoint and the viewpoint is subject to change based on the weight of that evidence. If science and math education in this country were geared toward teaching those ways of thinking, rather than toward the accumulation of information needed to pass a standardized test, I think not only would the population be more scientifically literate, and not only would we maintain our scientific edge, but we would also have much better informed and more productive dialogues on the issues facing society.
(Este blog tambien esta disponible en Español.)
This week, IMACS asks Dr. Arturo Cifuentes to share his colorful opinions on a variety of topics. Dr. Cifuentes received his Ph.D. in applied mechanics and M.S. in civil engineering from Caltech. He spent five years at the prestigious IBM Thomas J. Watson Research Center. Dr. Cifuentes then moved to Wall Street, where he spent 15 years working in the fixed income market. During the recent financial meltdown, he was invited to testify before Congress as an expert witness on the subprime crisis. Dr. Cifuentes is currently an Adjunct Professor in the Department of Industrial Engineering at the University of Chile and writes a monthly column for El Mercurio.
As you were growing up, what made you realize that you had a talent for math and science? How did you become interested in pursuing degrees and a career in engineering?
My father was an engineer who did a lot of consulting work. He enjoyed very much what he did and talked quite often about the “problems” he was trying to solve. I found that fascinating. I think, in a way, that enthusiasm motivated me to investigate in more detail what he did. And I liked it.
Also, having early access to all the books by Yakov Perelman was a turning point in my life. Those books were fun to read, intriguing, and very powerful and persuasive. My father did not believe in libraries; he felt that any book worth reading should be at home. The fact that I had access to many books since I was a child was fantastic. And the Perelman books convinced me (I am still convinced) that any career in science or a closely related field could be rewarding and interesting.
In your opinion, what needs to happen with math and science education in the United States in order for US students to remain competitive globally?
Parents should turn off their TVs, buy more books, and tell their children the truth: Sure, learning something like math or physics can be a lot of fun and can be rewarding, but it involves a lot of hard work and effort. And if those who believe in Intelligent Design could be persuaded otherwise, that would be quite helpful.
Two tendencies, or perhaps ideas, which in my opinion are pretty bad and should be eliminated, are the following (and I acknowledge that most people will disagree with me here):
[i] The growing emphasis on group work and team effort. Learning something like math is pretty much a lonely effort, a solo journey. People have to accept that. There is nothing wrong with team effort (soccer, for instance, is about that). But certain things (playing the piano, for example) require a lot of NON-group work. Math is one of those things.
[ii] Computers in the classroom. There is nothing wrong with using computers. But introducing them at an early age (with the idea of making learning fun) is a disaster. Children must learn to think conceptually first. And when introduced to computers, they should learn how to program them instead of learning how to react via a mouse to some external stimulus.
Now that the space age seems to be coming to a close, what is going to be the stimulus for intellectual and scientific pursuits going forward?
Well, in science and technology, whenever a door closes, several windows open. The advances in genetics, bio-engineering and neuroscience are very exciting; the same with computer science and communications. In physics, whoever manages to reconcile relativity and quantum mechanics will be the new Einstein (or Newton). Not to mention many more practical problems that still remain unsolved: earthquake prediction, for example.
You are a voracious reader. What book or books would you recommend to today’s students and why?
I was fascinated by Tom Sawyer and Huck Finn when I was a teenager. I read them in Spanish, and they were as good as in English. I also read Kafka, Cortazar, Hesse and Poe. Unfortunately, Etica para Amador by Fernando Savater is not available in English. I think every teenager should read that book. Finally, Richard Feynman’s Surely You’re Joking, Mr. Feynman is a must. If anyone thinks science is boring, this is the book to read.
How did you go from doing structural engineering research on thermal stress and circuit boards to analyzing complex financial securities?
I had been working at IBM Research in New York for five years, doing a lot of interesting stuff, and never thought about going anywhere else. Unfortunately, IBM was having a difficult period and they decided to cut costs. That meant that instead of using 100% of our time and effort to do research, we were supposed to go out and find funding (i.e., write grant proposals, etc.). The minute I saw the first few forms and all the paperwork involved in getting a government grant, I was done. I decided that I was not going to spend the rest of my life begging for money. That took the fun away from the research.
I loved (and still love) New York, and my wife had a good job there, so I decided to stay there and look for work. I quickly became aware that there were not many options for scientists in the New York area. Fortunately, a friend who worked on Wall Street asked me if I would consider interviewing with his firm.
“I don’t know anything about finance,” I said.
“As long as you can do Monte Carlos,” he explained, “you will be fine.”
I knew Monte Carlos. And in a few weeks I moved to the financial field.
But at the end of the day (as bankers like to say), it is all the same: thinking analytically and logically about problems. If you have a good background in math, it is easier to jump from one field to another. You learn to quickly identify the essentials and then the math helps. The key is to acquire good quantitative skills when you are young; you can easily learn the rest later. But if you don’t get your math tools under control by the time you are twenty, it is probably too late.
You currently write a column on business and economics, and you previously wrote an opinion column reflecting your varied interests in topics such as soccer and travel. Technical people are often stereotyped as having narrow focus and weak communication skills, so to what do you attribute your broad range of interests and abilities?
When I grew up I never had that impression. (I mean, that technical people had a narrow focus.) My father, who was a civil engineer, spoke several languages, and he often quoted Shakespeare in English and Goethe in German. He had a great library at home and read a lot. And his interests were very wide. I remember one Saturday (many years ago, I was ten or twelve probably) we went to his favorite bookstore and came back with three books: one dealing with humidity in high rise buildings and how to control it; a second book was about the evolution of financial markets in Chile; and the third book was about Freud. I still remember what the salesperson said: “I have seen many people buying these books before, but I have never seen the same person buying all three!” Well, that was my father. He was a very important influence and example when I grew up. He was a guy with many interests and skills. I owe him a great deal.
Any parting words of advice to the students and parents who are reading this?
When you are older than fifty, you tend to give more advice than you should. So I will be brief: Do what you like and follow your instinct. And remember, life is not about career choices or promotions. It is about love and friendship. Nothing else matters. Although having good math skills is always a plus.
When students or their parents think about career choices for computer programmers, they often think of software development and gaming. No doubt, working for Google or Blizzard Entertainment would be awesome, but not everybody will land one of those coveted jobs. Operations research and various areas of engineering may also come to mind as places to put your programming prowess to work. Less frequently, however, do people think of the financial industry.
Now before you go ranting that these smarty pants are the ones who brought down the global financial markets with their esoteric models that only a Ph.D. could understand, let’s skip that debate and merely point out this fact: programming jobs in finance are challenging and pay well. Ignoring them because you think they are on “the dark side” simply leaves you with fewer options. So let’s take a look at three areas of finance where computer programming is more than just a peripheral activity.
Computational finance. Computational finance was historically the domain of math and science Ph.D.’s who moved from academia to Wall Street (“quants”), especially as the use of financial instruments such as derivatives increased. The work of pricing these complex securities was roughly divided between the quants, who came up with the methodologies, and the programmers, who implemented the mathematical models. Over time, the focus has shifted to refining and optimizing the models. According to the Wikipedia entry on computational finance, “[A]s the actual use of computers has become essential to rapidly carrying out computational finance decisions, a background in computer programming has become useful, and hence many computer programmers enter the field either from Ph.D. programs or from other fields of software engineering.” Programmers are no longer solely relegated to the IT department, on call to do the bidding of the brain trust. The best ones are now part of that brain trust and are considered essential to financial institutions’ ability to maximize profits and minimize losses.
Algorithmic trading. What is algorithmic trading? Let’s go to the Wikipedia page: “… the use of computer programs for entering trading orders with the computer algorithm deciding on aspects of the order such as the timing, price, or quantity of the order, or in many cases initiating the order without human intervention. … A special class of algorithmic trading is ‘high-frequency trading’ (HFT), in which computers make elaborate decisions to initiate orders based on information that is received electronically, before human traders are capable of processing the information they observe [emphasis added].” So one set of humans (i.e., computer programmers) creates mathematical rules to replace a different set of humans (i.e., traders). And they’re paid handsomely for this disservice to their fellow man. Maybe you can see yourself doing this as sweet revenge upon those evil trader dudes who, some say, blew up the financial markets. Not such a bad idea now, eh?
Actuarial science. Finally, actuarial science. Wikipedia, don’t fail me now! “Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. … Actuarial science includes a number of interrelating subjects, including probability, mathematics, statistics, finance, economics, financial economics and [trumpets, please] computer programming.” Who knew that figuring out when a given cohort of individuals will, uh-hum, kick the bucket could be so interesting? Well, as it turns out, one of our former students knows this well as he was able to pass all of the actuarial exams at a fairly young age and is currently the chief pricing actuary of a major global life reinsurance company. We’re pretty sure he’s done well for himself.
So if you have a knack for computers and want to explore where these talents might take you, don’t forget about the financial industry as a place that can provide a rewarding career. Try to make room in your class schedule for the programming courses you will need to put you on the right path. If you don’t have access to these courses at your school, think about taking online computer programming classes. If done right, learning computer programming online can be just as effective in preparing you for the next level.
Do you or someone you know use computer programming skills in a non-traditional field? Tell us about it.
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