There is an interview with Harold Reiter at Cogito.

I have not yet poked around Cogito enough to know how much of it is really valuable.

MC: Garrett, first off, thank you for giving me the opportunity to interview you. I am excited about the opportunity, mostly because I want to ask the very first question. I hope many of my students read the answer and that the different way in which you approach life inspires them to think about they way their approach their own careers. After that, I just hope I figure out what to ask next.

For a moment, let’s forget that “An Exceptionally Simple Theory of Everything” is just a theory that you and many other brilliant minds are debating and refining. Let’s look at the upside — that after years of failed attempts by physicists to describe the universe entirely through string theory, you step in with a paradigm shift. Right or wrong, science needs radical new ideas. We really only move forward when we discover previously unconsidered ways of looking at the world. So, whether your theory works out in the end, you achieved something magnificent.

So, why you? Why a surfer instead of a nerd? Why not one of the countless throngs of violin playing Ivy League physicists who spend fewer of their days figuring out how to fit a toilet in the van, and where to park it at night to siphon internet access? (Let me know if I’m recounting the last part incorrectly.) Why not somebody who can’t spend their time jumping out of a helicopter onto a steep slope because they didn’t grow up developing that particular talent? Why not somebody who instead spends that time…thinking even more about science? What about who you are makes you the guy who even has a chance to reshape the world of theoretical physics?

GL: Just because I’m a surfer doesn’t mean I’m not a nerd. One simply can’t be happy working with equations all day, every day. It’s very important to get out in the world and play. We’re not machines. Well, maybe you are… But, anyway, most of us aren’t machines. And surfing and playing with friends keeps me happy, and it makes the time spent working in science that much more enjoyable, because I don’t burn out on it.

I’m not sure my experience of problem solving, throughout my life, has been so different from that of others, but I can describe it. As a student, it always felt like I was doing worse than my classmates during the beginning of courses. But then, towards the end, I always seemed to be doing better. And I eventually figured out why this was: my classmates were memorizing the class material, when I was actually trying to understand it. Understanding is harder than memorizing, but it builds on previous understanding, when memories just fade.

I also used to go off on a lot of tangents. Some of these tangents, which I might work on for hours or many days, would take me a way from spending time on the required material. But it turns out following tangents on my own was a good thing, because that’s more like what actual research is like. As an undergraduate, I would repeatedly go to a professor with a bunch of equations and graphs I had been playing with, thinking I was playing with something new. They would invariably smile and point out that this stuff was well known, and point me to books that covered it. But in grad school I would follow some tangent and people wouldn’t have seen it before. I’d have to do a literature search, and find out someone had done the same thing in a paper, thirty years ago. It was kind of frustrating. But, eventually, you’re following a tangent, and you find something cool that no one has done before, even if others have come close, and that becomes your PhD thesis. Then, as a researcher, you can build a whole successful research program out of finding new tangents and building on them. That’s been my experience, anyway.

MC: Much is made of your status as a “maverick” — somebody working outside the traditional academic path. What would you describe as the advantages in taking this different approach to your career?

GL: Working outside academia has advantages and disadvantages. The two largest disadvantages are a lack of prestige and not having colleagues nearby to bounce ideas off of. Colleagues can sometimes tell you very quickly when ideas have been tried before, or summarize what’s going on in other fields. Working on your own, you have to figure these things out yourself. But, sometimes this is an advantage, as you can find cases where the “lore” was wrong, without people around to discourage you. And the lack of prestige correlates with an unusual freedom to explore whatever ideas you wish, without the pressure to follow an established research program. Overall, living as an academic outside academia is a harder path, but it can be a rewarding one, because of the flexibility it allows.

MC: You discuss your theory in online physics forums and you are one of the pioneers of what you describe as “open source science”. Describe the ways in which social software propels your work forward. Do you think the advantages of social software will allow more scientists to take their research outside of academia to enjoy the advantages of freedom while avoiding the downside of lacking institutional resources (including proximity to quality colleagues)? On the same front, how do you see the upcoming evolution of academic institutions as a result of social software?

GL: When I got my PhD ten years ago, I realized most of the resources I needed to do research were available over the net. Researchers are no longer anchored to university research libraries, as has been the case for hundreds of years. This is a huge change, and I took advantage of it by adopting a peripatetic lifestyle — deciding to “think locally, act globally.” Virtually all recent physics papers are available on the arXiv, people can keep in touch via email and social networks, and books and manuscripts may be easily digitized. Personally, the trickiest part of this transition was organizing my own research notes; but I’ve been using a LaTeX enabled wiki that has greatly improved my notes, and made them available for others. Many universities have “open courseware,” allowing students free access to courses at top schools. As academia opens up this way, I think students all over the world will benefit, and science will benefit as a result. To accommodate this new geographic freedom, I’ve been working on the idea of creating a Science Hostel — a more casual kind of research institute, where theoretical researchers could live and work on their projects in beautiful places.

MC: Did you grow up knowing that you would find a vocation in science, or did you head to college wondering what might inspire you once you got there?

GL: I never thought much about what I’d do for a job. And I was never lacking in inspiration. All I’ve ever done is follow my interests where they’ve led me. It’s been a fun ride. I may have spent too little time worrying about making a living, but I don’t regret it, because I’ve enjoyed having a lot of freedom. People should be able to do what they love.

MC: I’m going to be a mathematician for a moment and try to generalize…perhaps limiting the hostel network to scientists would be overlimiting…I mean…could I hang out at one in Maui while I work on my next book?!

GL: I consider mathematicians to be scientists, just a bit further from the lab; so mathematicians would certainly be eligible. The number of researchers in the “hosteling pool,” and the entrance restrictions, would rise and fall with the housing resources available. I think a good baseline qualification is “PhD or equivalent” and the potential contribution to science, so you’d qualify. A Science Hostel on Maui would be a perfect place to write a book — that happens to be my plan too.

(I am flattered that Garrett is under the impression that my qualifications are equivalent to those of a PhD.)

MC: Last question. This one is a little on the cookie-cutter side, but it’s the cookie-cutter question that came to mind after reading a little about the funding you’ve received that allows you to follow a such a different path from the traditional university physicist. Pretend for a moment that a billion dollars falls in your lap, and you survive the crushing weight of all that paper. Your job is to use that money to propel science forward. What kind of programs would you design?

GL: Wow, a billion dollars… think of the sweet lair I could build with that in Maui. After the lair, I think FQXi has set a good precedent for advancing science by giving money away efficiently and responsibly. Most basic science research is motivated by idealism, not by money. But money makes it possible. It would be great to establish a foundation that provided a comfortable living to any qualified researcher interested in spending their time working in math or science. Supported projects could include making new scientific software tools, improving the content of Wikipedia, writing books, science blogging, or even developing new branches of research — projects which don’t currently advance a career under the shortsighted metric of Impact Factor. With a billion dollars, we could provide support to about 3,000 people for ten years, and significantly improve the scientific landscape and the quality of life of scientists. This runs counter to the usual, politically correct philanthropic strategy of helping the needy; but many organizations like that already exist, and I think the world would be a better place if there was more support for the gifted, allowing extremely bright people to follow their dreams.

MC: Kate, I would like to start off by thanking you for giving me the opportunity to interview you and share your responses with my students. To begin with, please tell us a little bit about where you are in your math education.

KS: Thanks! I’m excited about this opportunity.

If you read my résumé, you’d find out that I am currently a Ph.D. Candidate in mathematics at the University of South Carolina. I’ve been in graduate school here for four years, and in May 2007, I finished my Master’s degree. Before coming to South Carolina, I lived in California, where I graduated with a B.A. in Pure Mathematics in 2004 from the University of California: San Diego.

But this is a really unfulfilling answer to your question! Really, I am at the stage in my math education where I have just begun to get paid to do math. My full-time job is learning how to teach math effectively, learning how to write professional math research papers, and learning how to be a professional mathematician.

MC: I understand that you have won awards for teaching math. Tell us about those and what you think makes you an excellent math instructor.

KS: For the 2006-2007 academic year, I won the “Outstanding Graduate Teaching Assistant Award” from the University of South Carolina’s Department of Mathematics. In April of 2008, I was awarded the university-wide “Outstanding Graduate Teaching Assistant Award” by the USC Education Foundation. Each academic year the university gives only two teaching awards for graduate students: one for teaching in humanities, social sciences, and education, and one in science, math, and related fields. Because there are only two awards and over 8000 graduate students, I was very excited to win!

I think there are probably two big ideas that influence the way that I teach. The first one I heard in May of 2004, while attending a lecture given by Professor Leonard Haff at the University of California in San Diego. Professor Haff said, “Mathematics should never be abstract and difficult. From Kindergarten to Ph.D. it doesn’t matter; there should always be a simple way to look at things.” His statement immediately became my goal as a math student, and later became my goal as a math educator: to translate the abstract, difficult, and detailed ideas found in a math textbook into smaller pieces that are easy to understand. It’s not always the concepts that makes math tough. The difficulty most students have is they can’t translate between the math jargon – the vocabulary, the notation, the phrasing – and their own experiences. My daily goal is to explain the strange-looking equations found in their textbook into normal language describing experiences they have all the time.

The second thing that influences my teaching is something I hear most often from math students. Nearly every student I have ever taught has told me, “I’d be great at math if I didn’t make so many stupid mistakes!” I don’t know why students believe that being good at math requires never making mistakes; if this were the case, there wouldn’t be any human mathematicians. Stupid mistakes happen. They happen to math majors, they happen to math teachers, and they happen to math professors. I tell my students that their goal as math students should not be, “Never make a stupid mistake.” This is unattainable and is very frustrating to attempt. In order to be successful at mathematics, you need to be able to catch your mistakes quickly. Most students would do far better in math classes if they learned to check their answers and ask themselves, “Does this answer make sense?” If not, you need to go back and check your work. That’s the beauty of mathematics: things are supposed to make sense.

MC: As you move closer to finishing your Ph.D., what career options are you currently considering and why?

KS: I’ve considered several different career options along the way. When I was in high school, I was very interested in astronomy, astrophysics, and engineering. At that time, my career goals were to become an aerospace engineer, get a job at NASA, and build neat orbital machines. I went to college for engineering, but in taking the introductory coursework, I realized I didn’t enjoy the laboratory aspects of the courses - I much preferred the more mathematical classes, like General Relativity and Quantum Theory. That’s when I decided to pursue mathematics.

As my college graduation date came closer, I started wondering about what I’d do now that school was over. Someone explained that if you attend graduate school in mathematics, most universities will pay you! I thought, “Wait, someone will pay me to take more math classes?!” This sounded like a good deal! Graduate assistantships are common in math. Generally they come in two types - either you’re a teaching assistant or you’re a research assistant (or sometimes you’re both). Going to graduate school gave me the opportunity to get paid to learn more math while gaining experience as a math educator. I had never taught a math class before. I didn’t know if I’d enjoy it or if I’d be any good at it.

Since starting graduate school, I learned that I do enjoy teaching math quite a bit! Occasionally, I have thought about pursuing a job with NASA, or working as an actuary, or as a statistician, or a ton of other options. Currently, the largest employer of Ph.D. mathematicians in the U.S. is the National Security Agency (NSA). I’m sure most of my fellow math graduate students have at least thought about working there. When school is really difficult, I still think about what I could do given my current education level in math. For me, what it comes down to is my enjoyment of working with students. I get excited to teach my classes, I enjoy seeing my students grow and learn, and I’m not sure I’d find the same fulfillment working from 8am-5pm in a cubicle in corporate America.

MC: Given your interest in math education, describe what you see as the good points and the bad points about the American math education system.

KS: The goal of mathematics education ought to be to create skilled problem solvers and good critical thinkers. I really dislike the trend toward standardized testing to measure mathematical aptitude. Almost never do any “real world” problems involve choosing the correct answer from a list of potential responses. Not only that, but really great problem solving often requires group discussions. In contemporary advanced mathematical journals, many (if not most) publications come from more than one author. Mathematics is not an individual sport; if done well, it requires a team effort. This needs to be reflected in the math curriculum found in our schools. The ability to work in a group, to communicate complex ideas effectively, and to understand perspectives different from your own is as important in mathematics as in any other subject, but this kind of learning is too often discouraged in most math classrooms.

I do not think we are teaching mathematics well, nor do I think we are teaching good mathematics. As a culture, we are so caught up with memorizing the rules and performing arduous and dull algorithmic processes we have lost sight of the role of creativity in mathematics. We want our students to know how to factor polynomials, how to use the Quadratic Formula, how to carry out long division, and a thousand other skills. While these things are important, they are not the most important things in mathematics. We have added so many drills and memorization tasks to the math curriculum there is no room for fun mathematics, like number theory and combinatorics and cryptography and probability and game theory and… There are plenty of fascinating mathematical ideas accessible to pre-college students but none are ever taught. This is like teaching grammar and spelling, but never reading the great poems or the great stories or the great books.

I am having trouble pinning down what I think we are doing well. This is not to say that things aren’t being done well. There are plenty of talented and dedicated math teachers across the U.S. who make a huge positive impact on future mathematicians. The problem is that my path to mathematics was very non-standard. I have not taken a typical public school math class since I was in the eighth grade, and my recollections of that experience leave little in the “well done” column. I learned early that if I wanted to know more math, math class was the wrong place to do it. I carved out my own path and tried never to let my school get in the way of my education.

MC: Please share with us an anecdote or two about how a heightened understanding of math has changed the way you tend to see the world.

KS: This is a hard question. It’s a bit like asking, “Tell me about how the color blue has affected the way you see the world.” I don’t know what it’s like not to see the color blue so I don’t know how seeing blue has changed my understanding of the world. It’s the same thing with mathematics. I’ve seen math around me most of my life and it’s tough for me to think about what it would be like if I didn’t see math everywhere! Part of this is because my father studied math in graduate school, and since I was a child he always talked to me about math ideas that no one was teaching at my schools.

I think the process of learning mathematics is akin to the process of learning a foreign language. In college, I studied French. After studying the French language for a long time, eventually I realized I wasn’t thinking in English and translating to French. I’d look at objects - like tables or chairs or flowers or motorcycles - and I’d think of their names in French automatically. It seemed natural for the French words to pop into mind first; no translation was necessary. In knowing math, it’s much the same way. I can’t help but see math concepts when I look around. For instance, when I look at an ATM, I think about the RSA cryptosystem; when I look at my cell phone, I think about graph theory; and when I listen to the radio, I think about wave functions. This seems as normal to me as seeing the sky and thinking “blue.”

Recently I finished my first two math interviews.  I have not yet posted either because it requires that I reconstruct them from email, and I have been spending my free time finishing up the 2008 iTest documents.  But I am about to post the first interview — with Kate Scott, who is closing in on completing her Ph.D. in mathematics at the University of South Carolina.

When it comes to interviews, I don’t know what I’m doing, but hopefully I will learn a few things along the way, and hopefully I will have some good excerpts to quote as I compile a page on the MIST Academy website that displays to students what math (and fields of applied math) can do for them and for the world, and how to approach their education.

I was a student attending the prestigious Math Olympiad Summer Program (MOSP) during the summer of 1993 when it was announced that mathematician Andrew Wiles was believed to have solved the most famous unsolved theorem in all of mathematics. Unfortunately, for me, the post-proof hype turned to gloom. Wiles said something that I now regard as one of the most unfortunate and wrong statements ever made by a man at the top of the world of math and science. He said that the days of the non-professional, non-academic mathematician were over. He said, in so many words, that nothing particularly interesting and new would be discovered by anyone working outside an academic institution.

I remember being mocked by my peers for disagreeing. Of course, I must be completely loony to disagree with the greatest living mathematician! For the rest of the program, I kept to myself almost exclusively, and upon returning home, I stopped studying mathematics. Though I qualified as one of the 24 students to be invited for a third straight year, I declined the invitation to MOSP my junior year. The following year I wound up a fraction of a question, almost surely the result of a hole in my training, from earning a spot on the U.S. team to compete at the International Mathematical Olympiad. Had I made the team, I would have worked very hard not to embarrass myself at the event. I would have wanted a gold medal. It might have reignited my love for mathematics.

I have no regrets. I will do more for mathematics as an educator than I would have done for it as an academic. I am not a personality that belongs in a university setting.

And it’s best that we live in a world in which a diversity of personalities make different decisions.

A Different Scientist

Recently I began conducting a series of interviews that I plan to begin posting soon. Unfortunately, none are yet finished, but recently I began one with a now famous physicist named Garrett Lisi, whom I met a few times in San Diego, including at his own going away party just before he and his girlfriend took their converted van-home to Maui. So far, we’re only one question into the interview, but I’m excited because he already said something that I find very important for students to read. I won’t give it away yet…

Lisi, whom I found friendly and inviting in person, is getting attention in the physics world for publishing a “Theory of Everything” (a step up even from “Grand Unified Theory“), which relies on a surprisingly simple (this is a relative term of course) mathematical structure to explain the universe (in direct competition with string theory). There is a recent article in the New Yorker about it. Take a look at this excerpt:

Lisi had long harbored a deep skepticism about string theory. As a graduate student in theoretical physics at U.C. San Diego in the nineties, he was briefed on a recent string-theory development called the Maldacena conjecture by a young member of the physics department. “It was very interesting mathematics,” Lisi said. “But I remember walking out of this office and wondering what it had to do with any physical reality. And, as far as I could tell, it didn’t.” The influence of string theorists was growing at the time, and Lisi felt the academy closing in on him. “If you share an office next to a guy for twenty years, and you like him and you’re friends with him, it’s hard to tell him that you think that his whole idea of how the universe works is completely wrong,” he said. String theory, Lisi had come to believe, was “a mess.”

The article goes on:

Lisi didn’t think that he would ever return to academic physics. “It’s publish or perish, and I figured I was perishing,” he said. He became accustomed to working in isolation, in air-conditioned public libraries, or in spare rooms at home, when he had a home. There were times when he lived in mansions near Colorado ski slopes, house-sitting. At other times, he pitched a tent in a friend’s back yard. He always figured, he told me, “that my brain wouldn’t let me starve.” But he was hardly thriving.

Lisi’s working life was not steady, or easy. “Ninety-five per cent of my time is virtually wasted,” he said. “If I were in a university, one of my colleagues would say, ‘No, that direction makes no sense—other people have looked into it, and it doesn’t go anywhere.’ Here no one stops me.” He spent weeks searching for a reliable place to work, and months on projects he later discarded. Sometimes he felt like a crazy person, walking down the pier in Santa Monica and muttering equations out loud.

I think part of the reason why I’m rooting for Lisi’s theory is Lisi. This article tells a really important facet of Lisi’s story — that he’s not a conventional physicist. This is important on so many levels. Science includes a lot of things, including boring day-to-day experiments, looking for the 309th application of a certain well-known phenomenon, and the slow decay of politics. But first and foremost, science moves forward because of ideas that break that mold. And Garrett Lisi, as a human being, breaks the mold.

Edit: I removed “[in]famous” in favor of “famous” because I think few people will understand that I’m mocking people who bashed Lisi’s TOE before a complete review and giving Lisi (and others) a chance to work through the kinks.

Shortly after my online conversation with Jim Heaps-Nelson, I decided to dedicate a portion of this blog to interviews with math professionals — people who use math in their careers whether as mathematicians, technologists, business professions, scientists, etc.

My first interview (currently ongoing) is with Kate Scott, a budding young mathematician whom I met in San Diego shortly before she left for the University of South Carolina where she is pursuing her Ph.D. in mathematics. I picked her partially because we have had numerous conversations about math and education and I know that she is always developing her thoughtful perspectives on these subjects.

Recently, I was discussing with Kate the fact that we’ve both taught classes in subjects we had never previously studied (at least formally). As it turns out, this is not all that uncommon. Mathematicians become comfortable and confident with learning new ideas about mathematics, and new material is usually energizing (as well as educational).

Teaching Means Learning

Back in middle school, I had an insatiable appetite for math puzzles, games, and interesting problems. Both in math team and gifted class, I enjoyed explaining my methods to other students. I quickly developed a reputation for being a good teacher and I spent a great deal of time helping other math students — particularly math team students — develop their problem solving skills.

More than helping me to become a good teacher, teaching forced me to refine and communicate my own ideas about mathematics. With the exception of time spent focusing all my energy unraveling really difficult problems and concepts, there was nothing I did in school more educational than teaching.

Kate points out her father’s experience:

My father has always said that the first time you teach a math class, you learn quite a bit, but your students are at a disadvantage. The second time you teach the class, your students have a big advantage, but you don’t learn nearly as much. And the third time, you’re pretty burned out as far as the material goes, and so your students don’t get the best presentation of the material.

This insight does not hold only for professors of mathematics. It’s true for students as well. As much as possible, I encourage my students to spend time teaching each other. If you want to become better at mathematics, prepare a lesson for somebody else. Go back and volunteer to teach MATHCOUNTS, or tutor. Until you can explain it, you probably don’t know it as well as you think you do. And when you’re done learning what you can from teaching — teach something else. In fact, if you never develop good communication skills, you are not likely to become a very good mathematician at all.