快猫短视频

While some view origami strictly as an art form, Erik Demaine finds great theoretical challenges in the ancient Japanese practice. In MIT鈥檚 Laboratory for Computer Science, he is exploring how it might yield new insights into diverse areas such as protein folding, gift wrapping and the deployment of automobile airbags. Welcome to the arcane realm of computational geometry, in which the 21-year-old Demaine is one of the youngest and most accomplished practitioners. He also has a passion for puzzles of all kinds, developed during a childhood spent partly on the road with his father 鈥� a glass-blower, goldsmith, silversmith and puzzle maker.

You left school at the age of seven andspent the next five years on the road with your father. Why?

Mainly because it seemed like a fun thing to do. My dad, Martin, was a craftsman, which made it easy for him to travel and sell his stuff at craft fairs throughout the US. It was a very free-form existence. Our movements weren鈥檛 guided by anything more specific than 鈥淭hat seems like an interesting place to go.鈥�

What was the most important thing you learned in that time?

I learned a lot just from talking to people. My father always stressed communications skills, and that has served me well in academia. I鈥檓 not shy about approaching people to test out ideas. In fact, when I take on a big problem, that鈥檚 the first thing I do.

What happened to your formal education during those years of wandering?

My dad taught me from home-school manuals we got from an agency in Washington DC. When I was nine, it became more efficient for me to teach myself from the same materials. That approach worked well for everything but spelling, which is hard to test yourself on. But we figured out a system for that too.

Were you ever curious about what went on inside the classroom?

I checked out normal schools from time to time to make sure I wasn鈥檛 missing anything. My longest stint was a month in a Miami school because I was intrigued by a cute girl. But I left once I realised she had no interest in me. The main thing I learned was how much time is wasted in school. When you take away lunch, recess and other breaks, the nine-to-three day reduces to about one hour of real instruction. Home schooling is much more efficient. You get one-on-one training and can work right through summer when most kids forget everything they鈥檝e learned in the previous months.

When did you become interested in mathematics?

It started from playing video games when I was quite young. I asked my dad how people wrote those games, and he said you first have to learn how to write a computer program. He got hold of some books on programming so he could teach me, and soon I was reading the books on my own. After a year or so of that, he said, 鈥淚f you want to be good at computers, you have to be good at mathematics.鈥� So I said, 鈥淥K, let鈥檚 learn some mathematics.鈥� I started with a high-school algebra text, and things took off from there.

You must have learned a lot to have talked your way into Dalhousie University as a 12-year-old.

It makes it easier when you鈥檙e pursuing things you are interested in. But I still had to go through some political battles because of my age, plus the fact that I hadn鈥檛 been to high school. At the time, you had to be 16 to enter Dalhousie. After some discussion, they let me in under special status. During the summer I took some mathematics and computer science courses as a test and did well enough for them to admit me in the fall.

Do you feel any sort of age gap at MIT,being far younger than both your faculty colleagues and many of your students?

That鈥檚 becoming less of an issue now that I can go to bars legally, but age has never really been important in my life. Some people who accomplished a lot when they were young have stressed their age as a way of making their achievements stand out even more. I try to downplay the age thing because eventually everyone gets older.

What鈥檚 your father up to these days?

He鈥檚 a visiting scientist at MIT with an office in this lab. When MIT offered me a position, they offered him a position too, which was great. Sometimes we work together; other times we work separately. He has tried to keep up in mathematics, learning this stuff as I鈥檝e been learning it, but as I鈥檝e got deeper into the field our roles have changed somewhat. It鈥檚 amazing that he has come so far, given that he basically had to switch genres from art to mathematics, which is a pretty hard thing to do.

It must be especially hard for someone in his late 50s. People say you have to make your mark in mathematics before you turn 30.

I鈥檝e heard that too, but I don鈥檛 know where it came from, nor do I believe it. I can certainly imagine learning more slowly at some point, which is why I鈥檓 trying to learn as much as I can, as fast as I can. But I don鈥檛 see the process ending, and I hope to prove that saying untrue, though I can鈥檛 prove it with mathematical certainty.

Why do you list origami and computer programming as 鈥渉obbies鈥� on your resum茅, since they seem so close to what you do in your day job?

I make very little distinction between working and having fun, because work, for the most part, is fun. Still, when I have time, I like to make origami gifts. My hobby started after my research in this area, though most people do it the other way around. I also do computer programming for fun, even though it is part of my job. But my favourite hobby is juggling. For some reason, a lot of mathematicians like to juggle. There is even a mathematical theory of juggling. It鈥檚 all about timing, about how things go up and down.

I gather you are also interested in puzzles, and that you and your dad used to support yourselves partly through puzzle making.

We have always had a passion for puzzles. I think there is definitely a connection between puzzles and mathematics. With a puzzle, it鈥檚 usually clear what you have to do and the solution itself is often remarkably simple, yet finding it can be hard. Proving mathematical theorems is similar in many respects: the problem and the solution can be easy to understand, but finding the solution and proving it can be incredibly challenging. The solution, moreover, typically involves several pieces.

What was your first real accomplishment in mathematics?

Six years ago, when I began my PhD work in computational geometry at the University of Waterloo in Ontario, my dad remembered 鈥渢he paper cut problem鈥� from an article written in the 1960s on paper folding and mathematics. The idea is to take a piece of paper, fold it any way and as many times as you want, and then make one straight cut and see what shapes you get. The question is, are all shapes possible? I worked on this problem for two years at Dalhousie with my dad and adviser Anna Lubiw. After experimenting for a while, we realised you could make all kinds of shapes, such as butterflies, swans, hearts or stars. The hardest part was proving that any shape was possible.

How did you go about proving it?

That process, in a word, is mathematics.

What is your greatest preoccupation at the moment?

I鈥檝e been working on my favourite problem for the past five years, which is a long time for me. It has to do with a centuries-old question: what three-dimensional shapes can you make by successively folding a flat sheet? Questions like this come up regularly in the sheet-metal industry: how do you cut a sheet and then use bending machines to fold it in the right sequence? Theorists could make a big contribution here, but the mathematics is not yet fully developed.

What are you doing when you are not working on folding problems?

I like to have lots of things going on in parallel because you can easily get stuck on one problem and end up doing nothing. I prefer doing something. Only about half my work relates to the geometry of folding. I have a separate project that involves a new approach to organising data. My hope is to make web searches quicker and more efficient. Last week, a mathematician from Spain visited me and we looked at the classic problem in facility location: where, for instance, would you site 100 fast-food outlets to make them closest to the most people? I also work in combinatorial game theory, studying the complexity of computer games such as Tetris, which in fact is what got me into mathematics in the first place. My goal is to keep moving into new areas of mathematics and not be confined to a single branch.

Does it seem weird to you to have a tenured job and so much stability in your life, given your nomadic past?

I guess I鈥檓 getting used to it. Stability seems like a good thing to me, and I can鈥檛 see any downside. If you don鈥檛 want it, you can always throw it away.

But do you wonder whether your creativity might be hampered by being tied to a single place 鈥� even if that place happens to be MIT?

It鈥檚 true we moved around a lot when I was a kid and saw a lot of interesting things. But at this point I appreciate having a home base. If I get restless or feel stale, there鈥檚 a simple solution: it鈥檚 called travelling.