Changing society one math problem at a time

Dr. Anton Betten is an associate professor of mathematics at Colorado State University (CSU). Betten is active in an area of mathematics that uses large-scale computing to produce results. He created a C++ program called Orbiter that can run jobs on the Open Science Grid (OSG) using the OSG Connect service. Orbiter can be used to classify discrete structures from finite geometry like graphs, codes, designs and objects. Recently, Betten used Orbiter on the OSG to run around 130,000 separate jobs in batches of about 10,000 jobs per day. Each job takes around 50 minutes to run, and he has been pleased with the results.


Math Department at Colorado State University

Dr. Anton Betten
Photo courtesy of Colorado State University

 

Betten first learned of the OSG through the Renaissance Computing Institute in North Carolina.  “I am grateful for their help in getting acquainted with the OSG,” says Betten.  Later, Betten made use of OSG Connect, one of the OSG gateways.

The types of problems that attract Betten are those that would be hopeless if you tried to solve them using only pencil and paper. “I’m using the computer to do the hard work,” Betten says. “Once the data come back from the computer, we try to see patterns and find interesting constructions—we try to understand what’s going on. We have a Cray here at CSU with 2,000 cores that I haven’t tried yet. I could monopolize it for a long time to do what I can do overnight on the OSG. The OSG is useful because I can program a large number of jobs to run at the same time. I start with one script, run 10,000 jobs, and by the next day 90% of them are done.”

Betten admits that in doing large-scale computing, he is in the minority in mathematics. “Most mathematicians work on small, local machines,” he says. “Their training is not in computer science, and they don’t want to spend a lot of time on the computing side.” Betten is comfortable with both—he first studied computer science, then switched to mathematics and began studying math that was computational. During his graduate student years, he learned about combinatorics, the study of finite or countable discrete structures. Betten received his Ph.D. from Bayreuth University in Bayreuth, Germany. He joined CSU in 2002. “When I moved to the United States, I found more academic freedom and kept my computational interests going,” Betten added.

“I think of the type of work that I do as an experimental approach to math, like that in physics,” Betten added. “We run experiments to see what is out there. Sometimes, those of us in this field have no clue what will come back. The only way to find something is to run a program, just like running an experiment in science. The computations are enormous, and the amounts of data are huge. It’s like a farm where we grow our own data. We harvest it and look for interesting mathematical structures and then we can write mathematical papers based on what we find.”

One of the challenges Betten faces is getting the algorithms right. “They have to be fast,” he says. “I run small jobs on my own computer to see how they do, and then they are ready to be put on the big iron. Another challenge is not just the research but also how to fit this into the day-to-day work of teaching classes. I don’t have a month straight to do some work. I have a few hours here and there.”

“Societally, mathematicians are often in a box,” notes Betten. “The general public often doesn’t know what is going on in that box and perhaps they don’t really want to know. But, they should know that the information technology revolution is all about math. None of it would be possible without math. We care about our iPhone but everything about it is math. Math is behind internet security and credit card security—all hot-button issues right now.”

Betten likes pushing math forward using computers. He wrote Orbiter himself, but points out that it relies on the work of others before him. He is getting some requests for his software, but says it’s difficult for mathematicians to understand C++ if they are not familiar with it. “Mathematicians like systems like Maple or MATLAB where they can just type,” he added. “That’s not enough for me because these systems are closed. So, I came up with my own software, starting during my graduate student years 20 years ago. Hopefully, it will be of use to others.”

Betten says that Orbiter is especially useful in the area of combinatorics, where boundaries are not clearly defined. One of the Millennium Prize Problems stated by the Clay Mathematics Institute is the question of P versus NP (according to Wikipedia: “whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer”). “Isomorphism testing of combinatorial objects is one of the instances on which this question hinges,” notes Betten. “I am not trying to decide the Millennium Prize Problem. I am asking the follow-up question: If P is not equal to NP, then we know that we cannot find fast algorithms to solve certain problems in combinatorics. So, what are we going to do then? My work is focused on efficient algorithms that will come in handy if those types of problems need to be solved. Efficient is the next best thing when fast is impossible. I don’t like to sit there waiting until someday P versus NP is resolved. We need answers now.”

~ Greg Moore and Sarah Engel