Crandall: the ideas behind the machinesF24, the 24th Fermat number, has represented a significant conceptual challenge to mathematicians for more than 200 years. It was considered impossible to determine elementary properties of this immense, 5-million-digit number_the 24th in a series of numbers originated by Pierre Fermat in the seventeenth century_and it was unknown whether or not F24 is prime until now, thanks to the worK of Richard Crandall '69 and a team of research colleagues.
Crandall is Howard Vollum Adjunct Professor of Science, physics, and directs the Center for Advanced Computation (CAC) at Reed. He and his research partners_Ernst W. Mayer, formerly on the engineering faculty of Case Western Reserve University, and Jason S. Papadopoulus, a graduate student in the electrical engineering school at the University of Maryland, College Park_have completed the deepest computation ever performed in history for a single, yes-no answer; it is roughly the same computational effort as Pixar's entire rendering of A Bug's Life. "With that much computational effort, actually 100 quadrillion machine operations, you either get a full-length Disney-Pixar movie or you get this one-bit answer," Crandall said.
Crandall has been instrumental in the development of algorithms allowing the resolution of F24 and other thorny mathematical problems. One of Crandall's algorithms, called the irrational base discrete weighted transform (IBDWT), has been used to speed the search for gigantic prime numbers. In fact, this algorithm formed the basis for discovery of the three most recent record prime numbers, including the record-setting prime proved in June of this year.
Practical applications of prime numbers are surprisingly many and various. Crandall, recently named distinguished scientist by Apple Computer, is a leader in the use of primes in cryptography. He pioneered the use of fast elliptic encryption, a powerful scheme using Mersenne primes. These numbers are frequently used for encoding sensitive data, such as credit card numbers transmitted over the internet. Primes are also used on Wall Street for the generation of risk management and economic predictions. They appear in music theory and may underlie certain biological rhythms as well, such as the 13- and 17-year cycles governing the emergence of cicadas.
Crandall himself is now retired from tenure at Reed, but still teaches a course in scientific computation. He regards his current post as director of the CAC as part of the natural trajectory of his career. "After initiating Reed's strategic computation plan with former Reed president Paul Bragdon and other members of the faculty, I started forging more and more linkages with industry and technology friends of the college," he said. "More and more I came to depend on resources like computing power and access to engineering colleagues. I started doing computational science using resources that are not available at any liberal arts college."
He went on to join NeXT Software and has continued in that vein, working with several companies such as Apple and Pixar. The IBDWT was actually a by-product of research into cryptography performed at NeXT. In addition, he is currently preparing a textbook, Prime Numbers: A Computational Perspective (Springer-Verlag, 2000), with University of Georgia theorist Carl Pomerance.
"I now have about five careers going but I do not feel hard-pressed. Once retired, always retired. In some ways I feel like a butterfly, who having breached the cocoon suddenly enjoys all this new freedom," he said. Citing his nonstandard relationship with the college and with industry, he proposed that his own activities might help others establish similar positions: "In my proudest moments I feel like I might be paving the way for someone in the future," he said, "someone whose work is most efficient if it crosses interdisciplinary boundaries or even_dare I say it_engages the outer academic boundary."
By Mike Axley '94