Ferguson's mother died when he was about three and his father went off to serve in the Second World War. He was adopted by an Irish immigrant and raised in New York. He learned to work with his hands in an old-world style with earthen materials from his adoptive father who was a carpenter and stonemason by trade. An art-inclined math teacher in high school helped him develop his dual interests in math and art.
Ferguson was a graduate of Hamilton College, a liberal arts school in New York. In 1971, he received a Ph.D. in mathematics from the University of Washington. Ferguson and his wife, Claire, later moved to Utah, where he continued to teach math and she studied art at Brigham Young University. The couple raised their seven children—counting mathematicians, musicians, a software developer and a potter among them—while Ferguson was tenured at BYU for 17 years.
In 1977, Ferguson and another mathematician, Rodney Forcade, developed an algorithm for integer relation detection. It was first viable generalization of the Euclidean algorithm to three or more variables. A more notable integer relation detection algorithm he developed, the PSLQ algorithm, was selected as one of the "Top Ten Algorithms of the Century" by Jack Dongarra and Francis Sullivan.
In January 2014, Ferguson and his wife Claire Ferguson delivered an MAA Invited Address, titled “Mathematics in Stone and Bronze,” at the Joint Math Meetings in Baltimore Maryland. He is an active artist, often representing mathematical shapes in his works. One of the first bronze torii sculpted by Ferguson was exhibited at a computer art exhibition in 1989 at the Computer Museum in Boston. His most widely known piece of art is a 27-inch (69 centimeters) bronze sculpture, Umbilic Torus. In 2010, the Simons Foundation, a private institution committed to the advancement of science and mathematics, commissioned him to create the Umbilic Torus SC, a massive 8.5 meter-high cast bronze and granite sculpture weighing more than nine tons. With its installation completed in 2012, the torus sculpture was donated to Stony Brook University, in Long Island, N.Y., and sits outside the Math and Physics buildings of the same university, near the Simons Center for Geometry and Physics. Mounted on a stainless steel column, the torus has a 7.7 meter diameter as the granite base, where various mathematical formulas defining the torus are inscribed. TO create the humongous sculpture, Ferguson wrote a program consisting of 25,000 movements to control a 16-by-20 robot arm and its affixed foot-long industrial diamond-encrusted cutting tool.
- helaman ferguson sculpture: the artist
- The Best of the 20th Century: Editors Name Top 10 Algorithms by Barry A. Cipra; SIAM News, Volume 33, Number 4
- PSLQ Algorithm
- An Algorithm for the Ages: PSLQ, A Better Way to Find Integer Relations
- Helaman Ferguson, "Two Theorems, Two Sculptures, Two Posters", American Mathematical Monthly, Volume 97, Number 7,August–September 1990, pages 589-610.