The Tasker Funeral Home confirms that Appel, who was diagnosed with esophageal cancer, died April 19 in hospice care.
Appel was a longtime educator who chaired the University of New Hampshire mathematics department, retiring in 2003.
Before that, he was a faculty member at the University of Illinois at Urbana. In 1976, he and Wolfgang Haken used 1,200 hours of calculations from an IBM computer to prove that a flat map can be colored with just four colors so that contiguous countries have different colors.
Proving the 100-year-old "Four-Color Conjecture" was considered a major intellectual accomplishment.