Thomas Harriot (1560-1621) may be best known as the navigator and scientist for Sir Walter Ralegh’s 1585-1586 expedition to the Virginia Colony, but he also was the leading English mathematician of his day. Harriot made important discoveries in a wide range of mathematical sciences, including algebra, geometry, navigation, astronomy, and optics. He published only one work during his
lifetime, A Briefe and True Report of the New Found Land of Virginia (1588), but, at his death, left thousands of manuscript pages of mathematics. Harriot’s mathematical work is remarkable both in its content – he obtained many results generally credited to later mathematicians – and in its highly visual and symbolic presentation. We examine Harriot’s results on figurate numbers, finite differences, and interpolation in his unpublished treatise, DeNumeris Triangularibus et inde De Progressionibus Arithmeticis. We also examine some of Harriot’s work on algebra (polynomial equations and their roots), Pythagorean triples, and combinatorics, focusing on his very clear and visual presentation of his work and offering, when available, his contemporaries’ reactions to his style of presentation. We invite reaction from the audience as to the effectiveness of such presentation in communicating mathematics for us and for our students today.