Hariot (or Harriot) is best known as a pioneer figure in the British school of algebra, although his interests and activities were very wide ranging. Born in Oxford, he was an associate of Sir Walter Raleigh, whom he accompanied on a voyage to Virginia (1585–86) in the capacity of navigator and cartographer. He later wrote a book about this journey – A Briefe and True Report of the New Found Land of Virginia (1588). Among his many innovations in algebra Hariot introduced a number of greatly simplified notations. His central mathematical achievements were in the theory of equations where he discovered important relationships between the coefficients of equations and their roots. This work was published in his Artis analyticae praxis ad aequationes algebraicas resolvendas (1631; The Analytical Arts Applied to Solving Algebraic Equations).

Outside mathematics Hariot's achievements as a practical astronomer were noteworthy. He designed and constructed telescopes and made detailed studies of comets and sunspots. Independently of Galileo he discovered the moons of Jupiter. Hariot also discovered the law governing the refraction of light. He was granted a pension by the earl of Northumberland and was briefly imprisoned along with the earl during the Gunpowder Plot of 1605. Hariot conducted numerous experiments in a variety of fields including optics, ballistics, and meteorology. However he published few of his discoveries and it was only after his death that their extent was realized from his voluminous notes and papers.