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Harriot was a mathematician and astronomer who founded the English school of algebra.
From 1580 to 1598 he was a tutor and mathematics advisor to Sir Walter Raleigh. After a trip to Virginia for Raleigh, Harriot published A Briefe and True Report of the New Found Land of Virginia (1588). He became the leading scientist in the circle around Raleigh.
His mathematical work included the introduction of simplified notation for algebra and research on the theory of equations. Harriot invented many symbols used today. For example he used . for multiplication, < for less than and > for greater than. He influence Viète and some of his notation and ideas reach us through Viète's work.
Harriot did outstanding work on the solution of equation, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution. He made the observation that if a, b, c are the roots of a cubic then the cubic is (x-a)(x-b)(x-c) = 0. This is a major step forward in understanding which he carried forward to equations of higher degree.
He was far ahead of his time but his work had far less influence than it should since he published no mathematical work in his lifetime. His Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas (1631) was published 10 years after his death and was edited by people who did not fully appreciate the depth of his work. We know of Harriot's work mainly through the algebra book of Wallis.
In astronomy, Harriot made the earliest telescopic observations in England. He discovered sunspots and the moons of Jupiter independently of Galileo but did not publish his discoveries. He discovered the refraction of light before Snell but again failed to publish.
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