Thomas Harriot invented the signs for "greater than" (>) and "less than" (<) in use today, and was one of the first mathematicians to use a number of now-commonplace symbols. Much of his work involved astronomy, navigation, and geometry: an employee and associate of Sir Walter Raleigh (1554-1618), he was at the center of English efforts to conquer the seas and the New World.
Harriot was educated at St. Mary's Hall, Oxford University, from whence he received his B.A. in 1580. For a time, he appears to have worked as a mathematics tutor in London before securing employment with Raleigh in 1584. The famous gentleman-explorer needed someone to teach navigation to his sailors, and for this purpose Harriot composed a manuscript—long since lost—called the Articon.
During the following year, Raleigh sent Harriot with a group of colonists to Roanoke Island off the coast of what is now North Carolina. (These were not the inhabitants of the famous "Lost Colony": the first settlement lasted only 10 months before being disbanded, and the doomed Lost Colony settlers arrived in 1587.) Working with artist John White (d. 1593?), Harriot was responsible for studying the indigenous peoples, as well as the local vegetation, animal life, and other natural resources. He published A Briefe and True Report, an account of his findings, in 1588.
During the three decades that followed, Harriot's patrons—first Raleigh and then Henry Percy, Earl of Northumberland (1564-1632), for whom he went to work in 1595—ran afoul of the English royal house. Harriot himself, though occasionally caught up in the turmoil even to the extent of being accused of atheism in 1603, in general passed the time unscathed, and continued his scientific observations. He studied the parabolic path of projectiles; determined the specific weights of materials; calculated the areas of spherical triangles, and thus confirmed that the Mercator projection preserves angles; independently discovered the sine law of refraction associated with Willebrord Snell (1580-1626); built telescopes; and in 1607, long before the birth of Edmund Halley (1656-1742), observed what came to be known as Halley's Comet.
As an astronomer, Harriot also made a map of the Moon (1609), calculated the orbits of Jupiter's moons (1610-12), studied sunspots and the Sun's rotation speed (1610-13), and observed another comet (1618). In his writings as a mathematician, not only did he become the first to use > and <, he was one of the first to adopt the plus sign and minus sign, lowercase letters for variables, and the equal sign of Robert Recorde (1510-1558). He was also among the first to write an equation with the sum of all terms equal to zero, as is common today.
For a decade, from the mid-1580s to the mid-1590s, Harriot had lived on an Irish property granted him by Raleigh. From 1595, however, he had resided at Northumberland's estate at Syon, and continued there even after Northumberland was arrested by King James in 1605. By the time his patron was released from the Tower of London in 1622, Harriot was dead, having succumbed to a cancer of the nostril on July 2, 1621. (Raleigh was dead, too, executed by James in 1618.) Harriot left behind a vast array of papers, many of them published as Artis analyticae praxis, a significant algebra text, in 1631.