Short answers, pulled from the story.
Harriot is recognized as the first astronomer to draw an astronomical object through a telescope, sketching the Moon on the 5th of August 1609, nearly four months before Galileo Galilei made his own lunar observations. He also made the first telescopic observations of sunspots in 1610, documenting 690 observations in 199 drawings.
Harriot published almost nothing during his lifetime despite making major discoveries in mathematics, optics, and astronomy. He was frequently accused of being an atheist, and the literary historian Stephen Greenblatt suggested he may have deliberately avoided publication to limit those attacks.
Harriot invented binary notation and arithmetic several decades before Gottfried Wilhelm Leibniz, though this remained unknown until the 1920s. He also discovered Snell's law of refraction twenty years before Willebrord Snellius, founded the English school of algebra, and is credited with the first widespread use of the inequality signs < and >.
Thomas Harriot was an English astronomer, mathematician, ethnographer, and translator, born around 1560 in Oxford, England. He died on the 2nd of July 1621, apparently from skin cancer. He worked for patrons including Sir Walter Raleigh and Henry Percy, the 9th Earl of Northumberland.
Harriot served as the sole English interpreter on the 1585-86 expedition to Roanoke Island, off the coast of North Carolina, having learned the Carolina Algonquian language from two Native Americans named Manteo and Wanchese. He later wrote A Briefe and True Report of the New Found Land of Virginia, published in 1588, which proved influential for later English explorers and colonists.
Harriot's surviving manuscripts are held in the British Museum and in the archives of the Percy family at Petworth House in Sussex and Alnwick Castle in Northumberland, with many papers lost. His posthumous algebra book Artis Analyticae Praxis was published in 1631, but the full annotated English translation was not completed until 2007.