Briggs was born in 1561 at Yorkshire, England. Selecting mathematics for his major course of study, he attended Cambridge University and went on to receive his master's degree in 1585. Seven years later, Briggs began to lecture at Cambridge, but left in 1596 to become the first professor of geometry at Gresham College in London. He later lectured at Oxford University from 1619-1630. Briggs kept up-to-date on the latest developments in mathematics and was greatly enthused to learn of John Napier's discovery of logarithms through the publication of logarithmic tables in 1614.

After studying the logarithmic tables, which simplified calculations of large numbers. Briggs was amazed by their simplicity, although somewhat embarrassed that he had not come across the concept himself. He began to employ the use of logarithms in his teachings and also encouraged others to make use of them in their work. Wishing to meet Napier in person in order to discuss a possible improvement to the tables, Briggs journeyed to Edinburgh, Scotland, to meet with Napier in 1616. A friend present at their initial meeting relates that Briggs and Napier spent fifteen minutes gazing in admiration at each other before either spoke a word.

Briggs stayed with Napier for a month, discussing possible improvements and new ideas. Briggs proposed to simplify the logarithms by using base ten, a recommendation with which Napier heartily agreed. Briggs began the enormous task of computing the new tables, but exhaustion forced him to abandon the project in 1624. Although only partially completed, less than 0.04 percent of Briggs' tables contained errors.

Briggs returned to his work at Oxford University, where he held the position of professor of astronomy. In addition to his work on logarithms, Briggs was influential in promoting the common use of the method of long division, which has been a major aid to mathematics. Briggs died at Oxford in 1630.