In his work as a clockmaker and astronomer, Joost Bürgi needed accurate mathematical information, and for this reason developed the concept of logarithms into a practical method of computation. He did this as much as a decade before John Napier (1550-1617), the Scottish mathematician generally credited with the foundational work in logarithms; but because Bürgi did not consider himself a mathematician, he waited to publish his findings in 1620, long after Napier. Thus Bürgi was destined to become much less famous than either Napier or his young assistant, Johannes Kepler (1571-1630).
Bürgi has the distinction of being one of the few people in world history from Liechtenstein, a principality smaller in area than Washington, D.C. At the time of his birth in 1552, however, the region was still part of the German-controlled Holy Roman Empire. He probably received little in the way of a formal education, since he was unable to read Latin, the language of educated men during that era, but from an early age he excelled in the practical realm of clockmaking. In 1579, 27-year-old Bürgi received an appointment as court watchmaker for Duke Wilhelm IV of Kassel, a city in what is now western Germany.
The art and science of making and maintaining clocks was very much in its infancy then, but rulers and merchants quickly recognized the importance of these skills; thus Bürgi's position was analogous to that of a youthful computer whiz in the 21st century. Just as the latter might go to work for a major corporation to avail himor herself of the company's resources and equipment, Bürgi made use of the duke's observatory for astronomical work. Not only did he build clocks, but he developed instruments for making astronomical measurements, among them a proportional compass that in some respects improved on a similar instrument constructed by Galileo (1564-1642).
His most important work while at Duke Wilhelm's court, however, was his computation of logarithmic tables. Bürgi did not approach this as a theoretical problem, but as a practical one: in order to process astronomical data, he needed to make computations quickly. Thus as early as 1584, he began making improvements to the existing system of prosthaphairesis, a method of applying trigonometric formulae to problems as a means of converting multiplication to addition. Eventually he chanced on the idea of logarithms, exponents that indicate the power to which a number is raised to produce a given number. These would greatly facilitate quick multiplication, and to this end, Bürgi compiled an extensive logarithmic table.
Eventually Rudolf II, a Holy Roman emperor noted as much for his mental instability as for his interest in science, took an interest in Bürgi. Upon the death of Wilhelm, Rudolf summoned Bürgi to his court, and gave him Kepler as an assistant. Arriving in 1603, Bürgi again set to work in the observatory, working on astronomical calculations and the development of better instruments for measuring. Among Kepler's unpublished notes are papers containing evidence that Bürgi used the decimal point, and improved on a method for calculating the roots of algebraic functions.
Bürgi remained at the court of the Holy Roman emperor after the unstable Rudolf ceded power to his brother, Matthias, in 1606, and again after Ferdinand II succeeded Matthias in 1619. His stint at the court lasted until 1631, at which point he returned to Kassel, where he died a year later. By then Napier, who had published two works on logarithms and established himself as the mathematician who developed them, was long dead. The sole complete copy of Bürgi's logarithmic table is in a library in Gdansk, Poland.