James Stirling Scottish mathematician. Date of Birth: 22.04.1692 Country: Great Britain

Biography of James Stirling

James Stirling was a Scottish mathematician who was born during a turbulent time in history. Four years before his birth, King James II, also known as James VII of Scotland, was overthrown. In 1707, Scotland was merged with England. When James was about 17 years old, his father was arrested as a Jacobite, a supporter of the ousted monarch, and accused of treason. Fortunately, his father was acquitted, but Jacobite uprisings continued for a long time.

Stirling received his education at Oxford and possibly in Glasgow. However, obtaining a diploma was hindered by the requirement to swear allegiance to the English queen, which Stirling vehemently refused to do. Now, the threat of arrest loomed over him. Stirling decided to leave for Italy, where he lived until 1722.

In Italy, Stirling began his scientific career. He published a work called "Newtonian Cubic Curves," where he studied algebraic curves of the third degree that had already been investigated by Newton. Stirling discovered four new types of these curves that Newton had not noticed. Additionally, his work proved several theorems that Newton had stated without proof. Stirling also explored the curve of fastest descent, the catenary, and solved the Leibnizian problem of orthogonal trajectories. He revealed that an algebraic curve of the nth order is determined by its n(n+3)/2 points.

Stirling initiated correspondence with Newton, sent him a copy of his article, and asked for help in finding employment in his homeland. In a friendly and welcoming response, Newton promised his assistance. Before the end of 1717, Newton published Stirling's aforementioned work, as well as another one titled "Newton's Method of Differences."

In 1724, Stirling arrived in London and worked as a lecturer while actively conducting mathematical research. In 1726, recommended by Newton shortly before his death, Stirling was elected as a member of the Royal Society. In 1730, Stirling published his most significant work, "Differential Methods," one of the first substantial textbooks on mathematical analysis. It not only covered the fundamentals of analysis but also presented many of Stirling's personal discoveries. The topics included infinite series, their summation and acceleration of convergence, integration theory (quadratures), interpolation, properties of the gamma function, and asymptotic representations. One of these representations, slightly modified by de Moivre, is now known as Stirling's formula. Some details of Stirling's research can be gleaned from his correspondence with de Moivre, Euler, and Cramer.

In 1733, Stirling published another important work called "Twelve Propositions on the Figure of the Earth." In 1735, he returned to Scotland after being invited to manage a mining company. While his administrative work was well-paid, it left him with little free time. The only published work during this period was related to mining ventilation problems. Stirling remained in this position until the end of his life.

In 1745, a new Jacobite rebellion occurred, which was unsuccessful but resulted in significant bloodshed. Stirling's sympathies for the rebels hindered his appointment to the chair of mathematics at the University of Edinburgh. In 1746, he was elected as a member of the Berlin Academy.

James Stirling passed away in 1770. The Stirling numbers and Stirling's formula were named in his honor.