Short answers, pulled from the story.
Joseph-Louis Lagrange was an Italian-born mathematician and physicist who lived from the 25th of January 1736 to the 10th of April 1813. He is known for founding the calculus of variations, developing Lagrangian mechanics, discovering the Lagrangian points in celestial mechanics, and proving that every positive integer is the sum of four squares.
The Lagrangian points are five special positions in space where a small object can maintain a stable position relative to two larger orbiting bodies. Lagrange identified these solutions to the three-body problem in 1772, studying the Earth, Sun, and Moon system. They are now used to position space telescopes and satellites.
Lagrange was born and educated in Turin, where he became mathematics assistant professor at the Royal Military Academy in 1755. In 1766 he moved to Berlin at the invitation of Frederick the Great and spent over twenty years at the Prussian Academy of Sciences. In 1787 he moved to Paris, where he lived until his death in 1813.
The Mécanique analytique, first published in 1788, is Lagrange's comprehensive reformulation of classical mechanics using the calculus of variations. It derived all of mechanics from the single principle of virtual work and introduced the method of generalized coordinates. Sir William Rowan Hamilton described it as a scientific poem, and it formed a foundation for mathematical physics in the nineteenth century.
After Antoine Lavoisier's execution in 1794, it was largely Lagrange who influenced the commission of 1799 to adopt the metre and kilogram with decimal subdivisions. He was also a founding member of the Bureau des Longitudes in 1795 and was involved in the broader decimalisation process in Revolutionary France.
When a decree in October 1793 ordered all foreigners to leave France, Lagrange was specifically exempted by name, partly through the intervention of Antoine Lavoisier. Though he had been preparing to flee, he was never in danger. Different revolutionary governments and later Napoleon continued to honour him, and he was appointed senator in 1799.