Caroline Lucretia Herschel was a towering early contributor to the science of astronomy. The asteroid 281 Lucretia and the lunar crater C. Hershel are named after her. Since women were not allowed membership, she was elected an Honorary Member of the Royal Astronomical Society and of the Royal Irish Academy. She was awarded a gold medal by the Royal Astronomical Society in 1828 and, on her 96th birthday, a gold medal for science by the King of Prussia was conveyed to her by Alexander von Humboldt, “in recognition of the valuable services rendered to Astronomy by you, as the fellow-worker of your immortal brother, Sir William Herschel, by discoveries, observations, and laborious calculations”.

**She was also the first woman in the modern era to get paid to do science.**

King George III of England awarded her the paid post of assistant to the royal astronomer (her brother William Herschel) with a yearly salary of fifty pounds — a respectable sum at the time. Caroline Herschel’s discoveries include over 500 stars, eight comets, and a number of “nebulae” — which we now call galaxies. She also completed, with her brother, an extensive catalog, correcting and extending earlier works, that was the cited reason for her first medal. This woman was an extraordinary scientist in an era when women were, for the most part, barred from being scientists. She did a great deal to support her brother’s work as well as incredible amounts of meticulous record keeping and organization. In essence, Caroline Herschel did for William what complex assemblies of microchips do for modern astronomers. All this, while also taking care of her brother for the first half of his life.

Astronomy is a deeply mathematical science, motivating a good deal of the early development of mathematics. The meticulous observations of Nicolaus Copernicus, over two centuries before Caroline Herschel worked, permitted Johannes Kepler to dismiss the notion that planetary bodies had orbits composed of awkward compilations of perfect circles (*epicycles*) and were instead elliptical. This, in turn, led to the discovery that orbits were conic sections and the mathematical deduction that the shapes made by slicing cones with a plane were the shapes one body orbiting another must follow if no other forces act. Shown below are the three possible conic-section orbits (1) the parabola, (2) the ellipse (including the circle), and (3) the hyperbola. Determining which of these shapes an object orbiting our sun follows requires piles of tricky mathematical calculation.

Navigation is a highly mathematical enterprise and it relies on a solid working knowledge of astronomy. Before radio and satellite technology, the position of a ship on the earth was determined by celestial navigation which required both knowledge of the position of bodies in the heavens and a very accurate clock. This means that Caroline Hershel’s work was part of a body of science that not only advanced knowledge, but was of commercial and military importance.

There have been many recent milestones for women in space science. In 2015 Katherine Johnson was awarded the Presidential Medal of Freedom. In 2016, Margaret Hamilton, whose accomplishments included saving one of the Apollo moon landings with really good software, also won the Presidential Medal of Freedom. The year 2016 also marked the death of Vera Rubin who was the next woman after Caroline Herschel to be awarded the Royal Astronomical Societys gold medal (in 1996) for the discovery of what turned out to be dark matter. Caroline Herschel was the matriarch of the women of space science, one of the early lights in the inclusion of all types of people in the twin enterprises of science and mathematics.

Occupy Math has the goal of letting as many people in on math as possible. Caroline Hershel was from a musical family and was building a career when her brother dragged her off into astronomy. Once she got there she proved not only to enjoy one of the most mathematical of the sciences, but also to have remarkable talent at it. Her successor, Vera Rubin, who faced only discrimination and prejudice, not complete non-personhood, was able to encourage young women to study science and take up scientific careers. Change is inevitable, but it is possible for people to stack the deck in favor of change for the better. One change that is badly needed is to get rid of the myth that women are bad at math.

Occupy Math with now repeat his perennial call for suggestions of other worthy individuals who have done good service in the cause of mathematics. Remarkable people abound and that includes people with remarkable mathematical ability and insight. If you have a good subject for a future Occupy Math, please comment or tweet! Happy New Year!

I hope to see you here again,

Daniel Ashlock,

University of Guelph,

Department of Mathematics and Statistics