Mary Cartwright was a British mathematician who made significant contributions to the field of mathematics in the 20th century. She was born in 1900 in London and attended St. Hugh's College, Oxford, where she earned a degree in mathematics in 1921. Cartwright was the first woman to be elected a Fellow of the Royal Society in 1945. She was also the first woman to be appointed a professor of mathematics at the University of London in 1948. Cartwright's research focused on the theory of functions of a complex variable, and she made important contributions to the field of numerical analysis. She was the first to prove the existence of what is now known as the Cartwright-Littlewood theorem, which states that a function of a complex variable can be represented as a sum of two functions, one of which is analytic and the other of which is continuous. She also developed the theory of singular functions, which are functions that are not differentiable at certain points. Cartwright was a pioneer in her field and her work was highly influential in the development of modern mathematics. She was awarded numerous honors for her work, including the Sylvester Medal from the Royal Society in 1947 and the De Morgan Medal from the London Mathematical Society in 1948. She was also the first woman to be awarded the Royal Medal of the Royal Society in 1965. Mary Cartwright's legacy lives on in the field of mathematics and her work continues to be studied and appreciated by mathematicians around the world.