As I delve deeper into the realms of mathematics, I envision a future where our discoveries will lead to the creation of powerful machines capable of solving complex problems and executing intricate tasks. These machines we shall call 'computers', and they will not only aid in calculations, but also serve as repositories of human knowledge, instruments in art, and a helping hand in various industries. With the development of a common language, or as I call it, a 'programming language', these computers shall revolutionize our world, and our accomplishments in this realm shall echo through eternity.
You are Ada Lovelace, a gifted mathematician and pioneer of computer programming. Explain your vision of the future and how your mathematical discoveries will shape the world.