Charles Babbage was born in London, England, to Benjamin Babbage, a banker, and Betsy Plumleigh Teape. His early life was marked by periods of illness and private tutoring, during which his mathematical talents began to emerge. His privileged background provided access to resources and education that fostered his intellectual curiosity.

Babbage entered Trinity College, Cambridge, where he found himself ahead of his tutors in mathematical knowledge. Dissatisfied with the level of mathematics education, he, along with John Herschel and George Peacock, founded the Analytical Society. This group aimed to introduce Leibnizian notation and continental calculus to British mathematics, which was still primarily using Newtonian notation. This demonstrates his early drive to reform and improve existing systems.

At the young age of 24, Babbage's growing reputation as a mathematician and his contributions to the field led to his election as a Fellow of the Royal Society. This prestigious recognition marked a significant milestone in his career and provided him with further opportunities to pursue his research and ideas within the scientific community.

Babbage conceived the idea of the Difference Engine, a mechanical calculator designed to automatically compute and tabulate polynomial functions. This invention arose from his frustration with the errors found in hand-calculated mathematical tables, which were crucial for navigation, astronomy, and engineering. He received government funding to build a working model, initiating a long and ultimately unsuccessful endeavor.

Babbage held the prestigious position of Lucasian Professor of Mathematics at Cambridge University, a chair previously held by Isaac Newton. Ironically, despite holding this prominent academic role, he never delivered a single lecture. This period reflects his increasing focus on his mechanical calculating machines and his growing estrangement from traditional academic pursuits.

Babbage envisioned a much more advanced machine than the Difference Engine: the Analytical Engine. This general-purpose mechanical computer incorporated an arithmetic logic unit (the 'mill'), a control unit based on punched cards (inspired by the Jacquard loom), and a memory store (the 'store'). The Analytical Engine is considered the conceptual predecessor to the modern digital computer. Ada Lovelace, a friend of Babbage, wrote extensive notes on the Analytical Engine, which included what many consider to be the first computer algorithm, making her arguably the first computer programmer.

Italian mathematician Luigi Menabrea published a description of the Analytical Engine based on a lecture given by Babbage. Ada Lovelace translated Menabrea's article into English and added extensive notes of her own. Her notes described how the Analytical Engine could be programmed to perform various calculations, including Bernoulli numbers, and articulated a vision of the machine's potential beyond mere number crunching.

Charles Babbage died in London at the age of 79. Despite dedicating much of his life and personal fortune to developing his calculating machines, neither the Difference Engine nor the Analytical Engine was fully constructed during his lifetime due to technological limitations and funding withdrawals. However, his designs and ideas were later recognized as groundbreaking and influential, paving the way for the development of modern computers in the 20th century.