Augustus De Morgan was a 19th century mathematician and logician who made significant contributions to the fields of algebra, logic, and probability. His work laid the foundations for modern mathematical logic and set theory, and his ideas continue to influence mathematics and computer science to this day.

One of De Morgan's most important contributions was his development of the algebra of logic, which he used to prove the validity of logical principles and to solve logical problems. He developed a system of symbolic notation to represent logical statements and used it to define the laws of logic, such as the principle of non-contradiction and the principle of excluded middle. He also developed the concept of a logical function, which is a function that takes one or more input values and returns a single output value based on a set of logical operations.

In addition to his work in logic, De Morgan made significant contributions to the field of algebra. He developed a system of algebraic notation that is still in use today, and he introduced the concept of a negative number. He also made significant contributions to the development of the theory of equations, and his work on the theory of matrices laid the foundations for modern linear algebra.

De Morgan was also interested in probability and statistics, and he made several important contributions to these fields as well. He introduced the concept of a distribution function, which is a mathematical function that describes the probability of a random variable taking on a particular value. He also developed a method for calculating the probability of an event occurring based on the probabilities of individual outcomes, which is now known as De Morgan's rule.

In addition to his contributions to mathematics and logic, De Morgan was also a pioneer in the field of computer science. He was one of the first to propose the use of machines to perform calculations, and he developed a machine that could perform simple arithmetic operations. This machine, known as the De Morgan Calculator, was an early prototype of the modern computer and helped to pave the way for the development of more advanced computing systems.

Overall, Augustus De Morgan's contributions to mathematics, logic, and computer science have had a lasting impact on these fields and continue to be studied and applied today. His work laid the foundations for modern mathematical logic and set theory, and his ideas continue to influence the way we think about and use mathematics in the 21st century.