During his life Gödel received several prizes and honourable memberships (and rejected some others). Among the prizes he received are the Einstein Award (1951) and the National Medal of Science (1974). He was a member of the National Academy of Sciences of the United States, a fellow of the Royal Society, a member of the Institute of France, a fellow of the Royal Academy and an Honorary Member of the London Mathematical Society."
See entire biography @ The Kurt Godel Society
"Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.
Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers."
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