Incompleteness Theorem

Born #onthisday 118 years ago, Kurt Gödel was an Austrian mathematician and philosopher. Gödel discovered the “Incompleteness Theorem”, which essentially states that there will always be theorems in mathematics that are impossible to prove. Gödel''s discovery of the Incompleteness Theorems effectively drove a stake though the heart of Hilbert's Program [1] (or at least badly damaged it; see Hilbert's Second Problem [2]).

In 1949 Gödel demonstrated the existence of solutions to Einstein's field equations in General Relativity which involve "rotating universes" and featured closed timeline curves which allow for time travel to the past. Gödel's solutions are known as the Gödel metric and are an exact solution of the Einstein field equations [3].

Along with Aristotle, Alfred Tarski and Gottlob Frege, Gödel is considered to be one of the most significant logicians in history and had an immense effect upon scientific and philosophical thinking in the 20th century (and beyond).

Read more about Gödel's life and times here: https://mathshistory.st-andrews.ac.uk/Biographies/Godel.

References
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[1] "Hilbert’s Program", https://plato.stanford.edu/entries/hilbert-program/

[2] "Hilbert's second problem", https://en.wikipedia.org/wiki/Hilbert%27s_second_problem

[3] "THE GODEL SOLUTION TO THE EINSTEIN FIELD EQUATIONS", http://www.math.toronto.edu/~colliand/426/Papers/A_Monin.pdf

#godel #incompletenesstheorems #math #maths #physics