David Meyer<dmm>:
Born #onthisday 118 years ago, Kurt Gรถdel was an Austrian mathematician and philosopher. Gรถdel discovered the โIncompleteness Theoremโ, which essentially states that there will always be theorems in mathematics that are impossible to prove. Gรถdel''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 Gรถdel 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. Gรถdel's solutions are known as the Gรถdel metric and are an exact solution of the Einstein field equations [3].
Along with Aristotle, Alfred Tarski and Gottlob Frege, Gรถdel 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 Gรถdel's life and times here: https://mathshistory.st-andrews.ac.uk/Biographies/Godel.
References
--------------
[1] "Hilbertโs 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
https://mathstodon.xyz/@dmm/112349313059106134
Born #onthisday 118 years ago, Kurt Gรถdel was an Austrian mathematician and philosopher. Gรถdel discovered the โIncompleteness Theoremโ, which essentially states that there will always be theorems in mathematics that are impossible to prove. Gรถdel''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 Gรถdel 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. Gรถdel's solutions are known as the Gรถdel metric and are an exact solution of the Einstein field equations [3].
Along with Aristotle, Alfred Tarski and Gottlob Frege, Gรถdel 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 Gรถdel's life and times here: https://mathshistory.st-andrews.ac.uk/Biographies/Godel.
References
--------------
[1] "Hilbertโs 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
https://mathstodon.xyz/@dmm/112349313059106134
Maths History
Kurt Gรถdel
Gรถdel proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system.
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