Gödel's Incompleteness Theorems
In any system of arithmetic strong enough to be useful, there are true statements it can never prove. Including this one.
193125 min read
British mathematics and the theory of computation
Alan Turing
1912 – 1954
British mathematician who in 1936 defined the abstract machine model that bears his name, proved that no machine can decide whether an arbitrary machine halts, and used that result to settle Hilbert's Entscheidungsproblem in the negative. His argument recast Gödel's incompleteness as a fact about computation, and founded computer science in the process.
2 entries
The Halting Problem
No program can ever be written that reliably tells you whether another program will finish running. This is not a limit of our cleverness.
193620 min read