1928
Hilbert and Ackermann pose the Entscheidungsproblem
David HilbertDavid Hilbert — posed foundational questions for mathematics, including the Entscheidungsproblem. and Wilhelm Ackermann's 1928 textbook Grundzüge der theoretischen Logik gave the canonical statement of the EntscheidungsproblemHilbert's decision problem — whether every mathematical statement can be proved or disproved algorithmically. — whether an algorithm can decide if any logical formula is universally valid.
What it was for
The decision problem asked whether truth in first-order logic could be mechanized. Church and TuringAlan Turing — mathematician who defined computability, broke Enigma, and posed the imitation game. answered no in 1936; GödelKurt Gödel — his incompleteness theorems showed limits on what formal mathematics can prove. had already shown completeness of first-order logic in 1929. This 1928 text is the challenge statement that launched computability theory.
People
- David Hilbert — researcher
- Wilhelm Ackermann — researcher
Why it's here
The EntscheidungsproblemHilbert's decision problem — whether every mathematical statement can be proved or disproved algorithmically. is the explicit question Church and TuringAlan Turing — mathematician who defined computability, broke Enigma, and posed the imitation game. proved unanswerable.
Why it mattered
It turned philosophy-of-mathematics into a concrete problem about algorithms.
What it solved
Logicians lacked a precise target for what 'mechanical proof' should mean.
Media
ImageDavid HilbertPublic domain, via Wikimedia Commons