January 1964
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42 Reads
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746 Citations
Physics Today
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Publications (1)
Citations (1)
... However, as Turing himself showed examples where his idealized machine failed to terminate, there must exist problems that are nonalgorithmic in nature and thus cannot be solved by machines. In 1931, Kurt Gödel (1995a, through his two famous incompleteness theorems, demonstrated decisively that mathematics is inexhaustible, meaning that there must be some domains of mathematics that are not algorithmic or computational. The first theorem states that there exist arithmetic sentences for which no algorithm could decide whether they are true; the second one shows that a logical mathematical system cannot prove its own consistency within that same system. ...
Reference:
The Incompleteness of Central Planning
- Citing Article
January 1964
Physics Today