Odd at Heart

A problem proposed by Charles W. Trigg in the Spring 1970 issue of the Pi Mu Epsilon Journal (Volume 5, Number 4):

The digits 1-9 can be arranged in a square array so that the digits in no column, row, or long diagonal appear in order of magnitude:

trigg pmej paritypuzzle

Prove that, however this is done, the central digit must be odd.

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