Geometric Proliferation

by Katharine Merow 

note: This poem appeared in the November 2007 issue of the Mathematical Association of America's Math Horizons.

Saccheri guessed, and Gauss kept mum,
But Bolyai spread the news:
What version of the Fifth to take?
The scholar's free to choose!
The Russian plumbed the new world,  too,
Awash in lines estranged:
A universe devoid of squares,
With angle sums deranged.
With Euclid but of many one—
No longer absolute—
The pious feared lest God Himself
Not stand beyond dispute.
But Riemann—dauntless—forged ahead,
With constructs as extreme:
No parallels—it's true—but still...
A yet coherent scheme!
Were 'common sense' the 'gospel truth,'
Were warnings ne'er ignored,
What vistas would remain unseen,
What wilds unexplored!