Apropos the science-and-religion question, a reader points me to the work of Clarence Wylie, who wrote his dissertation at Cornell on “Space Curves Belonging to a Linear Line Complex.”
Wylie also wrote:
Not truth, nor certainty. These I forswore
In my novitiate, as young men called
To holy orders must abjure the world.
“If …, then,” this only I assert;
And my successes are but pretty chains
Linking twin doubts, for it is vain to ask
If what I postulate be justified
Or what I prove possess the stamp of fact.
Yet bridges stand, and men no longer crawl
In two dimensions. And such triumphs stem
In no small measure from the power this game,
Played with the thrice attenuated shades
Of things, has over their originals.
How frail the wand, but how profound the spell!
Wylie’s poem assumes the “formalist” view of mathematics, as summed up by Bertrand Russell: “Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” That remains the dominant view among philosphers of mathematics, but the disconnect between the frailty of the wand and its evident power lends some support to the alternative view of Lakoff and Núñez that mathematics starts from basic human experience.
I must confess that my own views remain primitively Platonic; that is, I belive that it was the case that a group consisting of two pairs of trees contained four trees, even before there were humans around to notice that fact.