The book under consideration is Morris Kline’s Mathematics: The Loss of Certainty. Wonderful book—and a nice companion to one I’d recently read on Hellenistic Science (link on this blog). For as long back as I am able to remember, I’ve always thought of mathematics as a language—natural, perhaps, for someone like me who had to master three languages beyond my mother tongue before I was sixteen—and someone who got deeply into computers more or less by playing around with their insides. This work tells me that math was long and traditionally viewed as something else—the code deeply embedded in Nature and revealing the secrets of God’s design. The loss of certainty, therefore, is a modern phenomenon, another great disillusionment—but one I had been spared. Math viewed as language explains more. It suggests that math has two aspects: its rules of application, thus its grammar, and the meaning assigned to perfectly legal equations and functions—which may be quite defective.
‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe:
All mimsy were the borogoves,
And the mome raths outgrabe.
Lewis Carroll, Jabberwocky
Nothing wrong with the grammar here. Now when it comes to reality, some of the most familiar aspects of which quite escape genuine physical grasp—such as the workings of gravity—giving explanations for them using the pristine grammar of math but meaningless concepts is good fun for toves and the mome.