On the Power of Mathematics

As a math major in university, the subject is a dear one for me. I’ve often been puzzled by religious apologists who use the power and broad applicability of mathematics as evidence for the existence of a god. It’s an argument that can only be made by someone who doesn’t know much about how mathematics actually works.

Often people who don’t like science (or rather find the findings of science inconvenient for them ideologically or politically) will mischaracterize it as the body of knowledge — a set of facts from a textbook to be memorized from a textbook in time for the test and then forgotten — rather than the process of inquiry that produced those facts and more to come. They treat math in a similar but slightly different way, as though math is a fully understood subject, counting numbers up to calculus, that gets handed down from on high and if you can memorize the steps and do as you’re told you will get the right number at the end. The history is actually much different.

Our understanding of mathematics (and for the purposes of this essay, the way the Brits abbreviate it as mathS is useful) is not a single subject. It’s a messy hodgepodge of our attempt to understand spatial and numerical relationships in the world, much of which was achieved purely by decades and centuries by trial and error. It’s only been a gradual process after the fact that people have attempted to force it all together, shaving the edges off a poorly made jigsaw puzzle to get it all to fit together.

For example, someone had to invent place values to communicate larger numbers to one another. Otherwise we would need separate and distinct words for every single number as opposed to summarizing them in combination: Six Hundred Sixty Six. Likewise, we have always had a concept for “nothing”. Yet it took centuries if not millennia for someone to invent “the number zero” so that we could talk about “nothing” in a way compatible with rigorous calculation.

The other thing to remember is that all of our understanding of numbers and geometry has been motivated by a desire to understand and predict things in the real world. So mathematics was always developed in partnership with the real world rather than as some esoteric isolated discipline. It later became that when we understood so much more than could be assimilated by any student by the end of high school (or whatever they called it back when Hilbert and Cantor were musing about the nature of infinity.)

So the fact that mathematics has such a tight correspondence with reality, as far as I can surmise, is due entirely to the fact that it was developed in partnership with reality. And I’m suspicious of anyone who wants to extend it more credence than that.

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