From In the Light of What We Know, by Zia Haider Rahman:
“In science,” my father said, “nothing is worth a dime that doesn’t accord with our observations of the world. There’s really only one field in all of human endeavour where no observation can undermine the authority of a statement.” “Mathematics?” “Yes.”
That feels like something that ought to be true, but then why would anyone publish or read any mathematical work? No one’s understanding could possibly be changed in the process.
Viewed from another angle, you might conceptualize mathematics as a sociological investigation of what kinds of things people judge to be proofs.
There’s a line elsewhere in the book along the general lines of, “In math it doesn’t matter who you are, only truth matters.” I can’t find it now, of course. In any case, it’s been lurking in the back of my mind with a similar objection to that above: If this is true, it must be a great comfort to the hiring committees of the mathematics departments of the world’s universities. It doesn’t matter who you hire, nothing in math relies on contingent details about personal identity.
We tend to fall into an intuitive Platonism. We take the comparative independence of abstract fields like mathematics from empirical data to mean that they are also independent of. We should do the opposite. If a field of intellectual endeavor is coming less from observation of the external world, it is more a product of our minds, more contingent upon us.
In the context of Rahman’s novel, of course the point is that math is more meritocratic rather than relying on one’s class, nationality, or ethnicity. Sam Harris and Michael Sandel addressed this topic in some detail in a recent episode of the Making Sense podcast. Sandel argues, to me quite convincingly, that while evaluating people based on merit is useful if you need to find the right people for a task, as an evaluation of a person’s value it rewards traits just as unearned and accidental as social class. A mathematician engages in certain actions to arrive at that title, certainly, but the intellectual ability to become a mathematician isn’t something one chooses to have, or earns. Most people can’t become mathematicians regardless of their personal choices. There are good reasons to be skeptical of our ability to take credit for those decisions, too, but that is a rabbithole we need not pursue at the moment. For the moment we might just point out that there are many behaviors associated with being an aristocrat, just as there are many behaviors associated with being a mathematician.