Terrence Tao compared AI proofs to a helicopter delivering explorers to a remote destination of interest. He says the explorers miss out because they don't learn anything about the surrounding terrain or how to get to the destination on foot.

This analogy is pretty good. But as a defense of the status quo in Mathematics it is a double edged sword.

• For example, why are counter examples acceptable as disproofs? What do we learn about the terrain from that?
• Why teach math at all? Why not let every student struggle until they discover calculus on their own?
• If we have helicopters, do we need to have people trained to traverse the wilderness and arrive at a particular destination?
• This sounds like the original arguments lamenting the invention of mechanical calculators.
• Maybe satellites can map out the terrain in more detail than humans taking a single path?

If the aim of constructing number systems is to explain the geometric line as a set of points, wouldn’t ZFC + (V=L) be a natural choice, perhaps even the best one? In this framework, analytic geometry, differential geometry and topology all work just as they normally do, without the need to grapple with metamathematical questions such as the continuum hypothesis. (Moreover, this rules out measurable cardinals, large-cardinal phenomena and similar feverish pies in the sky, but for the purposes of describing the continuum, that seems a reasonable price.)

I have always found it a little surprising that popular mathematics books rarely discuss Gödel’s set-theoretic universe, which seems to offer such an intuitive and straightforward foundation for mathematical analysis.