> To Zeilberger, believing in infinity is like believing in God. It’s an alluring idea that flatters our intuitions and helps us make sense of all sorts of phenomena. But the problem is that we cannot truly observe infinity, and so we cannot truly say what it is.

I'm hoping this is just bad writing from Quanta rather than something "ultrafinitists" truly believe.

I really don't think it's that complicated. Even pre-schoolers, competing to see who can say the highest number, quickly learn the concept of infinity. Or elementary school students trying to write 1/3 as a decimal.

Of course you need to be careful mapping infinity onto the physical world. But as a mathematical concept, there is absolutely nothing wrong with it.

> Mathematicians can construct a form of calculus without infinity, for instance, cutting infinitesimal limits out of the picture entirely.

This seems like a useful concept that also doesn't require denying the very obvious concept of infinity.