That title bothered me too. If a trend continues, that means it would be exactly as much "approaching infinity" in 2026 as it was in 1960. It would also be exactly as finite in 2026 as it was in 1960.

That's incorrect. They did fit the population growth to a hyperbolic curve, which predicts (predicted) an infinite population in finite time: a singularity. It hyperbolic growth does not approach infinity, it actually reaches it.

Of course a singularity can't happen in reality, so this paper was in jest. (And in fact population growth stopped fitting a hyperbolic curve shortly after it came out.)

That did seem strange to me until I realized they were just describing a vertical asymptote. It doesn't make sense for such a thing to exist when the x axis is a time, but I think it's meant to be tongue in cheek and preposterous.