Writing in Quanta, Natalie Wolchover explains the race that's on to determine which new axiom will augment the nine that comprise Zermelo-Fraenkel set theory with the axiom of choice (abbreviated ZFC).
Wolchover hits the historical highlights—Cantor and the continuum hypothesis, Gödel and his incompleteness theorems—and lays out the cases for the two competitors: the forcing axioms and the inner models.
Her piece contains ample quotations from the mathematicians engaged in this work, as well as this to-some eye-opening commentary on the nature of mathematics:
Mathematics has a reputation for objectivity. But without real-world infinite objects upon which to base abstractions, mathematical truth becomes, to some extent, a matter of opinion.
Read the story.