Mathematicians have a tower of different infinities in their toolbox to tackle questions about the boundaries of logic and math.
But a recent construction of two new notions of infinity — which don’t fit neatly into the usual hierarchy of the large cardinals in the tower — has some thinkers wondering if those boundaries are much messier than they appear.
One of the new infinities implies the existence of an infinity far larger than anything anyone had previously imagined.
It’s hard to know if these new infinities really change anything, though.
The nature of infinity means that many questions are fundamentally unprovable, and uncertainty reigns.
To some, the discovery of the new cardinals is exciting, while others find it irrelevant.
But one thing is for certain: The mathematicians will keep trying to conquer the infinite.
“I always tell people that mathematics is infinite, but time is not,” one set theorist said.
