From Kevin Hartnett at Quanta:

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

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In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.

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Their work also finally puts to rest a problem that mathematicians had hoped would help settle the continuum hypothesis. Still, the overwhelming feeling among experts is that this apparently unresolvable proposition is false: While infinity is strange in many ways, it would be almost too strange if there weren’t many more sizes of it than the ones we’ve already found. More.

It sounds like a bit of sleight-of-math, maybe hype, but what do readers think?

*See also:* Is zero even?

The viability of an infinite past

and

Can the universe be infinite in the past?