Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.
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Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing…
In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly…
A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.
The highly-complex technology is increasingly being tipped to transform computing.
Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core…
Mathematicians finally understand the behavior of an important class of differential equations that describe everything from…
