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Is mathematics mostly chaos or mostly order?


Two new notions of infinity challenge a long-standing plan to define the mathematical universe.

Last winter, at a meeting in the Finnish wilderness high above the Arctic Circle, a group of mathematicians gathered to contemplate the fate of a mathematical universe. It was minus 20 degrees Celsius, and while some went cross-country skiing, Juan Aguilera, a set theorist at the Vienna University of Technology, preferred to linger in the cafeteria, tearing pieces of pulla pastry and debating the nature of two new notions of infinity. Gabe Goldberg, a set theorist at the University of California, Berkeley, points out that while the trio might feel confident in their evidence for consistency with ZFC, surprises frequently happen in the study of the infinite.

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