Ultrafinitism: The Mathematical Philosophy That Rejects Infinity Gains New Ground
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By Gregory Barber April 29, 2026
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Summary
This article explores ultrafinitism, a controversial philosophy in mathematics that rejects the concept of infinity. It profiles mathematician Doron Zeilberger and other thinkers who argue that numbers are finite and that the universe operates like a discrete machine rather than a continuous expanse. The piece examines how this once-dismissed heresy is now producing new mathematical insights and challenging long-held assumptions about the nature of reality, mathematics, and computation.
Key quotes
· 3 pulledTo Zeilberger, believing in infinity is like believing in God. It's an alluring idea that flatters our intuitions and helps us make sense of the world.
Look out the window, and where others see reality as a continuous expanse, flowing inexorably forward from moment to moment, Zeilberger sees a universe that ticks.
Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.
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