What can we gain by losing infinity?

14 hours ago

Doron Zeilberger rejects infinity as a mathematical concept, viewing it as unnecessary and false, akin to belief in God.
Ultrafinitism, advocated by Zeilberger and others, questions the existence of infinity and extremely large numbers, arguing for a mathematics based on feasibility and physical limits.
Most mathematicians oppose ultrafinitism, seeing infinity as core to mathematics, useful in describing the universe and embedded in foundational rules like set theory.
Alexander Esenin-Volpin pioneered ultrafinitism by emphasizing practical construction limits, suggesting numbers are valid only if they can be mentally or physically realized.
Edward Nelson attempted to rebuild mathematics without infinity but found weak axioms that hindered basic arithmetic, though his work influenced computational efficiency studies.
Ultrafinitism faces challenges in developing a coherent formal theory, but some see it as more realistic, aligning with physics where infinity may not exist in nature.
Physicists like Sean Carroll and Nicolas Gisin explore finitistic models, questioning if the universe is finite and using intuitionist math to address quantum-classical divides.
Zeilberger promotes a discrete mathematics approach, replacing continuous concepts with finite analogs, arguing for beauty in a finite reality rather than fictional infinity.

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