Ultrafinitism, a philosophical stance rejecting infinity, challenges mathematical orthodoxy. Doron Zeelberger, a Rutgers mathematician, argues that infinity is both "very ugly" and false. He sees the universe as discrete, like a flip-book, rather than continuous. Zeilberger believes practical mathematics can exist without infinity, stating "You don't really need it."

Most mathematicians dismiss ultrafinitism as "complete nonsense," according to Joel David Hamkins. Infinity forms the core of modern mathematics, embedded in fundamental rules and assumptions. Ultrafinitism advocates for a mathematics that reflects human limitations and potentially the physical universe. Even critics like Justin Clarke-Doane acknowledge it deserves consideration in philosophy of math.

The practical implications challenge how we approach extremely large numbers, such as Skewes' number. If numbers cannot be feasibly written or verified, Zeilberger questions their validity. Ultrafinitism lacks formal structure but offers a more realistic approach that mirrors computational limitations. The philosophy remains marginalized but continues to provoke important questions about mathematical foundations.