of ultrafinitists. Putting a limit on large numbers in maths seems a bit strange and pointless to me, but I do think that when it comes to physics, when numbers become very large or very small, we actually have no idea how stuff behaves under those conditions.

“There isn’t enough matter in the universe to write out the number 10^(10^10). To a fringe group of mathematicians called ultrafinitists, this means the number literally does not exist.

While standard finitists reject the concept of actual infinity, ultrafinitists take this skepticism a step further: they reject the existence of extremely large, strictly finite numbers.

To understand the ultrafinitist perspective, one must look at how mathematics relates to physical reality. The core argument rests on the idea that mathematical objects only exist if they can be constructed, represented, or computed. The observable universe contains a finite number of atoms—estimated to be roughly 10^80. Because writing out massively astronomical numbers would require more time than the universe has left, or more matter than exists to use as ink, ultrafinitists argue they are merely empty symbols, not valid mathematical entities.

The most famous proponent of ultrafinitism was the Russian mathematician Alexander Esenin-Volpin. He notoriously argued against the existence of numbers as small as 2^100 as distinct, fully realized mathematical objects. Modern advocates, such as Rutgers mathematician Doron Zeilberger, argue from a computational standpoint. Zeilberger suggests that continuous mathematics and infinite sets are a convenient illusion, and that only discrete, practically computable mathematics is true.

The main philosophical challenge ultrafinitists face from mainstream mathematicians is the successor function: if a number N exists, why shouldn’t N + 1 exist? If 10 is a valid number, 11 must be, and so on. Ultrafinitists counter this by pointing out that mathematical induction assumes infinite physical resources. They compare it to the “Sorites paradox” or the paradox of the heap: adding one grain of sand repeatedly eventually creates a heap, but there is no distinct boundary where it suddenly changes. Similarly, adding 1 to a number works for small quantities, but repeating this process blindly ignores the physical limitations of computation. A computer adding 1 repeatedly will eventually run out of memory, overheat, or break down.

To an ultrafinitist, standard mathematics relies on unquestioned axioms that divorce numbers from the reality of how they are generated. By demanding that every mathematical claim be backed by a physically possible computation, they seek to keep mathematics strictly anchored to the real, finite universe.”