What can we gain by losing infinity?

Math’s wildest rebel says infinity is fake — and the comments are absolutely not having it

TLDR: Doron Zeilberger argues math relies too much on infinity and should focus on numbers we can actually handle, a view most mathematicians see as extreme. In the comments, readers were torn between curiosity and outright disbelief, with many saying the article blurred philosophy with fact.

A mathematician has marched into one of the oldest ideas in human thought and basically declared: infinity? overrated, unproven, maybe not even real. Rutgers professor Doron Zeilberger argues that math should stick to what can actually be built, counted, or computed, and that giant impossible-to-write numbers may be more fantasy than fact. In plain English: he thinks numbers don’t stretch on forever in any meaningful way, and a lot of standard math leans too hard on a concept we can’t physically reach.

But the real fireworks were in the community reaction, where readers split into two camps: “interesting philosophy” and “please stop calling this math truth”. Several commenters were visibly annoyed by the article’s framing, saying it confused “you can do math without assuming infinity” with the much bigger claim that infinity is somehow wrong. One reader flat-out said, “I don’t understand, and I hope it’s just bad writing,” while others zeroed in on the line comparing infinity to God and asked, basically, what does “observe infinity” even mean? That became the thread’s mini-drama: was Zeilberger being profound, or was the article making him sound way weirder than necessary?

Not everyone was dunking. A few math-philosophy fans showed up with deep-cut paper recommendations and a kind of niche fandom energy, praising strict finitism as a richer way to think about reality. And then there was the comedy: one famous quote about being “reduced to counting on my fingers” gave the whole debate the vibe of a cosmic brain crisis meets kindergarten. In short, the article asked whether we can live without infinity — and the comments answered with skepticism, eye-rolls, and a surprising amount of existential popcorn.

Key Points

  • The article presents ultrafinitism as a mathematical philosophy that rejects infinity and is widely regarded as outside the mainstream.
  • Doron Zeilberger argues that mathematics does not need infinity in practice and says finite, computation-based methods can replace it in some areas.
  • The article says most mathematicians view infinite sets and indefinitely extendable mathematical objects as foundational to modern mathematics.
  • Zeilberger’s position extends beyond rejecting infinity to questioning whether extremely large numbers, such as Skewes’ number, should count as meaningful numbers.
  • A central criticism noted in the article is that ultrafinitism does not provide a clear cutoff for where acceptable numbers end.

Hottest takes

"I don’t understand, and I hope it’s just bad writing" — Ifkaluva
"When the author says we cannot truly observe infinity, what does that mean?" — getnormality
"reduced to counting on my fingers" — whimblepop
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