- Author
- Posted by susam, with replies from many commenters
- Published
- 16 May 2026
- Kind
- Hacker News discussion thread on a short 2007 mathematics opinion essay
- Original
- news.ycombinator.com/item?id=48157229
- Subject
- Mathematics and optimization
What it is
Susam submitted Zeilberger's essay to Hacker News, and readers replied. The essay argues that lemmas, the steps inside proofs, are worth more than theorems. The thread is the source described here.
What it says
- Zeilberger's linked 2007 essay holds that a good lemma outweighs even deep theorems.
- The commenter whateveracct says the Coyoneda lemma has helped in production for a decade.
- The commenter btilly asks whether Zorn's lemma matters more than the axiom it restates.
- ForceBru says lemmas often seem arbitrary and names none that changed their thinking.
- The commenter dchftcs says a theorem is the thing studied and a lemma the tool.
- A side thread debates whether the Johnson-Lindenstrauss lemma preserves inner products or only distances.
- The commenter or_am_i likens lemmas to library code and theorems to application code.
What evidence it gives
The thread offers opinion, examples and links to Wikipedia. One commenter reports using a lemma in production code. The essay names Szemeredi's Regularity Lemma as its favorite. It adds quotations from other authors.
Interests and limits
The thread has few comments from self-selected readers on one site. The production claim cannot be checked. The essay is a brief opinion from 2007 and gives no proof of its thesis. The technical aside on the Johnson-Lindenstrauss lemma is left unresolved.