Is the following statement true? Zeros of a non-constant holomorphic function cannot accumulate

Counterexample

Is this true?

Zeros of a non-constant holomorphic function cannot accumulate

No — it is false.

The counterexample

sin(1/z) on $\mathbb{C}$ ∖{0}

Why it fails

Zeros $1/(n\pi)$ accumulate at 0, which lies outside the domain. Inside the domain zeros are always isolated.

Keep practicing

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.