# Many proofs that $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$ can be found in the conformal invariance of planar Brownian motion

## TL;DR

This paper reviews recent probabilistic proofs of Euler's identity for the sum of reciprocals of squares, emphasizing their reliance on the conformal invariance property of planar Brownian motion.

## Contribution

It compiles and discusses new probabilistic proofs of Euler's identity based on conformal invariance, highlighting their methodological novelty.

## Key findings

- Multiple probabilistic proofs of Euler's identity are presented.
- Conformal invariance of planar Brownian motion is central to these proofs.
- The proofs offer new perspectives on classical mathematical identities.

## Abstract

A number of recent new proofs of Euler's celebrated identity are presented, all of which are probabilistic in nature and depend on the conformal invariance of planar Brownian motion.