# Frobenius's last proof

## TL;DR

This paper discusses the historical context and significance of Frobenius's final proof related to polynomial identities connected to the Rogers-Ramanujan identities, highlighting its presumed simplicity and directness.

## Contribution

It provides an analysis and reconstruction of Frobenius's last proof, shedding light on its presumed simplicity and historical importance.

## Key findings

- Frobenius's last proof is likely simple and direct.
- Schur's proof was more complicated than Frobenius's original.
- The proof is connected to polynomial identities underlying Rogers-Ramanujan identities.

## Abstract

Around about 1917, Issai Schur rediscovered the Rogers-Ramanujan identities, and proved a system of polynomial identities that imply them. Schur wrote that Georg Frobenius (his former advisor) had shown him a simple, direct proof of these polynomial identities. Schur did not see fit to reveal Frobenius's proof, preferring his own rather complicated proof. But it is easy enough to guess what this `simple, direct' proof must have been. As Frobenius died in 1917, we may call this `Frobenius's last proof'.