# Generalized Riemann sums

## TL;DR

This paper explores the historical and mathematical connections of Riemann sums to various branches of mathematics, emphasizing their classical and elementary nature while highlighting their interrelations.

## Contribution

It provides a cohesive overview of Riemann sums' role across different mathematical areas, celebrating their 150th anniversary with accessible explanations.

## Key findings

- Reveals interconnections between Riemann sums and other mathematical fields
- Highlights the elementary yet profound nature of Riemann sums
- Celebrates the historical significance of Riemann's work

## Abstract

The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and elementary, thus available to the "common mathematician in the streets." However one may still see here interesting inter-connection and cohesiveness in mathematics.