# Daniel Augusto da Silva, Poet of Mathematics

## TL;DR

This paper highlights Daniel da Silva's significant yet overlooked contributions to mathematics, especially his role in founding Discrete Mathematics and introducing the Principle of Inclusion-Exclusion, despite his isolation from main scientific centers.

## Contribution

It presents a detailed biography and argues for recognizing Silva as a key figure in the history of science and discrete mathematics, emphasizing his foundational work in combinatorics.

## Key findings

- Silva's work predates and influences modern combinatorics.
- He introduced the Principle of Inclusion-Exclusion.
- His contributions are crucial despite historical neglect.

## Abstract

Daniel da Silva was a remarkable Scientist and Mathematician of the mid 19th century. Working in Portugal, isolated from the main scientific centres of the time, his investigations in pure mathematics had almost no impact. Apart from giving a short biography of his life and work, this article makes the case for considering him an unavoidable character in the History of Science and one of the founders of Discrete Mathematics, through his introduction of a key method in Enumerative Combinatorics: the Principle of Inclusion-Exclusion.