Infomathic

TL;DR

This paper explores how computational tools have historically supported and inspired mathematical reasoning and proofs, illustrated through high school examples demonstrating their influence on mathematical thought.

Contribution

It highlights the dual role of computing in mathematics: as a practical tool and as a source of inspiration for reasoning and proofs.

Findings

Computers assist in numerical calculations and simulations.

Computational tools inspire new mathematical reasoning.

Examples from high school illustrate this partnership.

Abstract

Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature, probabilistic, ...) to verify or establish a conjecture. But, and this is another point on which we will concentrate our attention here, computing will also have served the cause of mathematics by inspiring certain reasoning or by taking charge of whole sections of a demonstration. We will illustrate this fruitful partnership with two example saccessible from high school.