Computer experiments and visualization in mathematics and physics. A subjective short walk among some historical examples

TL;DR

This paper explores how computer experiments and visualization have historically enabled the discovery of phenomena in mathematics and physics, emphasizing interactivity and providing examples with online resources.

Contribution

It surveys historical examples demonstrating the role of visualization and interactivity in scientific discovery, with links to interactive experiments.

Findings

Visualization revealed unnoticed phenomena

Interactivity enhanced understanding and discovery

Historical examples illustrate the impact of digital experiments

Abstract

In this short essay, we show how computer experiments, and especially visualization, allowed for the investigation and discovery of phenomena which would have passed unnoticed. We shall also highlight the importance of interactivity between the computer and the user. We do this by surveying several historical examples from mathematics and the physical sciences. Many pictures, and even hyperlinks to online interactive numerical experiments, are provided. Needless to say that we do not claim to be exhaustive, and that the chosen examples reflect our taste as well as our limited knowledge. Hyperlinks to several online interactive digital experiments are provided.