Leonardo Errati

Hamming, the man who defeated errors

first made: 2023-03-21

Abstract

Starting with the story of a bad day for Richard Hamming, we’ll explore how to create an error-correction system. Coding theory will show us how it’s possible to mathematically develop a topic that seems almost magical. We will also discuss some limitations but highlight real-world applications. The presentation concludes with a game: thanks to Hamming codes, allowing you to lie once, I can (1) guess the number you were thinking of, and (2) figure out where you lied.

Motivation

To show how mathematics allows us to generalize a problem that at first glance seems like a mere coincidence. The [7,4]-Hamming code is perfect for this, offering both an “intuitive” explanation (using sets) and a “mathematical” one (using equations).

To understand how mathematics can have significant real-world relevance.

Intended audience

This short talk is planned for a broad audience with different backgrounds. The only prerequisite: understanding what x+y=1 means.

Notes

This talk was my contribution to "Math Talks", my first self-organised event, with the goal to showcase what is actually studied in mathematics. I enrolled other students, one for each area of the Master's Degree in Mathematics at University of Trento

Material