Hamming, the man who defeated errors

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.

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.

The target audience is broad and with different background, perhaps even with little interest in mathematics. The only prerequisite: being able to read $x+y=1$.

The main motivation is showing 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). We will also show how mathematics can have significant real-world relevance.

Material

• slides (IT)