I recently read an article about Hugh Everett III, the physicist who proposed what later became known as the Many-Worlds Interpretation of quantum mechanics. The idea immediately caught my attention because it offers such a radically different way of thinking about reality. 

The basic idea is surprisingly simple to describe.

In the usual interpretation of quantum mechanics, when a quantum system is measured, its wave function collapses and we observe one particular outcome. Everett questioned whether that collapse was really necessary.

What if the quantum wave function never collapses?

Instead, every possible outcome remains part of the overall quantum state. When a quantum system interacts with an observer or its environment, the combined system can evolve into different, effectively independent branches. In one branch, we observe one outcome; in another, a different outcome. From inside any one branch, however, we experience only the result that happened there. 

This leads to the fascinating picture commonly called the Many-Worlds Interpretation: reality doesn’t necessarily choose one possibility and eliminate the others. Instead, the different possibilities become separate branches of the evolving quantum state. 

And this is where I find the connection with quantum computing particularly interesting.

A qubit can exist in a superposition of 0 and 1. A quantum computer manipulates these amplitudes using quantum gates, allowing different possibilities to coexist in the mathematical description of the system. But there is an important distinction: quantum computers don’t simply « try every answer in parallel. » Interference is what allows useful algorithms to amplify some outcomes and suppress others.

Still, the Everettian picture provides a fascinating conceptual backdrop. A quantum computation can be viewed as a continuously evolving quantum state containing multiple possible computational histories, with interactions and measurements producing effectively separate branches.

For someone like me, getting back into mathematics through quantum computing makes this particularly exciting. Concepts that initially look abstract—complex numbers, vectors, matrices, probability, superposition and linear algebra—start to feel like pieces of a much bigger picture.

Maybe the most intriguing part of Everett’s idea isn’t whether there literally are infinitely many « copies » of us somewhere.

It’s the possibility that what we experience as a single reality could simply be one branch of a much larger quantum reality.

And that’s a pretty fascinating reason to start studying the mathematics behind quantum computing.

The Hugh Everett article I read in Scientific American

One caveat I found particularly interesting while reading further: “branching” is an interpretation of the quantum formalism, not an experimentally established observation that new universes are literally created whenever someone looks at something. There is also ongoing debate about exactly what constitutes a branch.

I have been using Duolingo for more than 900 days in a row, mainly to learn French. At this point, Duolingo has become a small part of my daily routine. I like the idea of learning something every day, even if sometimes I only have a few minutes.

Recently, I noticed something new: Math.

I decided to give it a try.

My first impression was quite positive. The lessons are short, interactive and familiar if you already use Duolingo for languages. The exercises are really good for occasions when you can’t open a math book.

For me, the biggest advantage is refreshing things I learned years ago. Duolingo Math gives me a simple way to practice them again, a little bit every day.

After looking at other people’s experiences online, I found that my impression is not unusual. Many learners enjoy Duolingo Math as a way to practice and build confidence, while others criticize it for not explaining mathematical concepts deeply enough.

I think both opinions can be true.

I wouldn’t use Duolingo Math to learn advanced mathematics from scratch. If I wanted to properly learn algebra, calculus or statistics, I would still choose a book, a structured course or something like Khan Academy.

But that’s not necessarily what I need from it.

For someone like me, who wants to refresh mathematics, keep the brain active and rebuild some intuition, the format works surprisingly well. And Duolingo has been expanding the Math course considerably, including algebra, geometry and statistics content.

I recently started refreshing my mathematics with Mathematical Foundations of Quantum Computing: A Scaffolding Approach, by Peter Y. Lee, James M. Yu, and Ran Cheng.

The book was published in 2025 and is specifically designed to build the mathematical background needed for quantum computing. It starts with the basics and gradually moves toward more advanced topics. 

What I like about it is that it doesn’t assume that you remember everything from university. It begins with things such as complex numbers, trigonometry and summation, and then moves into vectors, matrices, linear algebra, tensor products, matrix decompositions, Dirac notation and probability. 

That makes it a good fit for what I’m trying to do: refresh my math skills while learning mathematics that has a direct connection to quantum computing.

For example, I’m currently going back through things as simple as summation notation and infinite series. These may look basic, but rebuilding that intuition is useful before moving deeper into linear algebra and quantum mechanics.

The book follows what the authors call a “scaffolding approach”, introducing concepts progressively and revisiting them with increasing complexity. It is intended for learners ranging from introductory to more advanced levels. 

So, for me, this isn’t really about becoming a mathematician. It’s about rebuilding the mathematical foundations I need to understand how quantum computing works, rather than simply learning how to use quantum programming libraries.

I’m starting this blog to document my journey into quantum computing.

I’ll share what I learn, the things I experiment with, some quantum programming, and interesting news from the quantum word.

I’m just getting started, so let’s see where this journey takes me.