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.