Hi, and welcome. My name is Guillaume P. Hérault, I’m almost 60, and I work in Human Resources at a bank. I’m not a mathematician. I’m not an academic researcher. Until recently, I had never even heard of Fourier transforms.

And yet, this website exists. LucasNTT exists.

I have an engineering degree, but I haven’t touched serious math in over 40 years. What I have done, though, is write software. A lot of it. For four decades, I’ve been programming in all kinds of languages, for all sorts of projects. And over time, I’ve developed a problem-solving instinct, break things down, isolate the hard parts, solve them one at a time. Classic divide and conquer.

A decade ago, I stumbled across an article about the discovery of the largest known prime number—a Mersenne prime—thanks to a distributed computing project (GIMPS). That got me curious. How are such huge primes actually proven? That question led me down a long, twisting path into number theory, fast multiplication, and Fast Fourier Transforms.

What I found was both fascinating and puzzling. We’re proving the primality of gigantic integers using algorithms that rely on floating-point approximations? That didn’t sit right with me. I wanted to know: is it possible to do this with pure integers?

So I dove in. I read hundreds of academic papers. Most of which were far above my head at first. And slowly, painfully, I started to understand. I’ve gathered those documents in the Library section of this site.

The result is LucasNTT, a project that brings together what I’ve learned. I decided to write and share what was missing at the begining of my journey: a set of accessible documents to explain the math and algorithms behind it all (FFT, NTT, fast multiplication, IBDWT) written for people like me: curious, motivated, but not trained mathematicians.

If I managed to get this far, I believe others can too.

Thanks for visiting—and I hope you’ll enjoy exploring the site.
You can reach me at lucasntt.theproject@gmail.com
I'm quite busy juggling work, family life, and my hobbies. I doubt I'll be able to respond to all messages, but you can always give it a try.