The Sign Before the Meaning

Some logos are born from an animal, an initial or an abstract shape. The deraison.ai logo comes from somewhere else: an algebra book printed in Zurich in 1659.

Back then neither artificial intelligence nor computing existed. Yet mathematicians were already stuck on a very current question: how do you write down an abstract idea? How do you give it a shape you can see on a page?

That question interests me more than any other. I hold a PhD in mathematics and deraison.ai is my artificial intelligence company. When I redid the site and the logo, I did not want one more stylized brain, one more glowing neural network, one more tech hexagon. AI logos are already full of them. I wanted to go much further back, to the time when mathematicians invented the signs we still think with.

1659: when an operation becomes a sign

In 1659, the Swiss mathematician Johann Heinrich Rahn published his Teutsche Algebra in Zurich. Almost nobody knows the book. It does contain a first in the history of mathematical signs: the ÷ of division, printed there for the first time. Rahn also uses the asterisk * for multiplication, and arrangements of three dots, among them ∴, to mean "therefore".

The passage on division is strikingly plain. Rahn states that ÷ is the main sign for dividing. That is all. The shape already existed before him as a printer's mark, and typographers call it the obelus. This Teutsche Algebra is where it first takes on a mathematical meaning.

This story has to be told carefully, the way mathematicians like. Rahn was working at the time with an English scholar, John Pell, who had in fact taught him mathematics. Historians cannot settle which of the two invented what. Who drew the ÷ first? We will probably never know.

That uncertainty makes the story better. What matters is not who put those three strokes of ink on a page, one afternoon in 1659. What matters is what happened: an operation you used to run in your head became a symbol.

A few dots and a line

A division is an idea. ÷ is its visible form. Three millimeters of ink, and a whole operation becomes recognizable, transmissible, usable.

This is one of the great strengths of mathematics. It does not only discover relationships between things. It also invents languages short enough for a human brain to handle. A bar, two dots, and what needed a full sentence now fits in one sign.

That is where the deraison.ai logo comes from. It is not a copy of a character from the Teutsche Algebra. It borrows the grammar: a dot, a line, punctuation, and separate elements brought into relation. A small constellation of signs. At first glance, almost nothing. But mathematics teaches you to be wary of simple shapes: =, +, ∞, ∫, ∴, ÷. Some of the most powerful ideas in our history fit in a handful of pixels.

From algebra to artificial intelligence

Three and a half centuries later, the scale has changed. The problem has not. Artificial intelligence also works by turning the world into things you can compute with. Words become tokens, the small chunks of text a language model reads. Objects become vectors, which are ordered lists of numbers. Relationships become matrices, grids of numbers. Observations become plain numbers. A model then tunes billions of internal dials, its parameters, as it learns. Out of that comes a representation a machine can compute with, predict from or generate from.

Between the ÷ of 1659 and a model with billions of parameters, the technical gap is dizzying. The work is the same: inventing a way of writing things down that makes them computable.

That is the idea I wanted in the deraison.ai identity. Artificial intelligence is neither magic nor an oracle. It continues a very long story: put the world into a form, then compute with it.

Why "deraison"?

The name deraison.ai deliberately carries a contradiction. Mathematics is often presented as the land of pure reason: proofs, axioms, those starting points everyone agrees not to argue about, rigor. Artificial intelligence blurs that picture. We build these systems with extremely precise mathematics. We then get behaviors we cannot always explain simply. Everything is computed. Not everything is understood.

The name comes from that gap. Not against reason: beyond obvious reason. There you have to try things, measure, understand. And sometimes accept that the phenomenon arrives before the elegant explanation we will give for it later. I enjoy the paradox. We use the most rigorous tools that exist. With them we explore systems that surprise us.

A logo as a program

So I wanted a logo that says very little out loud and a lot under its breath. No robot. No brain. No artificial spark. Only elementary shapes. Dots, because before the curve there is data. A line, because between points we look for relationships. Punctuation, because a thought only becomes usable once it is written down. And a nod to the time when mathematics invented its own alphabet.

The deraison.ai logo is therefore less a drawing than a small set of signs. It also says how I approach artificial intelligence: under the apparent complexity of models, go back to the basic structures. Look for the right way of writing things down. Strip away useless complexity, until what is left is simple enough to be understood.

A score, an emotion

Another story of signs has stayed with me all my life: written music. A staff, black notes, rests, dynamics, ties. To the eye, almost nothing. But when a musician looks at it, they do not see symbols. They see a shiver, waiting.

It is the same work as in 1659: catch something invisible, an intention, a feeling, a kind of vertigo, and store it in an object solid enough to cross the centuries. A Bach score is three hundred years old. It has outlived its composer, his instruments, his concert halls. And the second a bow touches a string, the emotion comes back intact, as if no time had passed. The sign carried it across.

A mathematical proof gives me a related feeling, in a different key. Music leads straight to emotion. Mathematics leads to a victory. I know that moment well. I even go looking for it, a little the way you go looking for the right note. The hypotheses finally lock together. The conclusion cannot be anything else. It is not just that it "works". It is a small silent triumph. Reality was resisting. It has just yielded to an idea born inside a human head.

That, I think, is what I like about this job. Not a model's score on a leaderboard, nor the race for more compute. Rather one precise moment. A blurry intuition, still too vague to say out loud, becomes a clean result. When the whole world fits, for a fraction of a second, inside one sign. A well-built artificial intelligence sometimes gives the same sensation: a huge, opaque system suddenly starts doing something right, something sturdy, something useful. Something you can finally show, the way you show a proof, the way you finally play the piece you had been rehearsing in your head.

Symbols outlive machines

Opening a 17th-century text today and recognizing a sign straight away is a strange feeling. Machines have changed, so have the media that carry them, and so have the theories. Paper became screens. Printed tables of results, prepared in advance to spare people long calculations by hand, became graphics processors, the GPUs. The handful of symbols on a page of algebra became billions of operations per second. But we are still doing what Rahn, Pell and their contemporaries were doing: looking for better languages to think with.

That, perhaps, is what the deraison.ai logo represents. A tribute to an old mathematical story, of course. But above all a conviction about today: before you can compute something, you have to find a way to write it down. In 1659, that fit in a few dots and a line. Today, everything still starts with a sign.

Thanks

Thanks to Audrey Dejoux, the artist who designed this website. She put real delicacy into it, as close as her imagination could get to my passion for science.

Sources

MacTutor History of Mathematics: Johann Heinrich Rahn
Sotheby's: Teutsche Algebra by Johann Heinrich Rahn, 1659
Wikipedia: Therefore sign