My previous series of blog posts—what I’ve been calling the Penelope posts—has been about revisiting past work. These are papers written with collaborators, work that has been peer-reviewed, presented, and, in some sense, settled. Writing about them is an exercise in reconstruction: not of the proofs themselves, but of their meaning. Why did they matter? Why do they still matter to me now?
This new series is different.
These are posts about things I do not understand.
I want to write about problems in logic and mathematics where I can see the shape of a solution, but not quite reach it. Situations where existing answers feel partial, or unsatisfying, or somehow misaligned with the question. Places where the definitions work, some theorems go through, but something conceptual still feels missing.
These are not expository posts. They are not surveys. They are not polished.
They are explorations.
I am calling them the Ariadne posts, after Ariadne of Greek mythology.
In the myth, Ariadne gives Theseus two things: a sword to face the Minotaur, and a thread—a simple ball of yarn—to find his way back out of the labyrinth. The thread is the real insight. It is not heroic. It does not solve the problem directly. But it makes survival, and return, possible.
That is what I am looking for here: not solutions, but threads.
In mathematics and logic, we are very good at celebrating the Theseus moments—the clean theorem, the decisive proof, the elegant framework. But much of the real work happens earlier, in the dark: when we do not yet know what the right definitions are, when multiple approaches almost work, when we are unsure whether the difficulty lies in the problem or in our understanding of it.
These posts live in that space.
Each Ariadne post will start with a problem or a line of thought that I find compelling but unresolved. I will try to articulate what is known, but more importantly, what feels unsatisfactory about what I know. Where do existing approaches fall short? What do they fail to explain? What intuitions do they obscure?
The goal is not to criticize for the sake of it, but to make visible the gaps—the places where a thread might be needed.
There is also something else I want to recover in invoking Ariadne.
In the story, her contribution is essential. Without her, Theseus does not return. And yet, she is not the hero of the tale. Worse, she is abandoned—left behind on Naxos, her insight overshadowed by the narrative of heroic conquest.
It is a strange fate for someone whose idea is, in many ways, the most mathematical part of the story: a minimal, structural intervention that transforms an impossible task into a tractable one.
These posts are, in part, a small act of correction.
They are an attempt to value the thread as much as the sword.
By the way painting by Angelika Kaufmann (1741-1807), another barely remembered woman
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