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John Wilson's avatar

Long awaited! Let us roil!

Gemma Mason's avatar

Lovely to see that broad ambition sketching out a worthy target. I’m currently finding myself arrested by the known-but-not-well-understood fact that pure mathematics, as a subject, is less than 200 years old.

To take a central touchstone for that shift: Principia Mathematica (1910-1913) is both a stark act of conceptual severing (of mathematics from everything else) and a bold attempt at consolidation (between mathematical disciplines). There is not a single person working with or thinking about LLMs who is not shaped by both its holistic ambition and its reductionist partitioning.

There’s an essay angle or ten, in all of this, but I haven’t done enough research to be able to write any of them yet. Which is a topic in itself: the interdisciplinary character of the history and philosophy of mathematics gives it a forbidding set of prerequisites. It’s charmingly, or perhaps alarmingly, under-studied in places; the book I’m currently reading about the rise of mathematical logic has some very amusing remarks on this.

So I’m thinking about what it means when we lose confidence in our ability to synthesise an understanding of even a small nexus between the different things that humanity knows. Do we accept splintering, and leave a few bold souls to row out into the interdisciplinary lacunae? Do we wish for a machine god with the power to read widely enough, whether or not it truly understands what it sees? Or do we recover human ambition even as we accept that we are going to make mistakes?

I’m finding my narrative, here, slowly. It’s going to make it easier to get through my vast and difficult list of research leads. And hey, if I think of a coherent sub-1800-word outtake, I’ll submit a pitch to Persona! But even if I don’t, I know the underlying wide scope of what you’re considering will help me orient myself. I look forward to seeing what you publish in the coming months.

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