Xenagogy

Born 350 years later, would Isaac Newton be a tech bro? I wonder if he'd drink yerba mate, write on Substack and have a banging Twitter account, @sirnewt. Honestly he'd probably be doing an internship at Jane Street over the summer, considering leaving sleepy Cambridge for that sweet $500k "total comp" in NYC. Maybe he'd sport a Patagucci gilet, an ear piercing, and put Claude stickers on his laptop. I'm sure he'd be into climbing too, getting chalked up with his mates on Wednesday nights, trying to scale harder routes than his rivals Leibniz and Hooke—the ultimate display of physic(al) superiority, of course. In this alternate timeline, I wonder then if Newton's famous words about standing on the shoulders of giants would instead read,

If I have climbed higher, it is by reusing the holds placed by those who climbed before me.

I'd say this is a far better analogy for science! (If only you were with us today, Isaac—you would've loved iced matcha lattes and GPT 5.6.) We are not statically standing on the shoulders of our predecessors, simply looking further with each new generation of thinkers. Science is probably not a human tower (if it was, Mr Al-Khwarizmi would need very broad shoulders when I solve for x). No, it is something dynamic and evolving. As hypothetical 2026-Newton aptly notes, the project of Science is the ascent of a vast, complex cliff face, uncovered only as we search its features. Collectively, we climb. We ascend the unknown, in an admittedly fuzzy and flawed process, that nonetheless takes us higher—and as we do so, it cures us, assists us, elevates our lives, and thus we are motivated to climb yet further. At times, we err, we diverge into many strange regions that are dead ends, and we lose our way. We forget about holds and routes, only to find them anew in dusty textbooks and croaky professors. And indeed, sadly, we are forever pulled downwards by the weight of disorder, of entropy, of violence and irrationality. Still, humanity inches upwards.

A PhD is well understood in this framework. Education from pre-school through to an undergraduate degree is defined by ascending existing routes. It is prescriptive. My teacher is (ideally) not wondering about the answer to 3+4 when it is assigned to me as a child. Instead, bolts are rigidly in the wall (arguably too rigidly?) and the route ahead is clearly marked, practiced by many before me. Pedagogy literally means "to lead the child," and here the pedagogy is in building strength, mastering the techniques, learning the ropes, rather than any sort of particular output. An era of the syllabus. Don't be mistaken, this ascent remains hard! You start at the very bottom and it sucks, but through the patience of you, your community, and the incredible teachers of this world, you somehow climb. We might say this is a chapter of pre-hoc epistemology: we gain knowledge that existed before we learned it.

As the educational ladder progresses, though, we start teetering on the edge of the new, the unknown. In my master's degree, I recall the pleasure of learning about a new algorithm first described in a paper that very year! This stands in great contrast to learning concepts from Principia Mathematica devised in the 80s (the 1680s, that is). You feel closer to the metal. The error bars are bigger too—corroboration and consensus take time, so there's a feeling that we're not yet sure of ourselves. And so, you start climbing dangerously close to the boundary of "what is known," finding that existing routes become increasingly sparse and precarious. This is, at least in principle, where a PhD tries to go, and then reach beyond: a concerted poke into the frontier.

I am emphasising doctoral studies here, because I am in and surrounded by that context, but this framing applies generally to those pushing some frontier, which occurs across a multitude of contexts. The important takeaway is the shift from the prescriptive to the emergent, from pre-hoc to ad-hoc epistemology—knowledge that is acquired en route. We forge a path as we climb and climb that path as we forge. It is a shift from pedagogy to heutagogy: "leading oneself." I have found this to be a great joy and challenge of my own PhD: there is no syllabus! How overwhelming, how liberating, this generative chapter of science.

Historically, I think that is where the exposition could end and we could cast our eyes to other topics in science, say, policy and funding—"how do we get more climbers on the wall, how do we support them on their journeys," and so on. Alas, there is a crucial problem: the above reflections were true in the B.C. era! (Before Claude). Now? I am less sure. It feels the very dynamics of our epistemology are evolving, and evolving rapidly.

To clarify, an anecdote from my own PhD: I am working with microbubbles in the context of focused ultrasound, trying to model and simulate them better, with the goal of making downstream therapies safer and more effective. In December last year, I had the idea of creating a differentiable microbubble simulator, which would unlock many cool tools to work at the cutting edge, where others have not yet climbed. Except, at that moment, I was still learning about the microbubbles themselves—frankly, I was catching up! I had many missing pieces in my physics knowledge and I was still ascending the prescribed knowledge route. Around this time, though, the AI models were becoming increasingly capable, particularly at coding and mathematics, and so, I took the leap: I ("we?") created a differentiable microbubble simulator, without me yet fully understanding the components below.

In the time since, I have learned much more about the bubbles, and I have changed and improved the tool a great deal—it is certainly not what was created on that day in December. However, fascinatingly, to do so I have used the code to learn about the code; I have used the artefact to learn about the idea, not used the idea to create the artefact. And that's a great way to learn, personally. Ignoring how it was conjured, ignoring how optimal or stylistically beautiful its code is, ignoring any such questions... it exists! And so: it can be probed, questioned, tested, felt and held and weighed. That process is enormously pedagogical. It feels like the pre-hoc syllabus from the school-era, despite being on the edge of something brand new. In the period since, I've done some exciting research upon the tool, and it has become the first pillar of (what will be) my thesis—a decidedly positive outcome.

Why is this curious? Well, creation preceded understanding! In the past, the roadmap towards this tool would first entail ascending the prescribed knowledge region extensively, and only then synthesising that knowledge into something new. I would need to climb up to where human knowledge currently is, before arduously going further. Some extras would be learned in situ, of course, but far more would need to be known upfront.

Instead, the machine (co-)created the tool and I... caught up?

Granted, the work done by the LLM here was mostly synthesising existing knowledge into new combinations—there's great work out there on differentiable simulators, and equally great work on microbubbles, which makes their marriage feel somewhat inevitable? But, honestly, this is what I would have done as my PhD work in the B.C. era, and it would have been recognised as having "poked the frontier" by the academy. The LLMs are still lacking in many ways, and they have not yet recursively ascended the cliff face of science (despite what AI marketing wants you to believe). Still, it would be remiss to ignore the bolts it secured for me in this specific research project—it helped me climb, undoubtedly. Four or five bolts this time around, and perhaps ten bolts in my next project. After that, though? It's unclear. How much higher will it be able to go? Will we be stuck in local neighbourhoods of progress, simply interpolating what is already known, or can we take a leap and extrapolate to entirely new regions of understanding?

I think this is an incredible opportunity for science, and I feel excited as a researcher! Alongside excitement, though, there is uncertainty and unease and maybe some fear too. Just over the horizon, it seems we will experience post-hoc epistemology, where action completely precedes understanding, and knowledge becomes retrospective—where will that leave us? And what are we losing? Many complex questions surround attribution, meaning, purpose, reward, play, status, achievement, satisfaction, joy.

Grant Sanderson, the incredible mathematics educator behind the 3blue1brown YouTube channel, recently posited that a future role of mathematicians will be to curate the creations of future AI tools. Not to explain the creations, Grant suggests, since the tools might be pretty good at explaining too, but to arrange the outputs with a distinctly human touch. And so, after being led as children in the form of pedagogy, climbing upwards to new heights ourselves, in the form of heutagogy, what awaits us? Mechanogogy—to lead the machine? Technogogy—to lead the technology? These prefixes may imply a degree of interpretability, yet these tools could prove to be opaque and undecipherable. Will science become more hermeneutic than generative? Perhaps we will instead practice xenagogy: leading of the stranger. The question, I suppose, is who goes upfront.