Recently I was a little overcome with fatalism while reviewing some potential PhD applicants (I do still have some studentships available).
I am not the kind of LLM hater that thinks they are incapable of doing anything. They are actually very capable of doing the kinds of small tasks that I used
to save for undergraduate projects or as training exercises for new PhD students. I felt that the capabilities of these tools made many of the research proposals
I was looking at kind of moot — essentially, thoughts along the lines of "Well, LLMs might eat our lunch for this project, so what's the point of trying it?". This
is particularly notable in the area of proof automation where LLMs can now quite successfully find proofs for theorems that old-fashioned automatic techniques
would struggle at.
This kind of fatalism is really toxic to creative thinking and research. It's the same as thinking "Well, climate change will eventually make this planet uninhabitable,
so what's the point of tending my garden?", or "the politicians in my country are all corrupt/feckless/irresponsible, so what's the point of agitating for political change?".
It's the result of an overly goal-oriented point of view, which casts research (or life in general) as a struggle towards an objective, and evaluates
the worth of that research (or life) by how much that objective is accomplished. Under this lens, if the objective is impossible, the struggle
is meaningless. I'm increasingly convinced that this view is wrong, and backwards. Life is the struggle, and the goal need not even be possible, let alone achieved.
In my personal life, I have become a lot more religious over the past 10 years or so. The goal, if there is to be one, is to be a virtuous and righteous person. In my religion,
this goal is considered basically impossible without divine aid. None of us are capable of it on our own, but we should try anyway. Giving up this struggle because the goal
is impossible is precisely what my religion counsels against. Something
that stuck with me from the first time I met Fr. Oliver Brewer-Lennon was how diligently conscientious he was, even in things that "don't matter" to his overall goals or ambitions.
Everything, and everyone, was worthy of care and attention. This, to me, is a sign of saintliness.
So, with regards to research too, I'm no longer evaluating proposals by their goals, but by their process. What might we learn by trying to accomplish this? How might the student
develop their skills by attempting to solve this problem? These are the questions that we should be asking. Down with objectives, up with methodology.