There has been some recent discourse regarding the advent of AI, and how this will affect the role of mathematicians in the near future. I think the surface-level aggrandizing that has arisen from people solving Erdős problems with the newest model on the block is far less interesting than it seems, so let us dig a little deeper.
If we are to take LLMs at the face value they are presented to us with, then it must be that a given mathematician has either benefited or been rendered redundant. I note that a hidden presumption in this claim is that a mathematician is, first and foremost, a producer of results. If we accept this premise, we arrive at our current anxiety-ridden discourse fairly mechanically. The whole conversation, however, starts to look strange if we reject it. But before rejecting it, let us follow it to its logical end.
If our primary worth is tied to our output, we can start plotting ourselves on a graph. Like any metric of human productivity, these AI tools will apply to us non-uniformly; those with the instinct and resources to leverage them will accelerate, while others will not. So, if we map researchers strictly by the volume or prestige of their results, are mathematicians normally distributed? Let us assume they form a standard bell curve, and try to qualitatively describe what the regimes of this distribution look like. On the left tail, a “bad” mathematician might be one who bloats arXiv with near-useless incremental results just to fulfill grant requirements, or one who does not publish at all despite their perceived intelligence. On the far right tail, we have the luminaries—mathematicians who have theorems named after them, and whom early-career researchers aspire to be.
But what about the vast middle? The peak of the bell curve is where most of us actually live. We are the ones spending months wrestling with a single intractable proof, and doing the quiet, unglamorous work that keeps the field breathing. Yet, it becomes quickly obvious that the entire AI discourse is a conversation exclusively about the tails (where almost nobody lives). Even worse, it has managed to say something degrading to the rest of us in the middle anyway: that if a model could have eventually proven your theorem, your time spent proving it was wasted. This worldview only holds up if you accept the earlier presumption that we are simply machines for producing results, each of us a mere data point in whatever metric makes us feel the best about ourselves.
I wholeheartedly reject this notion. I am, by any honest accounting, an average mathematician, and I expect to remain one. The caveat here is that I am happy with that, which is a reality many refuse to accept in their pursuit of artificial excellence. If the models keep getting better (and they will), they might eventually take over the brute-force production of results that people so desperately cling to. But you owe it to yourself to love the actual process of what you do, even if you are entirely mediocre at it.
Somewhere along the way, the word “average” was no longer a verdict on my potential, and started allowing me to learn what I love for no reason other than the fact that I love it. That is the entire transaction, and perceiving myself as average is the greatest gift I have been given, because it completely decouples my self-worth from my output. When we stop viewing mathematics as a race to be won, we remember that it is a human experience to be lived, a gift we take wildly for granted.