Speeding Up the Process of Mourning

The world of mathematics, including theoretical computer science, is in turmoil. Even the Millennium Prize Problems, and, worse still, our beloved FOCS/STOC open problems, are no longer beyond the reach of LLMs. Watching this unfold inspires genuine awe and excitement, yet it also brings a real sense of loss. In the stages of mourning, the community seems to have moved away from denial. No more “models are nice, but they cannot do real math.” Instead, within our different mathematical communities, we now live in some combination of anger, bargaining, and depression.

If you are a junior mathematician, you have every right to take your time processing this shift. You have my deep sympathies, and we must both support you and ensure you have a central voice in shaping the future of our field. But to senior colleagues, myself included, I say: Snap out of it.

This moment is not simple, but there is no time to waste. We need to rise to the challenge. The world is changing at an incredible pace, and our response needs to be decisive and continuous. That may not be the traditional forte of academics, but the magnitude of this moment demands it.

Among the reactions exhibited by senior mathematicians, I find bargaining and depression particularly harmful. Bargaining, a close cousin of denial, is the hope that our work can stay more or less the same with just a little adjustment. If only we could get the frontier labs to pause or stop proving our theorems, or if we slightly adjusted the rules of our publication venues, things wouldn’t be too bad. Sure, pushing back on frontier labs and addressing urgent concerns about the viability of our publication system are important. But we should not mistake these measures for a way to avoid a fundamental transformation of our profession.

Bargaining slows real action. It also prevents us from enjoying the positive aspects of the AI revolution, including progress on mathematical questions that we genuinely care about. We cannot suddenly move the goalposts and pretend that proving theorems was never the point, or that our open problems were merely proxies for building mathematical understanding. Those theorems are still of deep interest, and studying their proofs remains central to how we gain understanding in the first place. As for me, there are quite a few conjectures whose proofs I would absolutely love to understand, regardless of the source.

As for depression: the next time you have the urge to lament, or even celebrate, being “the last generation of human mathematicians,” perhaps keep it to yourself. Contemplating the end of your profession from the relative comfort of an established, tenured career is a privilege, and it comes with responsibilities. Senior academics are not merely individual researchers; we are stewards of our field, and we owe our junior colleagues active leadership rather than abandonment.

So, what do we need to do, and keep doing again and again?

Right now, the immediate, practical questions of how to adapt our institutions are getting the most attention, and we are already seeing thoughtful suggestions and encouraging initial steps. Today, this means increasing the recognition and incentives we provide for communication, understanding, and community building, and reflecting those priorities in our hiring, promotion, funding, and publication practices. For example, many are pointing out that we should no longer accept badly written papers just because we value the theorems. Similarly, we may now value conceptual work, such as new definitions, novel questions, and fresh techniques, more than ever before.

Yet we cannot treat these reforms as a one-time adjustment. We face the daunting task of continuously recreating our institutions as capabilities evolve. Tomorrow, models may surpass us at communicating their results, and eventually at conceptual work as well, which will force us to shift our core operations yet again. The same applies to how we educate future generations of mathematicians. If the human role increasingly centers on judgment, taste, and a broad perspective, how can newcomers reach that point? All of these questions are on everyone’s mind, and I urge us to be brave enough to pursue dramatic, ongoing transformations.

To guide those transformations, however, we need something deeper. Above all, we need to reevaluate our identity. What is it that makes mathematical knowledge and research valuable? What are we offering society, and how much of it survives in a world where models match or exceed humans in some or all relevant mathematical skills? For quite some time, the implicit social contract has been that society pays us to exercise our intellectual curiosity and we, in return, provide useful skills to the next generations and practical knowledge for the world. The current crisis is driven not only by the power of LLMs, but also by how rarely we have had to examine or articulate this contract. Now that the deal needs to be renegotiated, we should approach it with humility rather than entitlement.

It is easy to feel bleak when confronting these questions, so it helps to ask what a positive vision might look like, even in a future with artificial superintelligence (ASI). We are not there yet, as today’s models still make mistakes and flawed proofs can actively harm learning, but suppose we reach a world where models are much more capable. One optimistic possibility I have been toying with is a future that opens the best parts of the academic experience to everyone. Not that everyone would hold an academic job or create knowledge that is new to the world, but everyone could participate in serious intellectual exploration, in mathematics and beyond. Conversations with reliable models could be truly Socratic: helping us ask questions, develop ideas, and discover things for ourselves, rather than simply supplying answers. In this vision, everyone would have access to forms of intellectual creativity that are now reserved for a fortunate few. Within this world, professional academics (in mathematics and elsewhere) would need to find our own distinct role, and I believe we could. Even if this future supports fewer professional mathematicians, it could nevertheless support a much richer mathematical life.

Finally, we must look further than just our own small piece of heaven. Accelerating mathematics can bring tremendous good to the world if it speeds up applied fields, medicine, and other concrete benefits for society. At the same time, the disruptions and dangers extend far beyond academia: a professional driver losing their job is no less important than a professional mathematician whose work has become less enjoyable. We therefore have a duty to take our professional responsibility toward AI alignment seriously.

AI models are mathematical objects, and their development could not have happened without our collective work. Furthermore, mathematicians, especially theoretical computer scientists, have a critical role to play in helping to govern AI models so that they serve individuals and society rather than harm them. Of course, AI alignment is not merely a mathematical problem, but the mathematical perspective is invaluable. Some of us have long been calling for more significant involvement in navigating the interface between computation and society. It is time for many more to heed that call.

Acknowledgments: Thank you to Sílvia Casacuberta, Lee Cohen, Jabari Hastings, and Charlotte Peale for many meaningful conversations and thoughtful comments on earlier drafts, though the views expressed here are entirely my own. I also want to thank a couple of unnamed models that graciously helped me clarify my perspective.

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