SERIES · AI is making papers cheap to produce but they remain costly to referee. Proofs and Prompts is publishing a series of posts from 26 October on the future of publishing, papers and credit. Questions such as how to disclose AI use, who bears the cost of checking, what authorship means and what papers of the future might look like will be addressed. This post is part of the series. Each is written independently and reflects only its authors’ views. All posts in the series
For a long time, the standard format of a mathematical conference talk has been remarkably stable. A mathematician stands in front of a room. There are slides, or a blackboard. For twenty, thirty, or fifty minutes, the speaker explains a piece of work. At the end, if time remains, there may be a few questions. This format has always had limitations. But I wonder whether the arrival of increasingly capable AI systems gives us a new reason to reconsider it.
In a previous post, I argued that one of the important problems of AI-generated mathematics will be humanization. It is not enough that a mathematical argument exists, or even that it is correct. Someone should understand it, reorganize it, explain why it works, and connect it to the rest of mathematics. Perhaps conferences will have to adapt to the same problem.
A polished talk no longer tells us very much
Suppose I want to talk about a paper at a conference. An AI system may have helped substantially in producing the mathematics. It may have written parts of the argument, reorganized the exposition, prepared the slides, generated examples, suggested explanations, and perhaps even written the script of my talk. In principle, I could give a very polished presentation of a piece of mathematics that I understand only superficially.
Of course, something similar was possible before AI. People have always been able to present work they did not completely understand, and talks have never been examinations of their speakers. But AI changes the scale of the problem. Producing twenty beautiful slides explaining a technical argument is becoming very cheap. Producing a plausible explanation of why a theorem is interesting is becoming cheap. Producing answers to anticipated questions is becoming cheap.
Understanding the mathematics is not necessarily becoming equally cheap.
There is therefore a strange possibility: mathematical communication may become increasingly polished at exactly the same time that the connection between the person communicating the mathematics and the person (or machine) that actually produced the ideas becomes weaker. Perhaps the traditional conference talk is not particularly well designed for this situation.
What if a talk were a conversation?
I have been wondering about a different format. Imagine something closer to an interview than to a lecture. The speaker sits with a chair or moderator in front of the audience. The speaker still presents the work, perhaps with slides or a blackboard, but the presentation is not a forty-minute uninterrupted monologue. Instead, the chair interrupts.
Why did you introduce this definition?
What happens if this hypothesis is removed?
Can you explain the main idea without the technical machinery?
Where exactly does the difficult part of the proof occur?
Is this lemma really necessary?
How did you arrive at this argument?
What is the simplest example in which the phenomenon appears?
The chair would have read at least part of the paper beforehand and prepared a few questions. Members of the audience could also intervene during the discussion rather than waiting for the final three minutes. In spirit, it might look a little more like a late-night interview than a traditional mathematical lecture.
I do not mean that mathematics conferences should become entertainment shows. There need not be a desk, a band, and applause after every theorem. Although I would not completely rule out the band. The important difference would be that the presentation becomes interactive.
Understanding becomes visible
There is something that is quite difficult to fake in a sustained mathematical conversation. If you really understand an argument, you can usually move around inside it.
You can explain it from another direction. You can say which assumptions are essential. You can produce a small example. You can explain what you tried before finding the right proof. You can react when someone asks a question you did not anticipate. You can admit which part you do not understand as well as you would like.
This does not prove that you personally discovered the mathematics. Nor should it. Mathematics is collaborative, and AI will presumably become another participant in that collaboration. I do not think conferences should become detective agencies attempting to determine which sentence was written by a human and which by a machine. The interesting question is different. Has the mathematics passed through a human mind? Can the person presenting it actually discuss it? Can the result enter a mathematical community as something that people understand, rather than merely another object that has been produced?
If the answer is yes, then I care much less about whether AI was involved in obtaining it.
There would be some pressure
There is an obvious objection. This format would be more stressful. Standing in front of an audience is already stressful enough for many people. Being interrupted by a senior mathematician asking questions could make things considerably worse. I do not think this objection should be dismissed.
In particular, younger researchers should not be placed in a situation where a conference talk becomes a public oral examination. The same is true for mathematicians who are not comfortable speaking English, people who are naturally less quick in conversation, or anyone for whom this kind of interaction creates a substantial disadvantage. Understanding mathematics and performing well under pressure are not the same ability.
Any new format would have to recognize this. Perhaps junior researchers could receive some or all of the questions in advance. Perhaps the chair could meet the speaker before the session and discuss the structure of the conversation. Perhaps traditional talks could remain available for people who prefer them. Perhaps questions could be deliberately explanatory rather than adversarial. The point should not be to catch the speaker making a mistake. The point should be to create a setting in which understanding naturally becomes part of the presentation.
But perhaps a little pressure is useful
At the same time, I am not sure that all pressure is bad. If I know that presenting a paper means that someone may ask me why Lemma 4.7 is true, I have a rather strong incentive to understand Lemma 4.7 before I submit the paper. If I know that I may have to explain why a certain definition is natural, I may spend some time thinking about whether I actually know why it is natural. And if an AI system has generated an argument that I do not understand, perhaps I will be less tempted to immediately turn it into a conference submission if I know that eventually I will have to sit in front of other mathematicians and discuss it.
This seems healthy. At present, AI dramatically reduces the cost of producing mathematical text. Perhaps our institutions should increase the reward for understanding that text.
The chair would have a new role
This would also change the role of the session chair. At many conferences, chairing a session currently consists mainly of introducing the speaker, watching the clock, and saying “perhaps one last question.” In a conversational format, the chair would have a genuine intellectual role. The chair might read the paper beforehand, identify its central ideas, and prepare questions that help the audience understand what matters. A good chair could rescue a difficult presentation by asking exactly the question that half the room wants to ask but does not know how to formulate.
This work would take time, of course. But perhaps it should. We spend enormous amounts of collective time attending conferences. It seems slightly strange that so little time is usually invested in designing the actual intellectual interaction that happens there.
It might make conferences better anyway
There is another possibility. Perhaps this would be a better conference format even if AI did not exist. Many mathematical talks are extremely difficult to follow. A speaker has fifty slides and forty-five minutes, the notation accumulates, one crucial definition is missed, and twenty minutes later a significant fraction of the audience has become spectators rather than participants. A chair who can interrupt and say, “Before we continue, could you explain again what this object is supposed to represent?” might improve the talk enormously.
Questions during the presentation could reveal which ideas actually interest people. The speaker might spend less time covering every theorem in the paper and more time explaining the one idea that people will remember six months later. We might discover that the purpose of a conference was never really to reproduce the contents of papers orally. Papers are quite good at containing the contents of papers. A conference should perhaps do something else.
It should create understanding, discussion, disagreement, connections, and memories.
Conferences as part of verification
I have argued elsewhere that AI-generated mathematics may require new mechanisms of verification and humanization. Perhaps conferences could become part of that process too. Not formal verification. Not peer review. Not an examination establishing authorship. Something softer.
A result arrives in the mathematical community, and someone has to stand behind it, or perhaps better, sit beside it, and talk about it with other mathematicians. The audience sees not only a theorem and a proof, but a human being navigating the ideas around them.
Questions expose unclear points. Experts notice connections. Someone asks about a missing case. Another person suggests a simpler argument. The speaker realizes that one explanation is much better than the one in the paper.
The talk becomes another stage through which mathematical output is transformed into shared mathematical understanding.
An experiment
I certainly do not think every conference should replace all talks with interviews next year. Perhaps the format would fail completely. Maybe the speakers would hate it, or the chairs would not prepare enough. Perhaps discussions would constantly run over time. Perhaps the best researchers would turn out to be terrible interviewers and the best interviewees would not necessarily be the best mathematicians. These are good reasons to experiment rather than legislate.
A conference could try one session. Five speakers. Twenty or thirty minutes each. A chair who has received the papers beforehand. Ten minutes of presentation mixed with questions and discussion. Questions from the audience throughout. For junior participants, the questions could be discussed in advance. Then ask everyone whether they learned more.
My suspicion is that we eventually need to rethink several mathematical institutions that were built for a world in which producing mathematical text was expensive. Journals are one of them. Authorship is another. Conferences may be another.
If machines can increasingly produce papers, proofs, slides, summaries, and polished explanations, then perhaps the scarce object is no longer mathematical text. Perhaps the scarce object is understanding. And if that is true, our conferences should be designed to make understanding visible.
Received 1 October 2026.
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