Theory at the Institute and Beyond, February 2026
by Nikhil Srivastava (senior scientist, Simons Institute for the Theory of Computing)
Let me tell you about two lists of questions — one for humans, and one for AI — and how they were made.
Working in a workshop
What is the point of a workshop? This question has different answers depending on who you are.
As a graduate student in 2007, I wanted to share my results, learn new techniques, and feel more plugged into the TCS community. I don’t remember almost any talks or math, but I remember hanging out with other students, and how awkward it was to approach senior colleagues. At my first FOCS, I walked up to Sanjeev Arora and said, “Hi, I’m Nikhil.” He said, “Hi, I’m Sanjeev.” And I just said, “I know.”
As a young faculty member in 2017, I attended my first American Institute of Mathematics (AIM) workshop, in which we spent afternoons working on open problems in small groups. It was a window into the mysterious minds of probabilists: I saw them explore ideas, decide what is interesting, and be confused. Seeing this process was more valuable than any paper or talk. We spent a lot of time discussing questions, and I came away with one that I thought about for years.
As a workshop organizer in 2025, my goal was to spark unexpected interactions among participants from different research areas and give momentum to the field.
Yet, we spend most of our time at conferences listening to talks about finished research.
Personally, I feel fried if I listen to more than three hours of talks in a given day. So how can we use the in-person time to better meet the needs of the many kinds of participants?
Here is one prescription that seems to work well: Before lunch each day, schedule a structured small-group activity with a clear, short-term scientific goal, in which everyone can participate.
Let me tell you about a few experiments with this idea over the past year.
In the Linear Systems and Eigenvalue Problems workshop in Fall 2025, we scheduled one hour of “working groups” before lunch each day. We reserved five rooms in Calvin Lab for five broad topics and assigned a moderator to each. Participants were given the following instructions on Day 1:
Choose a room. Your goal is to have a small group discussion in which you formulate an open question and write it up by the end of the week. Each group should have at most six people and represent at least two research areas. You may switch rooms during the week.
People disagreed about the formulations of the problems. That was the whole point! It took a few days to agree, and the discussions were messy. What does it mean to “solve” a problem? Is a certain problem already solved, or is it open? Why is it worth solving?
It turned out to be easy for anyone to enter these conversations. Algebraic complexity theorists discussed floating-point computation. Graduate students wrote things up with senior folk they had just met. Discussions continued into lunch, coffee, and email threads, moving beyond the usual cliques. Some problems were solved as they were being posed, and were excluded from the write-up. No one I met seemed worried about credit.
Not all the groups were equally successful. Three failure modes were (1) the discussion became technical and dominated by experts, (2) chaos, (3) running out of time. A bit of structure — such as pre-soliciting problems from the participants to seed the conversations, and/or a moderated discussion on the first day — can help a lot.
The result of the working groups is here. The process was fruitful, because strangers got to know each other. The product is useful because it shares interesting research directions with the field, extending beyond the workshop. And, after writing up their problems, some participants wondered: Well, if I’ve put this effort into formulating this question, why not work on it with my small group?
This experiment was repeated in the Randomness, Invariants, and Complexity workshop, later in Fall 2025. Here is a picture of a working group, which clearly violated the six-person rule, taken at 3 p.m. on Friday after the last talk:
Many variations are possible. One is to produce exercises related to the workshop — such as filling in details from the morning talks — and have people work on them together. We did this in the Fall 2025 Complexity and Linear Algebra Boot Camp and plan to repeat it with longer two-hour slots in the upcoming ICM 2026 Satellite Conference in August. The point is to have a scientifically meaningful low-stakes activity as a backdrop for interaction. If I had met Sanjeev in such a setting, I might have had more to say.
First Proof
Meanwhile, in early December on the third floor of Calvin Lab, a small group of mathematicians also gathered to discuss and write up a list of questions. Their scientific goal was different: The questions were no longer open, but would AI be able to solve them?
The result of that collaboration was posted on February 5. This list is different from the Erdős problems and existing benchmarks in a few ways.
- The problems arose naturally in the research of the authors and span many areas of math.
- They have been solved by the authors, and are of typical research difficulty — not notoriously difficult, but not routine. Some are parts of papers in preparation. The solutions have never been posted online or publicly discussed.
We are curious how well AI systems can do on these problems without significant human input. This is a community effort, and we encourage you to experiment with them!
Solutions will be posted at 11:59 p.m. Pacific time on Friday, February 13. The hope is that we will learn something about how to measure the ability of AI to do research math, and use this in the future to design better benchmarks.
