Following our mini-series on Claude Code for applied research, Pietro Ortoleva and Fedor Sandomirskiy joined Markus’ Academy for a mini-series on AI and economic theory and mathematicians (a fifth episode will follow). Both are economic theorists at Princeton. Their slides are available here.
In the first video Pietro outlined where AI fits in theory research. In contrast with math, our models don’t seek to prove a conjecture, but rather try to illustrate certain mechanisms. As a result, writing theory papers is analogous to searching for a fixed point; iterating over defensible assumptions and proofs to arrive at the desired insights. AI speeds up the iterations to arrive at the fixed point. The takeaways:
Pietro outlined 7 use cases: (1) sketching and brainstorming, (2) literature reviews (3) suggesting proofs, (4) checking proofs, (5) extensions, microfoundations, and simplification, (6) general proofreading, (7) simulations
Sketching models is the most underused. Give the model a vague intuition and ask: “Give me three minimal models that capture this intuition. For each, say what is elegant, what is fragile, and what theorem would be worth proving.”
Despite often being notation-heavy, frontier models can prove the results of an economist’s typical model reliably. Reliable does not mean that they deliver what you want to (or should) submit. To be effective, weaker models need to have the tasks decomposed into parts
The higher-value uses are attack (a hostile referee), repair (which assumption rescues a false statement) and inspiration: even a wrong proof can have insights
The risk of wasting time with AI-driven rabbit holes scales with your own ignorance
Episode available here: https://www.youtube.com/watch?v=kVVggnIaw2Q
Timestamps:
[0:00] Introduction, and economic theory as a fixed point
[5:12] Seven use cases, and why sketching is the most underused
[8:46] Proofs: attack, repair, and inspiration
[15:12] Extensions, microfoundations, simplifications
In the second part Fedor asked whether models can actually generate new ideas. In econ this is hard to assess, as model quality is subjective. We should look at math, where a proof either holds or it doesn’t, for data points. The takeaways:
Poor at attribution, fantastic at aggregation. The October 2025 claim that GPT-5 had cracked ten open Erdős problems did not hold up: Bloom (2025) showed it had surfaced known solutions. The flip side: no lemma buried in an unread appendix is ever lost.
AI excels at obtaining counter-examples: for example OpenAI (2026) disproving the unit distance conjecture and Fable 5 disproving the Jacobian conjecture
Multi-agent workflows with frontier models can explore many proof strategies in parallel. Sol Ultra proved the cycle double cover conjecture using 64 agents
Episode available here: https://www.youtube.com/watch?v=LbedQKu-5XM
Timestamps:
[0:00] Can models be creative, and why the evidence comes from math
[2:20] The ten Erdős problems episode, and Terence Tao's ledger
[5:19] The unit distance conjecture falls
[8:44] Jacobian, cycle double cover, and what it means for theory
Aware of how fast the frontier is moving, Pietro compared the models available today. The takeaways:
Intelligence and stamina are substitutes. AI often gets further by running a weaker model for a long time than a smarter one briefly. Yet many of the deeper models are not built to work for 20 consecutive hours, while agentic environments are. Stamina is also about price considerations; it may be prohibitively expensive to run Fable for extended periods.
Their verdict for the best model for theory today: GPT-5.6, narrowly. Fable may be more intelligent, but it is outweighed by 5.6’s stamina
The best mix is combining GPT-5.6 Pro on the browser with Sol Ultra. For a $20 subscription, pick OpenAI’s. The best free option is Gemini Pro in Google AI Studio, though your chats train Google’s models. Set maximum effort when available to you
Agents are fundamental in empirical work, but the browser is still enough for brainstorming
Episode available here: https://www.youtube.com/watch?v=lLgD9WwFMvM
Timestamps:
[0:00] The frontier since June: Fable 5, GPT-5.6, Opus 5
[4:13] Intelligence and stamina are substitutes
[8:53] The verdict, and what to run on a Pro, $20, or free budget
[11:10] Browser or agents?
In the fourth video Fedor covered the current state of “prompt engineering”. Writing effective prompts is no longer as valuable as it was a few years ago. The takeaways:
The value has shifted to context engineering. Specify task, context, output, quality criteria and incentives, one task per prompt; the weaker the model, the more it matters.
Let the model write the prompt based on your lazy two-liner. Have the same model that will do the work expand the prompt. Spend 15 minutes reviewing the expanded prompt.
Never let a session grade its own work. Run a verifier, and even a third “judge” between the “prover” and the “verifier”.
Provide LaTeX files whenever possible, and always convert PDFs to Markdown before providing them. Restart sessions often
The published prompt behind the cycle double cover proof provides a template for how to implement swarms of agents: 64 agents working for eight hours minimum with a supervisor stopping those that converge.
Fedor adds a trick: give the agents an escape hatch. If they get stuck for an hour, they can write their blocking obstacle to a Markdown file and hand it up to a better model. Running Sol Ultra this way for 15 hours cracked a conjecture he and his coauthors had worked on for a year, which neither 5.6 Pro nor Fable had solved.
Episode available here: https://www.youtube.com/watch?v=OBJ0h8j_m8Y
Timestamps:
[0:00] Is prompt engineering still a thing?
[3:40] Prompt expansion: let the model write the prompt
[9:45] Prover versus verifier, LaTeX not PDF, and when to restart
[16:43] Agent swarms, and AI proofreading
* Hosted by Markus Brunnermeier, with the support of Pablo Balsinde (PhD student, Stockholm School of Economics).
Comments
Nothing yet. Say the first thing.
Sign in to join the conversation.