It started with a plate of ginger chicken.
In the late 1970s, physicist Richard Feynman – known for his earlier work manhattan project – Sitting down to lunch with my friend Ralph Leighton at a restaurant in Glendale, California. Leighton was torn between ordering his usual favorites, or risking something new.
Feynman turned the choice into a mathematics problem, and solved it on a piece of notebook paper. Their equation looks exactly like when Leighton – or any indecisive diner for that matter – should stop taking risks and stick with what’s good.
For decades, Feynman’s notes on the “Restaurant Problem” were illegible. But now, researchers have reconstructed the decision-making problem from Richard Feynman’s previously incomprehensible notes and proved him right. The findings were published June 1 in the journal Proceedings of the National Academy of Sciences.
problem choosing lunch
Imagine you are visiting a new city for a week. Each night, you can either try an unknown restaurant or return to the best restaurant you’ve ever met. You want to maximize your total dining experience throughout your trip.
This type of problem has a name in mathematics: the “optimal stopping problem.” The same logic is seen in apartment hunting and job hunting. But Feynman argued that you can always go back to the previous restaurant. The goal is to maximize your cumulative enjoyment, not just find a best spot.
A page from Feynman’s handwritten notes on the restaurant problem.
(Image credit: Caltech/The Feynman Lectures on Physics)
Feynman’s notes showed that the optimal strategy involves a quality threshold – a minimum score you need before you can commit – that starts high and falls as your journey ends.
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brian christiana computer scientist and cognitive scientist at the University of Oxford, began working on this problem with his colleague Tom Griffiths about 13 years ago. He tracked down Feynman’s original notes Feynman Lecture Website.
The team proved that Feynman’s solution was indeed optimal, then extended it to other versions of the problem: Do people really solve the problem this way?
They recruited 2,520 participants online and presented them with a digital version of the scenario: a grid of restaurants in a virtual city, each with a hidden quality score revealed on the first visit. The goal of the participants was to maximize their total score over a certain number of nights. Each person played only once.
“We really wanted to capture people’s inner intuition,” Christian told Live Science. “When you get into this situation, what do you do?”
Answer: People do not follow Feynman’s optimal curve in reality. Instead of a precise mathematical limit, participants used a much simpler rule. Their quality bar started out high and dropped by the same fixed amount every night, no matter how long the trip was or what the restaurant landscape looked like.
The simple strategy achieved about 90% of the value achieved by the optimal approach.
“People aren’t doing the best work. They’re doing some very simple things,” Christian said. “And yet the simpler strategy is being devised in a way that seems situationally appropriate.”
The slope of the decreasing range of people was the same in every situation – a week-long trip or a month-long trip, with restaurants being equally distributed in quality or skewed towards the extremes. What changed was that people set their own starting bar, and adjusted it appropriately based on the scenario they saw.
In other words, people used a universal rule for how fast to lower their standards, but also a calibration of how high to set them in the first place.
an order of redemption
The results fit into an emerging framework in cognitive science called “resource rationality”. The idea that humans are not perfectly rational, but make good use of the limited time and brain power they have.
“People don’t do things right, but they use their limited resources almost right,” Christian said. “I think it’s a somewhat more redemptive story about the human mind than the 20th century.”
This is a change from the long tradition in behavioral economics of emphasizing human irrationality and cognitive biases.
Christian says the findings also have implications for AI. Most AI systems assume that people behave as fully rational agents. This study shows that AI designed based on how humans actually think can – imperfectly – work better.
Feynman died in 1988, never publishing his restaurant analysis. But more than four decades after he wrote those notes over lunch, the puzzle he left was finally solved – and it says as much about the human brain as it does about what to eat.
Christian, B., Rusek, E.M., and Griffiths, T.L. (2026). Solving Feynman’s restaurant problem reveals optimal solutions and human strategies. Proceedings of the National Academy of Sciences, 123(23), e2509612123. https://doi.org/10.1073/pnas.2509612123