AI trained like a Rubik's Cube solver simplifies particle physics equations

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For years, Rutgers physicist David Shih solved Rubik's Cubes with his children, twisting the colorful squares until the scrambled puzzle returned to order. He didn't expect the toy to connect to his research, but recently he realized the logic behind the puzzle was exactly what he needed to solve a problem involving particle physics.

That idea led to a new artificial intelligence (AI) method that can simplify some of the extremely complex equations used in particle physics. Shih described the method in a study posted to the arXiv preprint server, a widely used site where scientists share new research.

"In reaching our solutions, we found that an analogy between mathematical simplification and solving Rubik's Cubes was key," said Shih, a professor in the Department of Physics and Astronomy at the Rutgers School of Arts and Sciences. "Both can be viewed as scrambling and unscrambling problems."

The project also led to something else: Shih conducted the research in full collaboration with an AI system that helped write code, run experiments and produce the paper. This offered a glimpse of a new model of scientific research in which scientists work alongside AI systems that help design programs, analyze data and test ideas. It also raises new questions about how graduate and undergraduate students should be trained for this kind of AI-assisted research.

"This research is also noteworthy for how it was carried out in full collaboration with Claude Code, an agentic AI system that did all of the hands-on work under my supervision," said Shih, also a professor in the New High Energy Theory Center.

Jack Hughes, a Distinguished Professor and chair of the Department of Physics and Astronomy, said the work highlights how quickly research is changing.

"This new style of research, which is done in collaboration with AI agents, has the potential to massively accelerate our research," said Hughes, an astrophysicist. "There is an urgent need to train our students and postdocs in this new style of research."

AI shifts what physicists can tackle

Shih said working with AI changed what he was able to attempt as a researcher.

"If we learn how to use these tools properly, it will allow us to take on more ambitious problems," he said. "It changes the scale of what one person can do."

In many fields of science and engineering, equations can become extremely long and complicated. In particle physics, equations describing subatomic particle collisions can contain hundreds of terms, but physicists insist underneath the complexity there is something simple and elegant.

"Particle physics, in particular, is a field where complex calculations are often expected to lead to simple answers due to symmetries and structures underpinning the fundamental theory," Shih said.

Simplifying these equations helps scientists see patterns more clearly, make more precise predictions and reduce the computing power needed for calculations. Simplifying an equation does not change its meaning, but it can make calculations more precise because it avoids subtracting or combining very large numbers that can introduce tiny rounding errors in computers.

From Rubik's Cubes to equations

Shih wanted to see if AI could help find new ways to simplify these equations using what is known as machine learning, a type of artificial intelligence in which computers learn by studying examples and recognizing patterns rather than following step-by-step instructions.

He realized that simplifying an equation is similar to solving a Rubik's Cube: A simple equation can be scrambled into a complicated one, and if you know the right moves, you can reverse the process and return it to a simpler form.

Shih used this idea to train a machine-learning system. First, he started with simple equations and scrambled them by applying mathematical operations. Then he recorded the steps needed to unscramble them. By studying many examples, the AI learned how to recognize patterns and reverse the scrambling process.

When the system was given new, complex equations it had never seen before, it was able to simplify them.

"Our new method achieved a nearly perfect simplification rate, far surpassing previous machine learning-based methods," Shih said.

The research shows that AI may become a powerful tool for symbolic reasoning, which is the kind of math thinking scientists use to discover new laws of nature.

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A new kind of lab partner

Shih said the most unusual part of the project was how the research was done.

"Claude is actually functioning here like a graduate student would," he said. "It did all the hands-on labor that a student would normally be doing in one of my projects."

The AI wrote code, ran experiments, generated data, created plots and helped write the research paper.

The system was incredibly fast and could write and test code faster than a human and could keep working around the clock. But it made mistakes and sometimes repeated the same errors, which meant Shih had to supervise it carefully and check its work.

The experience showed him both the power and the limits of artificial intelligence as a research partner.

Rethinking training for young scientists

The project led Shih to a bigger question about the future of scientific research, and the role AI systems may play.

"Can they reach total autonomy, or will they just remain a tool that will make us all much, much more powerful?" Shih said. "I think that's the trillion-dollar question right now."

The scientific community is divided between those who say AI could one day make discoveries on its own and those who see a partnership with humans guiding AI systems that can work faster and handle more data than any person, he said.

"There are some people who are saying that we're going to get 10,000 Einsteins, that humans are going to be obsolete and just going to be sort of watching the AIs do research," Shih said. "I don't know if that's going to happen. I think what is much more likely is that it's going to allow scientists to do much more than they can today."

Shih said the shift is already underway in his own lab. He is actively training his postdocs and students to collaborate with AI systems such as Claude, teaching them how to guide the work and validate what the system produces. Over time, he said, universities may need to formalize that training through new courses focused on "vibe coding" and "vibe research," a style of working in which scientists partner with AI to explore ideas, test solutions and push research forward more quickly.

Shih said he believes AI will become a standard part of scientific research, but human judgment will remain essential.

"The key skill for the next generation of scientists will not just be solving problems, but learning how to work with AI, guide it and validate what it produces," he said. "If we do that well, the payoff could be enormous in terms of faster progress and new discoveries."

Publication details

David Shih, Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories, arXiv (2026). DOI: 10.48550/arxiv.2603.11164

Journal information: arXiv

Key concepts

Optimization problemsArtificial intelligence

Provided by Rutgers University