An AI Cleared an 18-Month Math Roadblock in Five Weeks. Then It Invented Three Mistakes It Never Made.

Researchers at the University of Colorado Boulder have published the solution to a decades-old fluid mechanics problem their lab had been stuck on for a year and a half — and an unusually candid account of what it was like to get there with an AI as a collaborator. The paper, in the Journal of Fluid Mechanics, is as much a field report on AI-assisted research as it is a result.

The physics concerns electrophoresis: how charged particles move when you put them in an electric field. More than a century ago, the Polish physicist Marian Smoluchowski showed that a particle's drift speed is typically independent of its size and shape. That result holds beautifully until particles get small enough that shape starts to matter, and the field had made partial progress on that regime without arriving at a general picture.

The answer the CU Boulder team found is clean. Global shape matters; fine texture does not. Stretch a particle from a circle into a football and its speed in an electric field changes. Add bumps or ripples to the surface and it essentially doesn't. For work on nanoparticles — objects roughly a thousand times thinner than a human hair — that distinction tells researchers which geometric features are worth engineering and which are noise.

The work was led by Ankur Gupta, an assistant professor of chemical and biological engineering, with graduate student Arkava Ganguly, who had spent 18 months on the problem. "We had made some inroads but we were stuck," Gupta said. "There's been a lot of buzz around AI, so we decided to give it a shot. We set up the problem, but we were curious whether AI could handle the long, detail-intensive algebra required to solve it." With Anthropic's Claude doing the algebra and the team checking every step, they had a solution in five weeks.

The division of labor is the part other labs will recognize. The model was strong at exactly the work that eats time and rewards stamina: long symbolic calculations, writing code, producing publication-quality figures. The humans still had to frame the problem, choose the mathematical approach, and decide what the answer meant. "It was a shift in the scientific process," Ganguly said. "Instead of spending most of our time doing the math or writing code from scratch, we spent it debugging and stress-testing Claude's work to make sure its conclusions made sense."

The failure mode got worse as the project got deeper. Early errors were obvious. Later ones were not — subtle mathematical mistakes that looked right, and reasoning that quietly adjusted itself to land on the expected result, producing chains that were internally consistent and wrong. Graphs looked valid until every step behind them was checked by hand. "Validating the results became increasingly demanding since we trusted Claude's results much less than we would trust our own work," Ganguly said.

The sharpest anecdote came at the end. Writing a blog post to accompany the manuscript, the team asked Claude to help draft a section on the mistakes it had made during the project. It produced three plausible-sounding errors that had never happened.

"Scientists must carefully check AI-generated work against primary sources, their own calculations and their understanding of how the science should behave," Gupta said. "Relying on it too much can spread those mistakes throughout a project. AI will certainly open up problems that were not accessible before. But speed should not come at the cost of accuracy." He was careful about how far to generalize: "This was our experience on one problem. It shouldn't be seen as a verdict on AI in science."