No one likes a know-it-all, especially a digital one. It's a painful lesson that artificial-intelligence start-ups Anthropic and OpenAI are learning at a delicate time, with an AI backlash forming just ahead of their planned initial public offerings.

Solving a math problem that eluded humanity's greatest minds should have been a celebratory moment for OpenAI. But while its AI seemingly made a breakthrough on the Navier-Stokes problem-one of the greatest unresolved questions in mathematics-the achievement is mired in controversy. Competing researchers said OpenAI may have used their work without credit, although the company denied it.

That's messy, but what about squeaky-clean Anthropic, whose founders left OpenAI due to ethical concerns? Well, one of its researchers has just quit, claiming both Anthropic and OpenAI are "gambling with our lives" in a race toward self-improving AI. An Anthropic safety researcher posted in response that "we really do earnestly believe AI could kill all humans." It's not great pre-IPO marketing.

Anthropic has not responded to a request for comment.

You don't have to believe in killer robots to think AI companies are close to provoking political and regulatory action to curb the industry. AI-led cyberattacks are the immediate danger while opposition to the spree of data-center construction looks set to be a big U.S. midterm election issue.

Anthropic and OpenAI's argument has been that if they don't develop the next generation of AI, someone less ethical will do so-maybe China. But that looks to be wearing thin amid the stream of controversies. And while solving incredibly difficult math problems could lead to long-term scientific breakthroughs, so far the ordinary voter isn't seeing much tangible benefit from AI.

OpenAI and Anthropic have to pull off blockbuster listings to make good on their enormous spending commitments. They need to improve their image fast, or risk political and regulatory intervention which puts the whole AI trade at risk.