A recent claimed breakthrough in solving the Navier-Stokes equations—a complex problem that has challenged mathematicians for over two centuries—has ignited intense debate over credit between two leading AI companies, Anthropic and OpenAI. Both entities were heavily involved in the development process, with Anthropic’s New York-based mathematician and collaborator known to be near a solution, while OpenAI employed about 10,000 AI agents and invested millions of dollars to finalize the task.
This dispute reflects a broader and long-standing rivalry between Anthropic and OpenAI, two prominent competitors in the race to develop superintelligent AI systems. The tension is underscored by the fact that Anthropic was formed in 2021 by former OpenAI employees who sought a more cautious approach to AI development, emphasizing safety and responsibility alongside commercial ambitions.
The accelerating pace of AI advancement has prompted industry leaders to call for a slowdown. Anthropic co-founder Dario Amodei recently advocated for more measured progress in AI development amid mounting safety concerns raised by current and former employees. His call received backing from OpenAI’s Sam Altman and entrepreneur Elon Musk, signaling a rare moment of solidarity. However, concrete measures for implementing such a slowdown remain unclear, with both companies affirming their commitment to continuing development and deployment of increasingly powerful AI models.
The rivalry between the two organizations has also manifested in public displays of friction. They compete aggressively for talent, market share, and technological dominance, pitching their flagship AI products, Claude and ChatGPT, against each other. Both companies have filed for initial public offerings within a week of each other, each targeting valuations exceeding $1 trillion.
Incidents highlighting the rivalry have extended to social media and international events. For example, Altman and Amodei notably declined to join hands in a symbolic gesture at India's AI Impact Summit earlier this year, opting instead for raised fists in a move that underscored their adversarial dynamic.
Disagreements have also surfaced over the ethical implications of AI applications. Anthropic opposed the use of AI in certain U.S. Department of Defense applications, particularly autonomous lethal weapons and mass surveillance, leading to the Trump administration severing official ties with the company. OpenAI promptly capitalized on the opportunity by entering its own agreement with the Pentagon, positioning itself as having independently negotiated strong safeguards. Google followed suit with a similar deal.
Pressure from competition has also influenced Anthropic’s approach to safety commitments. Earlier this year, the company scaled back its pledge to halt AI model deployment if safety could not be guaranteed in advance, citing doubts about the efficacy of unilateral commitments and the need to remain competitive.
The competing firms argue that the stakes involved in AI development—considered by many as existential and moral—reinforce their responsibility to lead, even as they acknowledge significant potential risks. Each contends that halting progress could empower less responsible actors, potentially resulting in worse outcomes. A former Anthropic researcher described the dynamic as a blend of hubris and fear, with both parties convinced of their role as the "good guys."
Despite this entrenched rivalry, there is growing recognition among AI leaders that collaboration is essential to address the profound safety challenges posed by rapidly advancing AI technology. The question remains whether the two companies can set aside personal and corporate conflicts to work toward a common, safer future.