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Terence Tao warns that the proliferation of AI problem-solving is plunging the discipline of mathematics into a crisis
On November 2, 2026, mathematician Terence Tao warned in a lecture at Caltech that after AI successively conquered Erdős problems, the Jacobian conjecture, and even the Navier-Stokes problem, the mathematics community is moving from a scarcity of proofs into a flood of proofs, with vast numbers of AI papers lacking derivation details overwhelming journals. He mentioned that OpenAI's solving of the Navier-Stokes problem within a week sparked a dispute over authorship and prompted him to publish an open letter jointly with 25 Fields Medalists, warning that problem-solving and insight are becoming decoupled. Tao believes the most pressing issue is how to train graduate students, because topics that once took months to work through can now be solved by AI in a few hours.
athematics community is moving from a scarcity of proofs into a flood of proofs, with vast numbers of AI papers lacking derivation details overwhelming journals. He mentioned that OpenAI's solving of the Navier-Stokes problem within a week sparked a dispute over authorship and prompted him to publish an open letter jointly with 25 Fields Medalists, warning that problem-solving and insight are becoming decoupled. Tao believes the most pressing issue is how to train graduate students, because topi
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Aswath Damodaran publishes a valuation article on Anthropic
Aswath Damodaran, a valuation professor at New York University, published a long article valuing Anthropic at $1.475 trillion. In the article, he noted that Anthropic's revenue in the first half of the year was about 14 times that of the same period last year, but growth slowed in the third quarter because OpenAI took market share and Anthropic lacked sufficient computing power. He mentioned that the $80.7 billion book loss in the first half mainly came from $72 billion in non-cash bond expenses, while the actual operating loss was slightly over $8 billion; Anthropic said it had achieved operating profitability last quarter. He believes the biggest risk is over $600 billion in computing power commitments, and that seven co-founders hold 50.1% of voting rights through a single class of shares.
n the article, he noted that Anthropic's revenue in the first half of the year was about 14 times that of the same period last year, but growth slowed in the third quarter because OpenAI took market share and Anthropic lacked sufficient computing power. He mentioned that the $80.7 billion book loss in the first half mainly came from $72 billion in non-cash bond expenses, while the actual operating loss was slightly over $8 billion; Anthropic said it had achieved operating profitability last quar
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Altman says large models' ability to find vulnerabilities is growing exponentially
In an interview with Stripe founder John Collison, OpenAI CEO Sam Altman reviewed the "PHP crisis week," saying that large models' ability to uncover vulnerabilities has been growing exponentially. He said that previously no one dared to use large models to scan all the public code on the internet, and that after actually doing so, the number of critical vulnerabilities exposed exceeded everyone's expectations. Altman believes that fixing software alone is no longer enough, and that the lasting solution is to rebuild the entire stack, from router firmware and operating system kernels to upper-layer applications, and that AI tools capable of writing code in parallel have already led a group of startups to begin this work. Ten days after the crisis, he still did not dare to declare victory, and said that humanity's existing threat model assumptions are failing.
In an interview with Stripe founder John Collison, OpenAI CEO Sam Altman reviewed the "PHP crisis week," saying that large models' ability to uncover vulnerabilities has been growing exponentially. He said that previously no one dared to use large models to scan all the public code on the internet, and that after actually doing so, the number of critical vulnerabilities exposed exceeded everyone's expectations. Altman believes that fixing software alone is no longer enough, and that the lasting
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