A mathematician finds hope after AI's new dawn
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OpenAI's massive data dump of more than 300 solved math problems triggered a wave of despair about the end of human supremacy. But one mathematician has found reasons to push back against the doom loop.
Why it matters: As AI capabilities continue to advance across disciplines, beating humans at one task after another, every new feat requires important contemplation. What problems remain to be solved? Where can humans still have an impact? What does it all mean?
- For Vanderbilt University's Dan Margalit, the answer within mathematics is that the machines aren't replacing human intellect. They are deeply reliant on it.
- He sees AI as a tireless finisher of human-led ideas and imagines a future where mathematicians can thrive in the age of AI.
Catch up quick: The academic world has been reeling since OpenAI released hundreds of AI-generated math papers, offering solutions to major open challenges just a few weeks after also claiming to solve the legendary Navier-Stokes Millennium Prize Problem.
- The intrigue escalated this week when OpenAI announced its models had disproved the exponential time hypothesis, upending a foundational assumption in computer science.
- Rival AI giant Anthropic revealed that its own models independently made the same discovery on the same day, pouring 14 million tokens into the effort, according to The Information.
- Both companies also were working on the Navier-Stokes solution at around the same time.
The new findings have triggered more shock and awe in academia. Yet in all that frenzy, here are five ways Margalit, who chairs Vanderbilt's math department, says mathematicians are finding hope, and avoiding despair, in the age of AI.
1. AI is a finisher, not an originator.
- The hope: AI didn't solve these problems in a vacuum. It succeeded where humans had brought ideas close enough to a breakthrough.
- The context: "The problems solved were the ones humans were closest to solving," says Margalit. The AI failed on thousands of other problems where human literature hadn't already pointed the way.
2. The machines still make mistakes.
- The hope: Mathematicians and others reviewing the AI solutions have found flaws.
- The context: As mathematicians read the proofs, a number of the released papers are facing retraction because AI made the same logic errors as humans, Margalit said.
3. It's brute force, not brilliant intuition.
- The hope: AI approaches math the way machines approach chess, or Go.
- The context: OpenAI deployed tens of thousands of agents to tirelessly smash together known theorems in millions of configurations. "That's amazing, but like chess, it's about trying all possibilities to get from where we are to where we want to go," Margalit notes. The AI isn't asking interesting questions.
4. AI acts as an ultimate calculator.
- The hope: Humans used to write entire books of integrals until software came along and automated the process. AI can also be a tool for acceleration.
- The context: This didn't kill math, it freed humans to explore harder concepts. "When an integral appears in a sophisticated problem, I no longer devote my research to it," Margalit says.
5. Math is about understanding, not just correct answers.
- The hope: The ancient Greek word "mathematika" translates to "the study of learning," he says. Margalit credited mathematician Bill Thurston, the author of a landmark 1994 essay that has taken on new life, with this observation: If a computer spits out a list of 10,000 prime numbers, it can't tell us about why they exist or the patterns they form.
- The context: The universe already knows the answers. Math is the process of the human mind grasping them. "If a computer tells me an answer, that doesn't give me insight or satisfaction," Margalit says. "Mathematics is the human endeavor of understanding."
The bottom line: Just as humans learned not to care that machines were unbeatable at chess, we will always have a need to understand that AI can't replace, even if it can assist the process.
