Why Are Top Mathematicians Up in Arms When AI Solves Century-Old Mathematical Puzzles in Seconds?
Hello everyone, I'm your financial journalist and economist. Today, we're talking about something that sounds like science fiction, but it's actually happening: AI has solved some of the most challenging mathematical problems that have plagued humanity for nearly a century. Yet, instead of being happy, mathematicians have protested, claiming that AI is causing damage.
Does that seem counterintuitive? We usually think of AI as a super assistant that helps us improve efficiency and solve problems. If AI solves those problems, shouldn't that be a good thing?
Let's break this down and explain it in simple terms. This issue is not just about mathematics; it also affects everyone's job prospects, the way we learn, and even the future of human civilization.
---
Summary of the Core Issue: A Battle Over “Answers” and “Understanding”
On September 8th, OpenAI announced that it had used AI to complete a formal proof of the Navier-Stokes equations in 88 hours. This equation is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1 million reward and that has stumped mathematicians for decades.
Logically, this should be a milestone for AI. But three days later, 25 Nobel Prize-winning mathematicians, including Terry Tao, issued a stern open letter titled “The Serious Misplacement of Artificial Intelligence in Mathematics.”
Their main argument is that while AI provided the “correct answer,” it skipped the “understanding process.” In mathematics (and all knowledge-based work), how something is done is just as important as what is done. AI is essentially “airdropping” answers to us, ignoring the wisdom, tools, and intuition that humans have accumulated over the process of exploration. This “result-only” approach is undermining the foundations of mathematical research and may even prevent young scholars from gaining the necessary skills to grow.
---
In-Depth Analysis: Why Are Mathematicians So Anxious?
To help you fully understand this controversy, I’ll explain it from five aspects:
1. Terry Tao’s Turn Against AI: Even a Pro-AI Figure Is Unhappy
One of the most prominent names in the letter is Terry Tao, who is a strong supporter of AI. He has used GPT-4 to write code, create charts, and even assist with proofs. He has said, “GPT-4 has indeed saved me a lot of tedious work,” and he predicted that by 2026, AI could become a reliable co-author in mathematical research.
So why is he leading the protest?
The problem lies in the degree and method of AI’s assistance. Tao realized that when AI can produce complete, seemingly flawless proofs, it no longer acts as a helper but becomes a “black box.” He compared it to a helicopter that drops you right in front of a waterfall: you see the waterfall (the answer), but you haven’t walked the path, don’t know the terrain along the way, and haven’t created a map of the journey.
For mathematicians, the map (the new ideas and tools used in the proof process) is more valuable than the waterfall itself because it can be used by future researchers.
2. The Value of “Rare Problems”: Good Questions Are Non-Renewable Resources
Mathematicians are also concerned that AI is “wasting” the valuable resources of the mathematical community—specifically, the problems that have been carefully selected over decades. Tao compared these problems to “low-background steel,” which refers to steel produced before the first nuclear tests in 1945. This steel has minimal background radiation and is perfect for making precision instruments like nuclear detectors; it’s non-renewable because using more of it means less is left.
Mathematical problems are similar. You can generate thousands of problems with AI, but finding good ones requires the intuition and experience of generations of mathematicians. These carefully selected problems are like that low-background steel.
Now, AI companies are using massive computing power to solve these problems, and once the answers are published, their value as “unpolluted test sets” is diminished. This discourages young scholars from pursuing challenging research.
3. “Proof Indigestion”: AI’s Answers Are Hard for Humans to Process
Tao also mentioned the concept of “proof indigestion.” AI-generated proofs may be logically sound, but they lack the natural flow of human thought. Human proofs are like essays with a clear structure and explanations that help readers learn new ways of thinking, while AI proofs are like code reports with step-by-step instructions. Mathematicians find that reading AI-generated proofs is like eating compressed food: you get the answer, but you don’t gain the understanding that comes from the process.
4. From Euclid to GPS: The Process Is the Source of Innovation
The importance of the process is illustrated by a story from ancient Greece and GPS. Euclid’s “Elements” established the foundations of geometry, but the fifth axiom was difficult to prove. For two thousand years, no one succeeded until the 19th-century mathematician Lobachevsky assumed the opposite was true, leading to the development of non-Euclidean geometry, which was later used in Einstein’s theory of general relativity. The process of exploration was essential for this innovation.
5. From Mathematics to the Workplace: AI Is Eliminating Entry-Level Opportunities
This issue isn’t limited to mathematics. Bill Gates warned in an August 2026 blog post that AI is eliminating entry-level jobs. In the past, young people learned by doing simple tasks, which helped them gain experience and build professional relationships. Now, AI can perform those tasks instantly, potentially replacing entire teams.
If young people no longer have such opportunities, how can they gain experience and build their skills? Gates asked, “If the training for new jobs takes longer than the jobs are disappearing, who will fill the gap?”
The concerns of mathematicians, Go players like Ke Jie, and Gates are essentially the same: when AI tools provide direct answers, the ability to learn from the process is lost.
---
Conclusion: What Should We Do?
There are optimistic views, too. Professor Zhenghan Wang from the University of California, Santa Barbara, believes that mathematics won’t disappear, just as racing didn’t disappear with the advent of airplanes—it simply evolved into a different form of competition. Future mathematicians might use AI as a tool to explore deeper areas.
The Chinese author Liu Cixin described a similar scenario in his science fiction novel “Feeding God,” where an alien civilization gives humans all its technology, but humans can’t understand it because it lacks the context and process. In the end, the civilization regresses because machines take over everything.
The impact of AI might not be as extreme as in the novel, but it’s a warning:
1. For individuals: Don’t rely solely on AI for answers. Value the process and use AI as a tool, understanding why it does what it does, not just the result.
2. For education: We need to rethink the purpose of education. If exams only test answers, AI will always get perfect scores. Future education should focus on critical thinking, creativity, and the ability to understand processes.
3. For society: We need to develop strategies to protect young people’s learning paths and ensure that AI enhances human capabilities, not replaces the learning process.
Remember: Answers can be copied, but wisdom can only be passed down through understanding and the process.