Home of real teaching & learning
  • Full support for teachers
  • Focus on critical thinking
  • Engaging classroom activities
  • Integrated student eBook
  • Assessed tasks / qBank
  • Practice exam questions

The InThinking Guarantee: Our sites are written by expert practitioners and not by AI

See our AI policy

Disclaimer: InThinking subject sites are neither endorsed by nor connected with the International Baccalaureate Organisation.

Don't miss out, find out!

Has AI destroyed mathematics?

On 6th October 2026 Open AI released 722 mathematics papers on an unsuspecting mathematical community. These concerned 372 problem areas where mathematicians had been working on questions to do with topology, number theory, combinatorics, and even huge unsolved questions such as the Riemann hypothesis. These papers were generated by a hitherto unreleased frontier model being developed by Open AI. Is there any point in human beings doing research mathematics anymore?

Teacher only box

Aim: This activity is an extended investigation into the scope and methods of mathematics with attention to ethics. Students will need to think about what it is that human mathematicians can do that generative AI cannot. They will also consider the role of understanding and explanation in the process of mathematical proof. The first two activities are suitable for the whole class and take 50 mins. There are additional activities for interested students that could take an additional 60 minutes.

Time: 50 plus an optional 60 minutes.

Commentary: The strategy here is that the students are confronted with real mathematicians not just journalists. Students will read a short article by a populariser of mathematics who is herself an accomplished mathematician. They will then watch short video clips of real mathematicians and computer programmers discussing the implications of recent dramatic events. At the end of the activity they will have a clearer idea of what mathematics used to be like before AI and the nature of the crisis it is facing. They will be required to reflect on their own view and to link to other areas where AI seems to be making big changes to the way in which we make knowledge.

Hannah Fry: Has AI destroyed mathematics? (30 mins)

Read the text below and answer the questions in groups. Be prepared to share with the whole class.

Writing in New Scientist mathematician Hannah Fry described the collective shock of the mathematical establishment when it woke up to find that Open AI had solved 372 of their most cherished problems. Prof Fry notes that far from being exhilarated that these problems were now solved and that the sum total of mathematical knowledge had been increased, mathematicians were dismayed not only that the ‘solutions’ offered almost impenetrable and led to no new methods, insights, or mathematical intuitions, but that, in many cases, mathematicians who had been working on them suddenly faced a situation where the reason for their existence was gone.  

Hannah had been working on a particular set of equations for her PhD - the Navier-Stokes equations - way back in . These are super important in physics and engineering because they describe the motion of fluids, where they are a water droplet on a leaf, the movement of air around an aerofoil, or the rotation of whole galaxies. The big question was whether these equations could break apart and yield a situation known as a singularity where the fluid could whip itself up to infinite velocities. Hannah writes: “This was a such a big deal to the mathematical community that at the turn of the millennium, the Clay Mathematics Institute promised they’d give $1 million to whoever managed to solve it.”

The Navier-Stokes equations are basically Isaac Newton’s second law of motion: F=ma, but applied to fluids. AS Fry puts it: "They are, in my not entirely unbiased opinion, staggeringly beautiful, able to articulate everything from the drip of a water droplet on a leaf and the churn of an entire atmosphere to the gases swirling around in a galaxy in the sky.

"The thing is, these equations have a tricky little bit that pops out of the acceleration part, which contains a feedback loop within it. The faster fluid flows, the faster the gradient can get between two adjacent streams, and so the faster fluid flows. It’s a bit like the fluid version of putting a microphone next to a speaker. The feedback loop can get louder and louder until everything ends up breaking. Or, in the case of the Navier-Stokes equations, the speed of the flow heads off to infinity.

"To be clear: no one was ever worried about fluid dynamics tearing open a black hole when you stir your tea or anything. It was just that the weird behaviour of this little term left the possibility that the equations themselves would break.

“On the flip side, there’s another term in the equation – the viscosity – that acts as a brake and calms everything down, stopping the flow from getting completely out of control. So, the question was: does the brake always kick in?”

Various groups of mathematicians had been using AI to work on this problem, and by all accounts they were making progress. But apparently once OpenAI heard that others were getting close, in the words of Fry, “they threw everything at it: 10,000 AI agents, sending each other 3 million messages over 88 hours, costing millions of dollars in tokens, to find a single example where everything blows up."

Tristan Buckmaster from N.Y.U. continues the story. “At that time, you have to understand that the Navier-Stokes equation became this tech bro obsession,” Most of those tech bros didn’t even understand the equations, he said, but they’d heard mathematicians point to them as a place artificial intelligence might help. As Buckmaster put it, solving Navier-Stokes was becoming “the yardstick to say, ‘We’re better than that other AI company.’”

The Navier-Stokes equations did indeed fall, and an AI proved it, though at the same time unleashing a firestorm of accusations of plagiarism and the use of underhand methods. Fry laments this breakthrough in her article: “This should have been a glorious moment of scientific exposition, but instead, mathematicians have spent the last few weeks having a massive collective wobble.” Part of the reason is that nobody yet understands the answer. Terence Tao, arguably the world's most well-known mathematician, had devoted a lot of time to it, and is as puzzled as anyone. “A mathematical result is supposed to yield understanding rather than just being the exercise of a formal logic.” Yet this ‘solution’ is 166 pages of dense and terse text backed up by thousands of lines of formal code. There are no insights, intuitions, or beautiful methods to found here - no mathematical aesthetic. As Fry puts it: “they came for the glory without giving much back. So, we are left with a proof that almost no one wants to read, a $1 million prize that no one will want to collect, and no one who can stand at a blackboard and explain why this particular vortex makes everything break, when nothing else we tried ever did."

Fry observes that in the weeks since the release, mathematicians are having their own existential crisis about their role and purpose, like Lee Sedol did after AlphaGo, Gary Kasparov with Deep Blue, and probably every literature graduate, musician and artist since ChatGPT was launched.

For Fry, at its worst, AI is an engine of extraction, it extracts from the countless nameless individuals that have contributed, without their permission, to its training. “The real sting in the tail is that OpenAI set its sights on mathematics because the prestige, the respect and the glory was just another thing that could be mined. It didn’t need to be that way. They so easily could have been open and collaborative. But the moment when one of humanity’s greatest intellectual traditions became vulnerable, they chose conquest over stewardship.”

References:

Fry, H. (2026/14/October) Hannah Fry: How OPenAI has caused an existential crisis in mathematics. New Scientist. 

Howlett, J. (2026/22/October) The inside story behind OpenAI’s million dollar math proof. Scientific American. 

Discussion questions

  1. Why are mathematicians shocked?
  2. Why are mathematicians not celebrating the release of the new mathematical results as they would if human authors had produced them?
  3. Why might mathematicians fear their future?
  4. What is the Navier-Stokes problem?
  5. Does Fry consider the actions of OpenAI to be collaborative and in the spirit of the tradition of mathematics as an area of knowledge?
Teacher only box

Possible answers to questions.

  1. Why are mathematicians shocked?

    Mathematicians are shocked because of the sheer volume and scope of the released proofs, and that they are released in a form that is both difficult to understand, and not conducive of further mathematical insights or development.

  2. Why are mathematicians not celebrating the release of the new mathematical results as they would if human authors had produced them?
    They consider the releases a kind of short cut, that does not satisfy the unwritten rules of the profession, such as not working on problems that others are working on, or not using others' results without crediting them.
     
  3. Why might mathematicians fear their future?
    They fear that human mathematicians will be replaced by machines and that their stock of interesting problems to work on will be depleted.
     
  4. What is the Navier-Stokes problem?
    Navier-Stokes equations govern the motion of fluids, and there was an open question whether the equations hid a situation where the velocity of the fluid went to infinity - that the equations allowed singularities. It turns out OpenAI shows that this is in fact the case.
     
  5. Does Fry consider the actions of OpenAI to be collaborative and in the spirit of the tradition of mathematics as an area of knowledge?
    No!

Terence Tao and the OpenAI event (20 mins)

Watch the clip below and then answer the discussion questions in groups

Discussion questions

  1. Why does Tao say that we have reached the end of the Romantic Period of mathematics and that there are no more mathematical heroes any more?
  2. What are the two axes that Tao identifies in mathematical work?
  3. Which axis does AI generated mathematics ignore?
  4. If AI does not produce mathematical understanding, how might this negatively impact real-world applications?
  5. Describe what Tao means by the crisis caused by the depletion of mathematical problems?
  6. What general lessons can be learned from Tao's statement that “its harder to be motivated when you know that a problem has been solved”?
Teacher only box

Possible answers to questions.

  1. Why does Tao say that we have reached the end of the Romantic Period of mathematics and that there are no more mathematical heroes any more?
    Previously mathematics was largely about individual mathematicians working slowly on a problem over a number of years. These mathematicians Tao identifies as heroes in a larger metaphor for that golden age - the romantic period.
     
  2. What are the two axes that Tao identifies in mathematical work?
    Tao identifies two axes: technology and understanding.
     
  3. Which axis does AI generated mathematics ignore?
    Tao considers that AI generated mathematics does not generate the same kind of understanding as human produced proofs.
     
  4. If AI does not produce mathematical understanding, how might this negatively impact real-world applications?
    Tao thinks that it is dangerous to allow AI models to run real-world applications (such as energy grids) if human mathematicians have no understanding of the models that are used.
     
  5. Describe what Tao means by the crisis caused by the depletion of mathematical problems?
    Tao sees a problem in the very process of producing mathematicians in future generations. Part of the process of doing new mathematical research is working on a middle sized problem for a PhD. But the worry is that AI will solve all these problems but will not, unlike human mathematicians, replace them with new problems.
     
  6. What general lessons can be learned from Tao's statement that “its harder to be motivated when you know that a problem has been solved”?
    This may be a broader problem than just one in the mathematics community. Students may reflect that it is more difficult to become engaged in a task when one knows that AI can provide some kind of response at the push of a button. They may need to draw upon skills that they developed prior to the AI era.

Lex Fridman on the crisis in mathematics (15 mins)

Computer scientists and populariser of science Lex Fridman brings together three mathematicians to discuss OpenAI's foray into research mathematics: Ankur Moitra, Steven Brunton and Alex Kontorovich. The discussion allows us to deepen the ideas introduced by Terence Tao above. View the following video clip and answer the questions.

Discussion questions

  1. The panel in the interview take a more positive view of the role of AI in mathematics. What is the basis for this positive view?
  2. What conclusions can you draw about the impact of the next generation of AI models on mathematics?
Teacher only box

Possible answers to questions.

  1. The panel in the interview take a more positive view of the role of AI in mathematics. What is the basis for this positive view?
    One reason to be positive is that there is a lot that humans do that AI does not yet do such as being able to explain, understand and generalise proofs. There is also the creative process by  which new problems emerge from existing ones.
     
  2. What conclusions can you draw about the impact of the next generation of AI models on mathematics?
    There are many different conclusions that can be drawn. Students may be somewhat pessimistic seeing no real future for human mathematicians. At the other end of the scale they may be persuaded by the arguments for unique human contributions. The conclusion that things will remain the same, on the other hand, does not seem to be justified.

Extension topic: Looking at the problem in more depth  - a mathematician's viewpoint (30 mins)

This topic is for those of you who want to take this investigation further. The following clip shows a mathematician's view of the role of AI in the production of mathematical knowledge. The conversation brings in the larger issues surrounding the practice of mathematics - for example thinking about the world in simple generalisable ways, asking the right questions and the role of beauty. Watch the clip - the whole thing (14 mins) is well worth it.

Discussion questions:

  1. What is the ‘solved axiom’? So you believe that it will be true at some point in the future? Sketch the basis for your opinion.
  2. What is the doorman fallacy? Why might mathematicians be more than just provers of theorems?
  3. What role might beauty, explanation, and understanding play in human mathematics?
  4. What grounds for optimism exists among the mathematicians in the panel?
Teacher only box

Possible answers to questions.

  1. What is the ‘solved axiom’? So you believe that it will be true at some point in the future? Sketch the basis for your opinion.
    The solved axiom proposed by Alex Kontorovich is that AI will be capable of all mathematical activity that humans are capable of including finding proofs of conujectures, asking the right questions, and making conjectures.
     
  2. What is the doorman fallacy? Why might mathematicians be more than just provers of theorems?
    The doorman fallacy was first introduced by advertising executive Rory Sutherland in his book Alchemy. It is the fallacy of defining a role by its most visible mechanical task while ignoring its hidden harder to measure value. The argument that Ankur Moitra makes is that the most visible task of mathematicians is to prove theorems but at the same time they are deep thinkers about a whole set of other issues, and they are tending an intellectual garden that sits at the centre of what it is to be human.
     
  3. What role might beauty, explanation, and understanding play in human mathematics?
    Mathematicians often associate beauty with the solution of a hard problem or a proof of a difficult or powerful conjecture. However, AI may break this correlation. While the proofs produced by AI are not elegant or beautiful they are nonetheless (it seems) broadly correct. Maybe the human role in mathematics is to create beauty out of them, to create new concepts and definitions that simplify the AI-generated work and make these results intelligible and understandable to the community.
     
  4. What grounds for optimism exists among the mathematicians in the panel?
    The points listed above are taken as primary grounds for optimism by the panel.

Journal: Lauren Williams and First Proof (15 mins)

Watch the first 10 minutes of the interview and then write short answers to the reflection questions in your ToK journal. If you are interested then you might want to watch the whole interview later.

For your ToK journal:

  1. What is benchmarking? Describe the aims and methods of the First Proof project.
  2. What are the ethical implications of using machines to do mathematics?
  3. More generally what principles should we appeal to in deciding what tasks to delegate to AI?
Teacher only box

Possible answers to questions.

  1. What is benchmarking? Describe the aims and methods of the First Proof project.
    Benchmarking is a way of measuring the capabilities of AI systems, in this case regarding their mathematical capabilities. The idea is that AI systems are set loose on problems that human mathematicians have already solved. After the first benchmark trial where the systems often came close to the correct proof but did not explain it very well and often plagiarised the work of other mathematicians, new trials were developed where systems were awarded points for the clarity of their explanations and the effectiveness of attributing results to others.
     
  2. What are the ethical implications of using machines to do mathematics?
    There are a number of ethical problems. The first is that the systems are trained on large quantities of material often without the permission of the copyright holders. Secondly, systems do not seem to be very good at attributing sources - they are indulging in academic malpractice. Thirdly, because AI systems cannot take responsibility and do not care, there are issues to do with machine proofs trampling on the life work of human mathematicians. Students might also identify further issues to do with the consumption of resources in the building, training, and running of large AI models.  If these resources are taken by the system then they are not available for human beings, who might face huge price hikes in energy, raw material, and water costs.
     
  3. More generally, what principles should we appeal to in deciding what tasks to delegate to AI?
    This is a deep question and it touches on the motivation we have for pursuing knowledge in the first place. If we are interested only in the practical consequences of having knowledge - problem solving in real life then providing we are happy with the methods used to produce knowledge (a big ‘if’ in the case of AI) then it does not much matter whether the knowledge is mostly produced by machines or by humans. However, if we want to savour the journey taken, then it seems that delegating too much to AI is a problem. Most mathematicians are keen to preserve the ‘journey’ part of their work as we saw from the interview with Terry Tao.
All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other platforms is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.

Help