As you could see in my previous post, I was relatively positive about generative AI for the potential discovery of mathematical results, and I do not hide the fact that I used generative AI (Gemini and Claude) sometimes to get some intuitions or background study, or to generate simulations for better presentations. Mostly, I have used generative AI so far to

  1. prepare teaching materials to provide better learning experiences (historical survey);
  2. get some structural feedback first on an essay;
  3. understand basic research languages on different research areas;
  4. understand the nuances of English expression (break language barrier);
  5. feedback on my thoughts;
  6. find some good explanations or some proofs on mathematics related to my area (some lemma level)
  7. generate a numerical simulation (for presentation or to get initial intuition).

Hence I had several good reasons so far to use generative AI as a researcher to expand my knowledge outside my realm, but I gradually changed my mind when I read OpenAI’s announcement on the ‘resolution’ of the 10 problems and kept reading arXiv posts on the declaration of AI usage in preprints these days by different authors. While authors’ declaration on AI use is ethical, it is too awkward for me to see why we mathematicians promote AI models, not just mention AI usage. That started to change my mind, and the problem is that it is gradually breaking down the mathematics community. Currently, we are in a flood of mathematics papers, and the journal system is breaking down.

I had several attempts to find a potential approach to solve a problem using generative AI. Some of them were good, and I liked it before, while I think that I can find a way to prove it without using AI. I declare that I did not get satisfactory results on this activity. Maybe I could do prompt engineering better but I did not want to do it. I liked how I could plot some numerical simulations via Claude code first, and gradually ask my colleague how I could interpret this. Furthermore, I could taste some research area that I had interested in (like computer assisted proof, numerical analysis).

However, after reading these articles, I had changed my mind and I think we need to focus more on the mathematics community.

My current stand aligns with the paragraph “What could an ethical model of using AI in mathematics look like?” in Tasmin’s article. We might need to discuss this matter more seriously. The education system is breaking down, and the journal system is breaking down. I believe that those are not good for the humanities and mathematics community.

I have used generative AI from multiple perspectives: schedule controller, data collection, generating numerical simulations, coding problems, literature surveys from different disciplines, and some historical texts that I cannot read in an article, say, French. All of those are for my convenience to track potential mistakes and to deliver key ideas in mathematics to a broader audience better. I believe that this is for better understanding to the audience.

However, we are facing lots of danger to our community’s safety. The purpose of mathematics is not to prove many theorems and solve problems. It is for better understanding how our world works and to find a better perspective on research problems. This also aligns with the reason that I recently worked on the Muskat problem and kinetic equations. For me, those problems will help to find a good perspective to understand our world.

I was gradually used to generative AI as an early adopter, so it is hard to cut it down at once. From now on, I will not use generative AI for my mathematics research unless we find a way to keep the mathematics community vibrant. I don’t know how many days I will keep this oath for long times yet. However, I think raising an issue would be important at this moment.

My point of view seems naive since I have no better alternative. This new technology changes our life, and there is no turning back. However, refraining from alternative ideas dilutes the problem that we are facing. So we need to think about keeping us from potential dangers by finding issues and finding a way to keep our community.

I have several mixed feelings these days and some of my colleagues try to find a way to make it better. We will see very soon.

Add: 08/29 It is worth to read

I am more or less similar stand with Professor Duminil-Copin.

I am not fully against the potential possibility of using generative AI. However, the problem is how to find a way to keep our math research community vibrant. At least, I am glad that we have a forum to discuss in a lengthy way.