AI-assisted research in mathematics

I am currently very enthusiastic about using AI as a tool to assist in mathematics research. I want to provide a snapshot of the ways in which I am using it currently. I hate to read posts written by AI – knowing that content is AI-generated decreases my attention span. So here’s me!

• at the moment, I pay for Gemini Plus, which gives me plenty of access to the deep thinking (Gemini 3.1 Pro) mode, which is crucial for coherent thoughts.
• literature: Gemini has a very broad and also detailed knowledge of the literature. Something incredibly useful is its ability to provide precise references to Lurie’s HTT and HA. It can also point to references if it is only provided a vague thought or conjecture. Numerous times it spat out references that precisely proved my question or provided a counterexample. This does save a bunch of time, maybe at the cost of weakening my own intuition and understanding. For me, it more and more replaces googling.
• understanding calculations: Here’s are example question that I asked AI to explain to me: “How do you compute Pin bordism groups?” or “What is the connective ko-theory of BZ/2?” It provides answers you might expect from a colleague or collaborator.
• arXiv agent: I have set up an arXiv agent using Gemini Gems that provides a daily briefing on new preprints. It works fine, though I like the tool PaperDigest better.
• Webpage creation: Using Cursor I have set up my webpage without coding a single line. Cursor is an AI-powered IDE, where you tell your AI agent what to code or correct. It has the benefit of having access to your local files. My webpage is hosted on github, but Cursor can handle the commits and pushes.
• Debugging latex: Works so well, I expect to never deal with this again. Also helpful for spell-checking the bibliography file.

-Translating and TeXing old papers: Just for fun I have tried to translate and TeXify Algèbres de Clifford et K-théorie by Max Karoubi. Using Cursor, I could automate the entire process, but the result was horrible. A slower but better version was created by Gemini. In the end I do not need it, but it is definitely possible.

Things that I want to try:

• Using the DeepResearch feature productively, e.g. for a literature review or conference planning.
• Transcribing recorded talks
• TeXing homework solutions