There is of course some overlap which what we did in previous years, but there will be some new things, as technology moves fast. I certainly also want in one of the classes talk about puzzles and games. As in the previous year, the flow of the course will also depend on the preferences of the class. Technology is extremely exciting. Even for me, as a dinosaur, I still enjoy (and worry also) about the pace with which things progress. And I'm sure, we will learn about seismic shifts happening in real time during the semester. This summer had been a roller coaster with respect to mathematics and technology. [August 25: largest rank 30 and 31 elliptic curves.] Also a personal first start to get in. Example: I just updated a paper on "Graphs, Groups and Geometry". The paper was written originally in 2022 and corrected now 2026. (I might tell about this a bit rather embarrassing story). But it was also an opportunity to test how machines can do research now: On page 27 of this document, you see a theorem that was found, proven and written by a machine. We have already 2 and 1 years ago discussed the role of AI in math and visualization and the discussion this year will certainly look different. We thought here about AI already in the 2003/2004 project in a smaller research seminar with 3 students 23 years ago and this looks now like from an other century. I myself try to avoid AI as much as possible (automatically generating pictures or slides is so much ``2023" ...) but I will bring during one of the classes a guest speaker who has more experience with the newest vibe stuff. Here is a list of my personal firsts. (slide from a presentation from 2023).