Jan-Fredrik Olsen
Responses
My student wants to connect Claude to Canvas -- what do I say?
I am fairly close to the “let’s go all in on AI in our teaching” side of the spectrum, yet my immediate thought is that this would be a bad idea. While there is a lot to be gained by allowing students to go “all in” on AI use, this has to be balanced by “AI-free zones” to help students recognise the difference between “unproductive” and “productive” struggle, and more importantly, realise the dangers of the real snake in the grass: “unproductive AI-aided success”. So a question is whether “Canvas” should be one of those AI-free zones and why? But while I am sceptical, I also realise that I have never been a ‘young’ student trying to navigate the Canvas website among all the other noise of university life in a world with social media on all sides, etc. So, I think the best course of action is not to give the student any knee-jerk response (even if we all want to), but instead to engage with the student to figure out what they want to achieve by connecting Claude to Canvas and what the context of this request is. Would it be possible to get more information from the student?
How good is generative AI at maths?
Generative AI is not only good at mathematics, it is good enough to be a valuable help for professional mathematicians. For more on this, see the blog of Timothy Gowers and a recent essay by Terence Tao (links below). Both are highly respected in the mathematical community. However, generative AI is not reliably good. While expert users can use generative AI to prove theorems and solve problems beyond what was possible before generative AI, this makes it a problematic tool for non-expert users. Indeed, since generative AI is probabilistic (it does a little internal lottery for every word it outputs) it will make mistakes every now and then. This is not a big deal for experts, since they will be able to spot (or at least suspect) that something is off. But for novices, they can easily be misled and confused. I am not an expert on the technical reason why generative AI is as good at mathematics as it is, but it is related to the fact that mathematics is a highly structured and logical language -- just like programming languages, which generative AI is even better at. However, a reason generative AI may be a bit worse at mathematics than programming, is that its training data contains many executable programs, while mathematics is often written up in (partially) informal ways (and there is a lot of bad maths online). In recent years, a programming language called LEAN has been developped, and it actually represents mathematical arguments as programs. That is, when you first start using LEAN, you can program axiomatic proofs of simple statements by writing down the axioms you use, line by line, and connecting them with logical statements. You can then store such 'programs' and re-use them when making programs that prove more advanced results. These 'programs' are exactly the propositions, theorems and lemmas of mathematics. When using LEAN, the reliability with which generative AI can do mathematics seems to increase dramatically. But what does this say about teaching mathematics in school? I am actually an optimist. As I said above, the power of generative AI for doing mathematics is (still) linked to whether the AI is collaborating with a human mathematician. So, while I think role and status of mathematics may change in the future, I don't think humans will be taken out of the equation. And the humans will still need to have a solid manual and 'old school' mastery of mathematical concepts, techniques and ideas in order to get the most out of the AI (and vice versa, one could say). From this perspective, I think the more interesting question is: how can we use generative AI to have humans learn mathematics in a better, more robust and interesting way? I am myself teaching introductory calculus at Lund University, allowing free use of generative AI by students (even on homeworks and projects), and getting better results than ever on completely AI-free traditional closed book exams and on one hour theoretical oral exams. I think the trick is that by carefully changing the course structure, and course activites, I have been able to get students to use generative AI to experiment with mathematics, and 'see' much further than what they could before (learning mathematics has always been a bit like walking in a dense fog -- it is very hard to look ahead). In this way, students can become exited about mathematics they do not yet fully understand (just as students can in other subjects - such as in physics and in music), and then make it their business to actually do the hard work necessary to develop the 'manual' mathematical mastery of having the please of understanding and being able to grasp these advanced mathematical concepts and ideas themselves. The exact details of what I do are too long to explain here -- and I hope to publish more about it elsewhere. In the meantime, please contact me for addition details. Below, I provide links to course evaluations of the courses I have taught in this way. They are quite detailed, and at the very end, you can see free-text responses on what students appreciated and what they thought could be improved. Note that the most successful was One Variable Calculus in autumn 2024. The course taught in spring 2025 was a completely new course, which also had some "teething" problems. The evaluation for the same course from spring 2026 will appear soon, and this fall I will be teaching the One Variable course using the same AI-integrated approach. One Variable Calculus - Autumn 2024: https://www.maths.lu.se/fileadmin/maths/Matematik_NF/Kursutvaerderingar/HT2024/MATA31HT24.pdf Introduction to higher analysis - spring 2025: https://www.maths.lu.se/fileadmin/maths/Matematik_NF/Kursutvaerderingar/VT2025/MATB33VT25.pdf Blog of Tim Gowers: https://gowers.wordpress.com/2026/08/12/what-sort-of-maths-are-llms-good-at/ Essay of Terry Tao: https://arxiv.org/pdf/2608.16753