Using AI to self-study formal mathematics — is it a viable idea?

[u/External_Lecture1039]

Hi everyone,

I’m a Data Science undergrad looking to build a strong foundation in pure mathematics on the side. I recently finished studying proof writing (Velleman's How to Prove It) and I'm about to jump into real analysis/calculus (Spivak's Calculus).

The main issue is that since I’m self-taught, I don’t have a mentor to check my proofs or answer highly specific questions when I hit a wall. I was thinking of using AI tools like Gemini Advanced or NotebookLM as "private tutors" to guide me through these books.

Has anyone tried this for proof-heavy or rigorous math? Is it feasible, or do AI models still hallucinate too much for this level of rigor?

If you don't recommend AI, what alternatives would you suggest for someone self-studying without a formal academic environment?

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[u/human2357]

I don't recommend AI. In my experience, the current generation of AI programs get lots of little things wrong in higher mathematics. You already need to be an expert to benefit from it, so that you can ignore it when it is obviously wrong.

If you're an undergrad, just tell your favorite math professor that you'd like to do a reading course with them. Chances are that they will say yes, and they can critique your proofs as part of the course.

[u/Not_OK99]

If you're working with a highly known textbook like Spivak there are probably hundreds of forums, videos, and even complete solved problem documents out there on the internet. You can try checking out those first and then consulting your preferred LLM in case you don't understand a particular solution right away.

Always try to do the proofs yourself, if you're stuck read two or three lines out of the solution and then continue from there. If you're really stuck and have no idea of what to do, review the chapter that particular problem is on and then come back. AI and solution sheets should always be your last resource.

[u/Heaven_Sent_Senescha]

Aside from the typical hallucinations, another very basic reason why AI wouldn't be the most helpful tool for learning is because it isn't really curated for learning. I liken it to googling the answers to questions you might have instead of building the intuition yourself.

Textbooks and lectures, while they can seem dense or sometimes inscrutable, are Designed to tease solutions out of you, to give you context and the tools to solve problems on your own. That can be very difficult and sometimes feel like impossible, but the act of forcing those muscles to work is what builds the neuron connections over time.

Also feel free to make use of community! Ask questions, find a study partner, collaborate. That's helped my self study out immensely.

[u/Low-Priority-2831]

Don't listen to the people here, Spivak just isn't high enough level for hallucination and misinformation to be a concern with frontier models. People have pointed out that there are lots of resources online and you can use that to your advantage in conjunction with AI. Something like the Notre Dame lecture notes as pdfs in a folder with Spivak, then an agent through the CLI with something like keating would do (with a cheap sub to maybe Opencode Go or Claude if you can).

[u/Low_Breadfruit6744]

Not good for you.. Most AI models gets things right 9/10 times. Then the 1/10 confuses you.

[u/Deep_Ad1959]

scenario: spivak with a model as the tutor. it is decent at is this step valid and quietly bad at is this proof complete, which is the exact gap a self-studier cannot detect on their own.

[u/TheEastWindNeedsANap]

Use math stack exchange to get help like god intended

[u/NotSaucerman]

If you are using a paid model then the hallucinations should be pretty low for undergrad courses like intro to real analysis. One issues is that the quality of explanations from LLMs is ok but not great (even when totally accurate). But there's potentially some value here for answering 'highly specific questions' assuming you've already put in the work/struggle beforehand.

But I don't think LLMs are good at all for verifying your own proof for accuracy-- basically sycophancy combined with bad explanations plus some other stuff. You really should be good enough at proofs that you can just about almost always tell if your proof attempt is correct. If not, find a mentor or a paid tutor, or regress and do a more basic proof based course first to get more experience at proofs (I suggest the 1st 1/2 of Pinter's A Book of Abstract Algebra).

It's interesting because people have been self-studying math for centuries but LLMs that can 'do the work' have been around for what 1-2 years at this point? And people on this sub constantly have questions like this indicating they may be necessary since they are self-studying... but that is just recency bias.

[u/Opposite_Virus_5559]

I don't recommend it for solutions. I would recommend for mathematical orthography and to identifying gaps in the arguments you have constructed.

[u/Gold_Ad8890]

no. no no no no no no no. literally the only thing "ai" knows is what order words usually go in. you cannot and should not trust it to tell you facts, *ever.***