Baby Rudin is a special textbook: it comes from a time when mathematics textbooks were not at all judged by their pedagogical value, but instead by their aesthetic appeal to mathematicians (a la Bourbaki).
If you actually want to learn analysis, there are a nearly infinite number of friendlier resources (e.g., Understanding Analysis by Abbott).
Learning to unpack difficult text on one’s own is a valuable skill. Research papers often require a similar amount of suffering, and at the frontier of knowledge, despite all the advances we’ve seen, LLMs seem to have absolutely no understanding or intuition. They are much better at things that have been expounded at length by humans before.
I would argue that if you’re going to use an LLM to make Rudin easier to understand, you are not learning how to absorb difficult material, nor are you learning analysis efficiently.
> I would argue that if you’re going to use an LLM to make Rudin easier to understand, you are not learning how to absorb difficult material, nor are you learning analysis efficiently.
I would argue that if he can solve the problems on his own, without LLM assistance, than he has mastered it.
The same could be said for someone taking a university course where Rudin is the textbook, and they rely on the professor/TA to help them understand the book.
This is needlessly nitpicky. The stark reality is that the majority of undergrad math majors do not achieve what this person has merely be reading Rudin (assuming he is actually solving most/all the problems).
I don't think so. There are many objections to methods of making learning "easier" and the invalidity of one does not imply the invalidity of all of them.
We've also seen the effects of LLMs on learning, at least when used instinctively by students. An entire generation of students seems to have atrophied their critical thinking skills this way. Talk to 21-year-olds today and you'll see what I mean.
>There are many objections to methods of making learning "easier" and the invalidity of one does not imply the invalidity of all of them.
I am pointing out a pattern of technological hubris stretching thousands of years.
>An entire generation of students seems to have atrophied their critical thinking skills this way. Talk to 21-year-olds today and you'll see what I mean.
Ah, yes, the old "kids these days" routine... quite fond of it myself sometimes. But I find myself benefitted when I take care to learn from the young.
"For the correct analogy for the mind is not a vessel that needs filling, but wood that needs igniting - no more - and then it motivates one towards originality and instils the desire for truth. Suppose someone were to go and ask his neighbours for fire and find a substantial blaze there, and just stay there continually warming himself: that is no different from someone who goes to someone else to get some of his rationality, and fails to realize that he ought to ignite his innate flame, his own intellect, but is happy to sit entranced by the lecture, and the words trigger only associative thinking and bring, as it were, only a flush to his cheeks and a glow to his limbs; but he has not dispelled or dispersed, in the warm light of philosophy, the internal dank gloom of his mind."
If you actually want to learn analysis, there are a nearly infinite number of friendlier resources (e.g., Understanding Analysis by Abbott).
Learning to unpack difficult text on one’s own is a valuable skill. Research papers often require a similar amount of suffering, and at the frontier of knowledge, despite all the advances we’ve seen, LLMs seem to have absolutely no understanding or intuition. They are much better at things that have been expounded at length by humans before.
I would argue that if you’re going to use an LLM to make Rudin easier to understand, you are not learning how to absorb difficult material, nor are you learning analysis efficiently.