The era of ChatGPT is kind of horrifying for me as an instructor of mathematics... Not because I am worried students will use it to cheat (I don't care! All the worse for them!), but rather because many students may try to use it to *learn*.

For example, imagine that I give a proof in lecture and it is just a bit too breezy for a student (or, similarly, they find such a proof in a textbook). They don't understand it, so they ask ChatGPT to reproduce it for them, and they ask followup questions to the LLM as they go.

I experimented with this today, on a basic result in elementary number theory, and the results were disastrous... ChatGPT sent me on five different wild goose-chases with subtle and plausible-sounding intermediate claims that were just false. Every time I responded with "Hmm, but I don't think it is true that [XXX]", the LLM responded with something like "You are right to point out this error, thank you. It is indeed not true that [XXX], but nonetheless the overall proof strategy remains valid, because we can [...further gish-gallop containing subtle and plausible-sounding claims that happen to be false]."

I know enough to be able to pinpoint these false claims relatively quickly, but my students will probably not. They'll instead see them as valid steps that they can perform in their own proofs.

I see so many adults and professionals talking about how they are using LLMs to deepen their understanding of things, but I think this ultimately dives headlong into the “Gell-Mann amnesia” effect — these people think they are learning, but it only feels that way because there are ignorant enough about the topic they're interested in to not detect that they are being fed utter bullshit.

How shall we answer this? I think it speaks most urgently for people who actually know things, those with "intellectual power", to democratise our knowledge, throw aside the totems that make our fields inaccessible and obscure, and open the gates to the multitudes who wish to learn.

At first it seems like it would be easy to compete with LLMs (because they say only bullshit), but to actually compete with LLMs we need to produce educational materials that actually explain things properly. Any 'proof by intimidation' will immediately send our student to the LLM. The moment you rely on something that you haven't explained, same deal. So it may be that this era has a silver lining: we must finally teach mathematics properly.

@jonmsterling There is another lesson that I think is harder for us to get across that I was reminded of by recently seeing this
Mathoverflow answer (https://mathoverflow.net/a/51868/1199) again:

In a pressure cooker culture of high stakes, high anxiety, and easy distraction, we need to find ways to encourage people that seriously struggling with something will prove thousands of times more valuable than empty fast food AI "summaries". This is much harder to do currently, but fits with wider trends about how people struggle to read books any more, struggle to be alone with just their own thoughts, struggle to face what is at their current limit.

Do you read the masters?

I often hear the advice, "Read the masters" (i.e., read old, classic texts by great mathematicians). But frankly, I have hardly ever followed it. What I am wondering is, is this a princ...

MathOverflow
@boarders @jonmsterling Do you have a source for the claim that people struggle to read books nowadays or any of the other claims after this one?

@zvavybir @boarders @jonmsterling

This is a complex issue and evidence for social trends and facts is of course very difficult to nail down, given how sensitive it is to methodology and interpretation, but here are some supporting sources:

- "Collective attention spans" shrinking: https://www.nature.com/articles/s41467-019-09311-w
- "Americans Reading Fewer Books Than in Past": https://news.gallup.com/poll/388541/americans-reading-fewer-books-past.aspx
- "Depression, anxiety, and daytime dysfunction" correlated with higher smart phone use: https://akjournals.com/view/journals/2006/4/2/article-p85.xml
- "media multitasking" which is more common for younger people, is "mostly correlated with negative mental health": https://pmc.ncbi.nlm.nih.gov/articles/PMC8598050/

I don't mean to suggest these are definitive, but IMO there is ample evidence currently to support taking an interest and addressing this as a something that is potentially a real problem. Personally, based on my own personal experience, it seems pretty clear that many forces in modern socio-technical systems are aligned to stifle deep reflection and critical thought, and to drive us into modes of constant distraction. This is something that was well diagnosed already by early critical theorists.

Accelerating dynamics of collective attention - Nature Communications

The impacts of technological development on social sphere lack strong empirical foundation. Here the authors presented quantitative analysis of the phenomenon of social acceleration across a range of digital datasets and found that interest appears in bursts that dissipate on decreasing timescales and occur with increasing frequency.

Nature
The Elite College Students Who Can’t Read Books

To read a book in college, it helps to have read a book in high school.

The Atlantic