<p>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&#39;t care! All the worse for them!), but rather because many students may try to use it to *learn*.</p><p>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&#39;t understand it, so they ask ChatGPT to reproduce it for them, and they ask followup questions to the LLM as they go. </p><p>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 &quot;Hmm, but I don&#39;t think it is true that [XXX]&quot;, the LLM responded with something like &quot;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].&quot;</p><p>I know enough to be able to pinpoint these false claims relatively quickly, but my students will probably not. They&#39;ll instead see them as valid steps that they can perform in their own proofs.</p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@film_girl" class="u-url mention">@<span>film_girl</span></a></span> I have the bose ones, and they have been really stable. also multipoint.</p>

<p>For people looking for headphones deals, lots of good ones. Sonos Ace are $350 ($100 off), Sony XM4s are $200, Bose Quiet Comfort $200 and Beats Pro Studios with Apple Care for $180. <a href="https://a.co/d/12ug6VT" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">a.co/d/12ug6VT</span><span class="invisible"></span></a> <a href="https://amzn.to/3CG58VZ" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">amzn.to/3CG58VZ</span><span class="invisible"></span></a> <a href="https://amzn.to/4fGe7Fk" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">amzn.to/4fGe7Fk</span><span class="invisible"></span></a> <a href="https://amzn.to/4fLcINT" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">amzn.to/4fLcINT</span><span class="invisible"></span></a> <a href="https://mastodon.social/tags/affiliate" class="mention hashtag" rel="tag">#<span>affiliate</span></a></p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@AndreasZeller" class="u-url mention">@<span>AndreasZeller</span></a></span> Well earned, Andreas!</p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@dabeaz" class="u-url mention">@<span>dabeaz</span></a></span> Oooh, I need to check this out!</p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@whitequark" class="u-url mention">@<span>whitequark</span></a></span> and every “epoch” a new administration comes in and OSHA either gains or loses strength</p>

<p>Today, I was formally introduced as a new member of the prestigious <a href="https://mastodon.social/tags/Academia" class="mention hashtag" rel="tag">#<span>Academia</span></a> <a href="https://mastodon.social/tags/Europeana" class="mention hashtag" rel="tag">#<span>Europeana</span></a>, the Scientific Academy of Europe. I felt humbled in the presence of Nobel laureates and so many most excellent scientists! <a href="https://www.ae-info.org" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">ae-info.org</span><span class="invisible"></span></a></p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@gamingonlinux" class="u-url mention">@<span>gamingonlinux</span></a></span> Already following, boosting and fav‘ing. Not interested in the game, but I really appreciate your work and posts. Thanks!</p>

<p><span class="h-card" translate="no"><a href="https://mastodon.social/@whitequark" class="u-url mention">@<span>whitequark</span></a></span> yes I&#39;m interested in hearing more</p>