I assume that AI is quite capable of designing workouts, and creating audio files with instructions that I could take to the gym. But I have no interest in that; the appeal of the classes is the relationships I build with the other humans.

Perhaps this is overly optimistic, but I hope that it's the things that people actually value, where they find meaning and depth and human connection in the experience, that will prove most resistant to AI.

I joked to her that puppies beat SSRIs any day of the week, that she should write prescriptions to take to the animal shelter. And it's probably true! Unfortunately, I don't live the kind of life that's compatible with a pet.

Personally, I'm grateful that doctors mostly stay in their lane, although I would hope a good therapist might recommend physical activity to someone who needs it.

And as to what kind of exercise to recommend -- the advice I've heard is that the best kind of exercise to do is what you enjoy and will therefore stick to. Brisk walking three times a week for 20-30 minutes might work great for some people. But if someone finds that a tedious chore, they're probably not going to stick to it.

Yeah, I tried out an online weight loss program (Wondr) that made the same point. When it was video of psychologists, I could definitely understand what they were saying. Unfortunately, when it was video of a chef, saying words like "flavor" with great enthusiasm, I found it hard to stomach. Judging by how happy food makes many people, my loss I guess.

Something to think about anyway..... thanks for your input.

For some people, mealtime is special and a little bit sacred. I have friends who are avid cooks, and for whom eating is often the highlight of their day.

I have never been one of those people, and I'm old enough to I remember the days when, if I wanted a distraction at mealtime, I needed a physical book. Nowadays, I often watch chess videos over lunch, and quite enjoy them. I'm open to being persuaded that I should give this up; would you please try to persuade me?

It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it.

Of course, this culture could change under external pressure from AI tools. But, aside from cryptography and the applied fields, I'm finding it difficult to imagine any possible motivation for spending substantial effort on top-level math and then keeping it secret.

I can see that you're arguing in good faith, and indeed I have a lot of respect for anyone willing to argue an unpopular position. That said, I do find your suggestion to be completely farfetched.

The Jacobian Conjecture was one of the most notorious open problems in algebraic geometry, something that generations of grad students have daydreamed of solving. I've seen more immediate buzz around the Jacobian conjecture than around any other mathematical breakthrough of the last five years, at least. For example Terry Tao, arguably the most famous mathematician in the world, dropped what he was doing to study Alpoge/Fable's counterexample in detail, and wrote this blog post:

https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the...

For Alpoge to have solved it on his own, and then falsely claim to have used AI? That's like an athlete winning an Olympic gold medal, and then falsely claiming to have cheated and used illegal steroids. I agree that it's not completely out of the question, but it's beyond the bounds of human behavior that I can reasonably fathom.

https://alpo.ge/

So Alpoge and Fable found an example of a function that was believed to be too strange to exist.

That said, if it's possible to do better than random guessing, then does this reflect the fact that the five charts are presumably hand-selected to be "interesting"?

My naive guess, and I'd be very curious to learn if this were wrong, is that something very close to the efficient market hypothesis is true; that, if it were possible to beat the monkeys on randomly chosen stocks on random dates, then someone would have figured this out already and deployed bots to capture whatever profits are available.

Suppose the Belgian government declared the ambassador persona non grata, and sent them on the next plane to Washington. Presumably this would raise their popularity with their own voters, although if Trump noticed he'd throw another temper tantrum. What then?

I'd say it's now obvious, but previously I mistook a bishop for a pawn.

One suggestion: some way to tell what the enemy pieces are? Maybe a legend to the right of the board? I ended up discovering by trial and error.

There are two reasons for this:

(1) Popular materials are usually popular for a reason: they reflect an approximate consensus, across a significant fraction of the mathematical community, that their approaches are more-or-less the best.

(2) If you learn the same way everyone else does, you'll have an easier time talking to others and finding materials on the internet.

I know some very innovative books which I highly recommend, for example Visual Group Theory by Nathan Carter:

https://bookstore.ams.org/clrm-32/

But the innovation is pedagogical, in what Carter chooses to emphasize and how he presents everything. At the book's core, Carter agrees with everyone else about what the foundations of group theory are and should be.

Even Sheldon Axler's Linear Algebra Done Right (another excellent book), with its hilariously provocative title, only differs in its choice of emphasis and order of presentation. His choices are quite compatible with everyone else's.

https://linear.axler.net/LADR4e.pdf

Is this strange?

I'll be trying to solve some problem, half-remember an email conversation from several years ago on something relevant, and want to look it up.

This feels like the most natural thing in the world to me, and it's not like the ability to save emails is new. Why, exactly, would a forced change of habits be for my own good?

I'm happy to report that I've observed very little of what you describe.

In Canada the fight has gotten nasty, with governments in Alberta and Ontario putting forward legislation that could remove existing bike lanes.

https://www.cbc.ca/news/canada/toronto/ontario-ford-bike-lan...

https://www.cbc.ca/news/canada/edmonton/alberta-government-b...

Maybe "hatred" is too strong of a word, but if I were a cyclist in Toronto or Edmonton I'd feel rather victimized.

When I go to research lectures, I sometimes hear that in response to audience questions, although not especially consistently. Some speakers do this more than others, I don't think anyone does it all the time.

I'm not even sure I could have answered you at the time. In my memory, it was mostly students promoting the honor code. But I have to imagine that the university was quietly doing things to keep this going.