impendia

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.

Strictly speaking I'd agree with you -- but I would consider a higher baseline of morale to be itself quite special! Especially when it is shared amongst the entire community.

Is it propaganda? In some sense, yes, the only way to maintain such a culture is to repeatedly insist on its importance to prospective and current students. But if so, then it is self-fulfilling propaganda, and in my opinion the honor code made my experience richer.

It's not a place you'd drive across the country to see, but it's beautiful and highly worth a visit. There are some freaky trees -- with knobs of roots that stick out from the ground, like nothing else I've seen. The place is kinda creepy, as if you're about to be attacked by zombies, and I love that.

There is a two mile elevated boardwalk which takes you around some of the most scenic areas of the park, and further hiking trails which branch off of that. There is also a river that goes through the park, and it's quite atmospheric in a canoe.

When I started my Ph.D. program, there was a weekly seminar that I started going to. At first, I instinctively left each week immediately after the talk was over. But I noticed that a lot of people would hang around afterwards and chat. Even though I found it a bit awkward, I started following their lead -- a habit I'm very glad I developed!

This has several advantages: exercise is obviously good for you, and you can meet people while you're there. But more subtly, once you show up, someone is constantly telling you what to do. For me, this has meant much less of a drain on my mental energy and discipline than if I tried to work out on my own.

Good luck!

Academia, at least in math, has a tradition of being public. Conferences will advertise at least the list of speakers, and sometimes the full list of attendees. This is widely considered a good thing; people trying to decide whether to go to a conference will want to know who else will be there.

Moreover, the conference organizers have sent out multiple emails to the attendees warning that scammers were targeting them, and emphasizing that there were no third parties legitimately involved.

So I can't and don't fault them.

I understand that, if you have a current and active polo club running, then you either have to keep it going or run the risk of pissing people off.

But, if I can ask you to speculate, why might Harvard have revived its club in 2006?

Indeed, Tao himself has written criticism of the "cult of genius":

https://terrytao.wordpress.com/career-advice/does-one-have-t...

Picture him as the star player on a basketball team. He may be the strongest player on the court, but he's still playing the same game as everyone around him.

If your 74 traps solve your problem and in a month you have no more mice, then congratulations.

But it sounds like rather than buying more and more mouse traps, you should find and fix the underlying cause.

Also, how much of this communication is actually necessary? If someone doesn't care about an issue enough to write their own email, then why are they sending an email about it in the first place?

https://www.reddit.com/r/recruitinghell/comments/j1vm8j/gold...

You said it yourself, these are overwhelmingly people who've never built or maintained anything complex in their lives. If you're going to listen to what people on the Internet say, why not seek out people who can earn your respect?

This is a very interesting question, and a great motivator for Galois theory, kind of like a Zen koan. (e.g. "What is the sound of one hand clapping?")

But the question is inherently imprecise. As soon as you make a precise question out of it, that question can be answered trivially.

I couldn't find any way to actually turn off notifications in MacOS. But you can set "quiet hours" to be from 2:00 AM until 1:59 AM.