impendia

I have no idea what actually happened behind the scenes, but the human prompter, Levent Alpöge, indeed has deep math expertise. Princeton PhD, Harvard postdoc, and some excellent research (prior to this) to his name.

https://alpo.ge/

For the Jacobian determinant to be constant is a massive coincidence, in general it is some complicated and messy polynomial. The conjecture was that this coincidence couldn't happen, except for simple special cases.

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

This is fascinating.

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.

Indeed, I find this story quite interesting (and disturbing) from the Belgian point of view.

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?

Since I last looked, at least on my browser the gameboard has been significantly enlarged.

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

This is cool!

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.

Math professor here. If you want to learn math, then for the most part I recommend choosing time-tested avenues, using popular materials.

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

People treat email has a permanent data store.

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 an academic mathematician in a US research-oriented department.

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

Some drivers seem to resent the idea that they should have to share the road, or slow down for anyone. Even if cyclists do everything right, they're still slower than cars, and so will present at least a minor inconvenience for drivers.

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.

Math professor here.

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.

These are very good questions, but it was a long time ago and I'm afraid I don't remember well enough to answer.

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.

I’m skeptical that there’s anything special about high trust communities other than a higher baseline of morale

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.

I went to Rice which had a similarly strong honor code, and it absolutely inspired pride. In me, and from what I could tell in many of my classmates.

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.

I live in South Carolina, about half an hour from Congaree National Park.

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.

Definitely agreed!

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!

Personally, I've enjoyed classes in yoga and in group fitness.

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!

Yes, they likely scraped the conference web site.

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 got curious, and looked up the Harvard Polo Club. Apparently it naturally faded away as polo declined in popularity, but then was revived in 2006.

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?

I certainly didn't take it as a slight against myself. Rather, I've met Tao and several other top mathematicians, and I don't imagine any of them would say they fit that description.

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

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

I'm a research mathematician working in Tao's field. I'm not claiming to be as prolific as he is, not by a long shot -- but other mathematicians do understand, critique, develop, and engage with his work. Indeed, many of his papers are collaborative with a variety of other mathematicians.

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.

Are they working?

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.

If people are scared to share their thoughts, then that seems like the problem.

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?

If you find yourself spooked by LinkedIn "gurus", I recommend Reddit for some comic relief. https://www.reddit.com/r/LinkedInLunatics/top/ is full of goodies. Here is my personal favorite:

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?

I'm a professional mathematician and professor.

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.

Agreed. On my phone I turned off most of my notifications, and on my computer I turned off all of them.

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.

I haven't, but others have written about the same trip. There's lots of material online these days, I'm not really familiar with it but if you google "Shikoku henro pilgrimage", all the hits will be about the same trip I took.

There is a wonderful book, Japanese Pilgrimage by Oliver Statler. He goes into the history of the pilgrimage and of Kobo Daishi, the monk whose path the trail follows. He also discusses his own personal experience walking the trail.

A variant of this advice, that avoids some of the pitfalls, is to take time off to do something structured and specific.

Personally, in between jobs a long time ago, I chose to walk the Henro Trail, an approximately 800-mile Buddhist pilgrimage trail in Shikoku, Japan. To make a long story short, it was the experience of a lifetime.

Are you an expert?

I can't speak for ndriscoll, but I am a university math professor with extensive experience teaching these sorts of topics, and I agree with their comment in full.

You are right that some (other) statements are harder to formalize than they look. The Four Color Theorem from graph theory is an example. Generally speaking, discrete math, inequalities, for all/there exists, etc. are all easy to formalize. Anything involving geometry or topology is liable to be harder. For example, the Jordan curve theorem states that "any plane simple closed curve divides the plane into two regions, the interior and the exterior". As anyone who has slogged through an intro topology book knows, statements like this take more work to make precise (and still more to prove).

If the government's guidance isn't to be at least mostly trusted, then I'm not sure the government should be offering guidance at all. (Which is perhaps a sensible position in itself.)

In other words, if I learn enough about nutrition to be able to critically evaluate the government's guidance, then is that guidance adding any additional signal? At that point, I should just rely on my sources about nutrition.

I've never been one to rely on official guidance blindly. For example I don't show up to the airport two hours early, and cheerfully laugh at advice that I should. But I'd like to believe that this guidance is better than total nonsense.