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.
I used to have a view of a baseball field out my office window until they rolled up the astroturf to start construction of the new computing and information science building.
They got some money to build a really nice fan-friendly facility off-campus. Still the thing about baseball is that the season is early in the year and starts before the weather is comfortable for home games so they spend the first half of the season going to away games down south, far enough away that they're probably buying airline tickets instead of riding the bus the way that Ivy League (or ECAC) teams usually ride the bus to go to other Ivy League (or ECAC) schools.
If it wasn't for Lacrosse we wouldn't have anybody using our football stadium in the spring and hey, Lacrosse is both a men's and women's sport. (At Cornell we're lucky enough to have two football teams to keep it busy in the Fall)
Critics would say that Lacrosse is a boon to rich students since poor students don't go to high schools that have Lacrosse and it largely escapes the notice of the marginalization-industrial complex because those folks are aware that there is an industry in SAT test prep and not so aware that there is Lacrosse.
It’s an open secret that “expensive ancillaries” like polo, crew, equestrian teams, etc, are a sneaky way to have supposedly blind admissions while making sure that the incoming class still contains just the right number of students who can pay full tuition. Smart people are not all that rare.
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.
Yes I’m stretching this a bit, and certainly don’t mean this as a slight on Tao’s peers. That said I’m sure there’s someone out there who fits this description better. I was picturing a modern-day Ramanujan in my mind.
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":
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:
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.
Generally, the nth roots of 1 form a cyclic group (with complex multiplication, i.e. rotation by multiples of 2pi/n).
One of the roots is 1, choosing either adjacent one as a privileged group generator means choosing whether to draw the same complex plane clockwise or counterclockwise.
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.
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.
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).
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.
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