Mathematical “urban legends” | Hacker News Reader

Mathematical “urban legends”

mathoverflow.net

122 pointsmikevm52 comments

Since the thread there seems locked, I'll add:

I would be surprised if the snarky Ivy League mathematician from Japan was Hironaka. He was much too gracious for that, including in that he overpraised my thesis to my parents at my thesis defense.

Dean Yang's conjecture about Andy Gleason getting calculus onto the qualifying exams was very credible. I'll add the story that a significant fraction of Harvard math grad students passed their qualifications conditional on an passing a later oral exam in one or two sub-disciplines. Joe Harris' conditional was said to have been on calculus.

A Bulgarian visitor (this was in the 1970s) told me that all university graduates in his country, or at least in his university, had to write a senior thesis on applying Marxist-Leninist thought in their disciplines. He didn't go on to explain how he'd done this in mathematics.

A visitor from, I think, the UK had rock-star style long hair. It was set on fire by a candle at wine and cheese. I'm pretty sure Raoul Bott was the guy working most closely with this visitor, which was regarded as funny since he seemed a bit square in such respects.

I heard the Milnor story from Nick Gunther, who'd been a Princeton undergrad. Nick was a heck of a story-teller in general. (His father was John Gunther, of Death Be Not Proud fame.)

I have no stories about Andrew Wiles. He was quiet and polite.

Mackey was a character. I find the story believable.

Zariski's 80th birthday conference included a new paper by him, if I recall correctly.

David Kazhdan's English was so bad when he first arrived at Harvard that people kept dropping out of his class. Finally there were about two left, both of whom understood Russian, and he changed languages and conducted class in that language.

OK. I've gotten to the Ofer Gabber part now. Ofer was in my dorm, and indeed had the room next to mine. That dorm held a pajama party at midnight. At the party, he tried to engage me in mathematical discussion.

We had a bit of a math kid's row there. I started grad school at age 16. My roommate Ran Donagi started at 17. Ofer started at 16. I think they both were a lot more accomplished in math on arrival than I was, however, so that makes me the least precocious of the three of us. :) Perhaps not coincidentally, I'm the one who didn't remain in mathematics.

Please please please tell more Gabber and Donagi stories.

(Every time I stumbled upon an "unproved theorem of Gabber" in a paper, I would take a screenshot and throw it into a folder.)

Apparently the Putnam exam was given unofficially to Israelis, and both Ran and Ofer finished top 10 -- in their mid-teens. By way of contrast, my best finish was a little worse than 100th, when I was 14.

Ran was 3 years ahead of me, and pretty much the ideal roommate (my second semester; I invited him to swap rooms with a first semester roommate I didn't much get along with). No hassles about living conditions; some older-friend general advice; a lot of help studying for my qualifying exams.

Ran had a sadness about him due to political controversy -- he had gotten a special postponement of army duty due to his precociousness, he didn't want to go back to fulfil his commitment, and orthodox Jewish department chair Shlomo Sternberg pretty much expelled him (albeit with a PhD) in retaliation.

Of course, a much greater sadness later occurred in Ran's life, as his ex-wife killed their child in a murder-suicide. :(

Ofer was a stereotypical geek; Ran was a more socially adept guy, with girlfriends and so on. Not coincidentally, he spoke the much better English of the two.

If we had a hierarchy of who was quickest and smartest in the department, the top two were generally thought of as Ofer and Angelos Tsiromokos. In reality, Don Coppersmith was right up there as well. Angelos of course is the one who never got his PhD, instead going off to be a translator for the Common Market/EU. But then, he could beat me at Scrabble, despite English being his third language.

(On the other hand, Daniel Pipes, who briefly lived in my dorm, didn't take kindly when a math guy -- me -- took him down at a word game. :) )

Ran told me of a multi-day conversation in which guys progressed through the natural numbers, coming up with an interesting mathematical question to which the number was the answer. I think they got stuck at 93 or so.

When we were in the common room, it somehow came up in conversation that Jacobi was Jewish. I immediately said "Oh, THAT'S Jacobi's identity!" Angelos literally fell out of his chair laughing.

I'm not familiar with any of the people mentioned, but could you elaborate a bit on the unproved theorems? Were they generally supposed to be true?

And in an economics seminar, a graduate student made the claim "It is axiomatic that if there are more possible outcomes to a negotiation, it is easier to achieve a result." This is in fact nonsense, as can easily be seen by considering cases in which the set of all possible outcomes has cardinality 1.

And so I said "It may be axiomatic, but it also happens to be incorrect."

Relevant to the previous anecdote is that, as a game theorist, I of course had read and thought a fair amount about negotiation.

1) One of my high school buddies who went to the Courant institute for his math Ph.D. defended his thesis and then it turned out his proof was one that his own advisor had completed 10 years ago in a side note to a publication of a bigger result. They still gave him the Ph.D. (and I think the advisor was reprimanded); he wound up in finance.

2) Although I'm a biochemist, I did a math degree at the UofC - one memorable lecture was the analysis class lecture where we proved that pi was irrational (Professor Carlos Kenig). It started with the assertion, "assume pi is less than 6". Then he said, "actually it doesn't really matter what the number is it still works, I don't know how to count past 2, I'm sure 6 is big enough."

I'm surprised he can count to 2. In CS it's just 0, 1, infinity.

He works in L2 spaces.

http://math.uchicago.edu/~cek/bibliography.pdf

That must be a difficult commute each day from R3 space.

"Don't care" and "taboo" appear as well. Unsure if they actually exist...?

In theory, computer scientists and programmers only admit the existence of 0, 1, and infinity.

In practice, I've encountered the "tri-state boolean" at least three times, completely separately, and one coworker once joyfully produced a quint-state boolean, which is to say, in practice programmers will use without restriction all sorts of strange mathematical extensions to numbers.

(A "tri-state boolean" is a boolean field that probably started life with two values but grew a third on the side instead of being upgraded cleanly. A common case is in SQL, where you can make a bool value NULL and thus have true, false, and NULL, which may end up being treated differently by only some parts of the code. Happy debugging!)

This can be all sorts of fun in Objective-C, which for historical reasons has a commonly-used BOOL type which is an eight-bit integer. You're supposed to only store 0 and 1 in it and pretend the other possible values don't exist. Every so often I see some code that uses 2 as well. Once I saw some code, written far too late at night, which used a BOOL as a counter.

MathNews, UW Math department's student weekly newsletter, had/has a section 'profQuotes' - just about the only part worth reading.. samples from this week:

"Tragically, we will need to prove both cases. Fortunately, I can do one in class and assign the other for homework."

"I’m sure you’re familiar with the proof technique I’ll use here... [writes 'Exercise' on the board]”

What's their issue with pretzels? :P

Somewhat similar to some of the posted ones, my father relays me this story about a professor he TA'd for:

The professor taught a class with a single student enrolled, who would sometimes show up late. However, the professor would always start the lecture on time regardless, and so the student would have to quickly take notes to catch up. If the professor filled up the board before the student arrived, he would simply begin overwriting the old material, and the student, once he arrived, would be in a race with the professor to copy it down before it was erased. One day, the student missed the class entirely, and the professor gave the entire lecture to an empty room.

I thought this story was apocryphal, but my dad said it's likely true, as it was fairly specific about this professor.

If a professor gives a lecture to an empty room, how does anyone know?

Not quite the same, but one of the math professors from my alma mater could write faster on a blackboard than most people could write with pencil and paper and was not shy about erasing when he filled up the board. It was always crazy trying to keep up with him.

I remember a prof, I think math, might have been physics (there was one guy in the physics department whose MSc was in mathematical physics, was working on his PhD, taught in both departments, and seems to my shaky memory to be the best match for what happened) who actually had the eraser in the "other hand" one day, applying it as he went. I think he was just excited, cannot remember why. One or more us said something like "uh, professor...?", he noticed, put down the eraser, and continued, somewhat sheepishly.

I propose a new Law of SE: any topic of interest will eventually either get rejected or locked for being historical only.

That makes a lot of sense, right? Stack exchange is designed around making it easy to find and get good answers to questions, not to have more involved or less focused discussions, even if they're more interesting to read.

The problem with this is the Law of Internet Monopolies (I just made the name up): monopolies on the internet form very naturally and are tough to dissolve.

The sheer size of stackoverflow/mathoverflow means it attracts many mathematicians in one place, unlike almost any other online forum I know. If you restrict some subset of questions there, it is both impossible to look for such questions elsewhere (nobody goes elsewhere) and to create a trivial fork of mathoverflow where such questions are allowed (you'll never get critical mass because people will not spend their time on two similar websites).

It's the same reason why nobody can create a better Wikipedia, no matter how much pointless arguing is on the original and how clunky is the input editor.

---

To sum up, restricting questions on MO actually forbids such questions to be asked by a large online mathematical community for a few years, until some better Q&A forum appears. And that's what makes us upset, I think.

I recently had the experience of listening to Joel Spolsky talk on the subject of seemingly arbitrary and unintuitive rules in large internet communities. Basically what I gathered from it is that in order to keep the quality of the content at a higher level, some of these rules are the best ways that this can happen. Some of these rules sound dumb, but they come from the experience of actually moderating very large communities and still trying to maintain focus on the actual goal of the site. As for your concern on this seemingly monopolizing the space of mathematicians I think this is untrue. If the demand for a place to discuss this content exists enough to have a critical mass community in the first place, surely it can exist outside of stack exchange. There is no overlap there because that is not at all the same content that stack exchange is hosting. I can certainly imagine a scenario in which I would frequent one site to answer and receive answers on questions in mathematics, but also frequent a board for casual community driven math topics.

> I recently had the experience of listening to Joel Spolsky talk on the subject of seemingly arbitrary and unintuitive rules in large internet communities. Basically what I gathered from it is that in order to keep the quality of the content at a higher level, some of these rules are the best ways that this can happen.

I understand the creators must have done something right, but I believe it is chiefly the tight UI (focus on questions instead of posts that get hidden over time) along with the strong gamification (you get a lot of power if you amass points) that kept the early adopters hooked, thereby gaining enough mass for the site to become popular.

The tightness of the questions is for me just a quirk of the creators' personalities. Look at Reddit -- also partially gamified, very loose with its rules, and massively popular. If the rules were the magic that makes or breaks fora, Reddit would never have made it.

> If the demand for a place to discuss this content exists enough to have a critical mass community in the first place, surely it can exist outside of stack exchange.

I disagree. If you look at this discussion and many others, you'll see people expressing their discontent about questions being forced out of MO/SO. Do you think the people that complain do not want such a place?

In response to the comment on Reddit, Joel mentioned this in one of his points. His response related to the part where I mentioned maintaining a high level of quality in the content. It's not that everything is bad on Reddit, but it sure is easier to filter out the bad when we have these rules on what belongs and what doesn't. In other words, things must be sacrificed if you want to have lower troll density. Even HN has it's rules, even if they are community driven at this point, but that's how many of these rules begin on other sites (citing Joel's experiences with SO and his knowledge about wikipedia).

I don't think casual fun interactions should be banned on the internet, it's just more likely to involve undesirables that certain websites are a million times more effective by avoiding. Imagine if you searched up a question on MO or SO and the first number of responses were bloated indefinitely by other answer threads discussing the topic, but maybe not in the same context, their website becomes that much more ineffective for it's desired purpose.

As far as not seeing a place and the discussion on it, I think that is more indicative of the fact that people would like a place, but nobody has been particularly motivated enough to make it happen yet. Not to mention, at least currently you can get a similar discussion by linking the historic thread on a comments section with upvotes, so it seems another competitor for that community would be sites like HN and Reddit rather than MO where you can't post on it anymore.

Edited for spacing

There are basically two approaches to designing things on the Internet. One is where you pay attention to what your users want and find ways to satisfy those needs. The other is to run around shouting NO NO NO YOU'RE DOING IT WRONG and whacking the users on the nose with a newspaper any time the do something other than you intended.

Both sorts of approaches can work; Stack Exchange is decently successful. But I find the latter hopelessly arrogant. An example is Friendster, the social networking site that preceded MySpace and Facebook. The founder wanted something where he could get dates, so that's what he built. When people started creating identities for non-people things (bands, movies, places, groups, political parties) they could have said, "Hey, look, our users are trying to tell us something. Let's built those features right!" Instead, they ran around with the banstick trying to force everybody back to the intended behavior. That worked until MySpace and Facebook came along, and now people barely remember Friendster.

Stack Overflow could have created features that channeled the "let's talk about interesting things" energy properly. It would have served their community well, and it would have given them more eyeballs on things that are questions with definite answers. Instead, they've been unrepentant dicks about it and have driven many people away.

The problem is, whatever the intentions are I still see people posting and getting away with karma magnets while interesting questions which have real answers are closed on technicalities.

That presumes that "any topic of interest" does not have an identifiable correct answer.

I've heard the one where the professor is lecturing, and says, "It's obvious that..." A student challenges him: "Come on. Is it really obvious?" The professor looks at the board for a moment, and then runs out of the room. 45 minutes later, the professor returns, and says, "Yes, it's obvious."

Reminds me of this Feynman story:

http://pastebin.com/rW2QU5k7

“We have a new theorem–that mathematicians can prove only trivial theorems, because every theorem that’s proved is trivial.”

Not very related perhaps but I think this is a great quote:

So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.

I love this!

That's classic.

There's a common variation without the student. The prof just pauses after saying "obvious", puts down the chalk, stares at the blackboard, runs out and then comes back, says "it is indeed obvious" and continues the lecture.

Unfortunately I don't have any reputation on MO to post this story.

On the first math class during 5th grade our math teacher (who was giving her first class after Graduation) spend about one hour talking about how mathematics could be challenging and another hour talking about her thesis (now I know, at time I wasn't understanding a shit)

Once she finished her non-sense lecture, she dictated us our home work.

"Go to the library and find what's Pie"

With a couple of classmates we spent our afternoon on the public library's culinary section writing our essays about measuring pies.

   Here's another great one: a certain well known mathematican, we'll call him Professor P.T. (these are not his initials...), upon his arrival at Harvard University, was scheduled to teach Math 1a (the first semester of freshman calculus.) 

   He asked his fellow faculty members what he was supposed to teach in this course, and they told him: limits, continuity, differentiability, and a little bit of indefinite integration.

   The next day he came back and asked, "What am I supposed to cover in the second lecture?""

The funny thing about this is that we covered all of that in a total of 6 hours (2 hours per day) during my first year in CPGE.

The non-funny thing is 99.99999999% of people won't understand the basics of calculus is such a time span.

That's when personal effort kicks in, 6 hours of courses followed by, say 18 hours of working on exercises, proofs and problems, will get you going.

Hah. I thought: "That sounds like an interesting topic. How could it have escaped Stack Overflow's ruthless prohibition against interesting reading?" And of course it hasn't.

I was once taking a class with Csaba Szabo in Hungary, who, as usual, was writing furiously on the board, when the quietest student in the class raised her hand. Without turning around, Csaba yells, 'YES, QUESTION?!'

The girl says, 'Csaba, what's going on with you? You're always yelling, you slam the boards down, throw chalk constantly... Last week you even broke a window? Why are you so angry?'

Csaba responds, 'Yes, yes, angry always. A storm is coming, and algebra is the thunder!'

It boils my blood every time that I come across an interesting topic on SO just to see it locked. Something is wrong with the site when you see more topics locked than open.

Locked is all right, maybe it has the answer you're looking for. The shitty part is when you get a hit from google going to SO and the SO page is deleted because "this problem is too localised and unlikely to happen twice".

This is a trend in Google search results for forum threads. Especially common (and frustrating) is getting a link to a locked thread with a single response telling the OP to search for the answer to their question.

Rubbish. you're experiecing selection bias. Popular questions get posted to HN. Popular questions also get locked. These questions are in the tiniest minority.

Shouldn't they be able to do something better with popular content that is beneficial to the community and appropriate to the forum than "lock" it on a technicality?

Like this one I found useful the other day - http://stackoverflow.com/questions/81584/what-ide-to-use-for..., favorited by 1600 people, 1000 points, 5 answers with over 100 points ... locked because it's a bad question that doesn't suit the site. Just that it suits a lot of people using the site. Its score puts it at about 180 in their rank of 8.2 million questions and makes it the 8th most popular python question out of 350k.

Shouldn't they be able to do something better with popular content that is beneficial to the community and appropriate to the forum than "lock" it on a technicality?

Like what? The content is still accessible, and it's even CC licensed, so anyone can repurpose it. What more would you want them to do with it?

Celebrate it, encourage it, keep it open for further improvement ...?

If that mod had got to it earlier then it would have been "hidden" and the community wouldn't have created the great resource that it has in that question & its answers.

You can say "well just create that content elsewhere", but the community that creates that good content is at stackoverflow, and they want that content there (based on upvotes, responses, favouriting).

There is this no nonsense, star faculty in the department where I did my undergrad.

Urban Legend in the department says that in one of the offerings of his classes, there was this smug student, who would chime in, and comment on the material being presented at every chance he got.

One day, while the faculty was presenting a particularly tough topic material to the class, the smug student raised his hand and asked, "Would it be OK if I ask a stupid question?"

The faculty looked at the student's face, grinned and said, "It is perfectly fine. After all, there is nothing such as stupid question." He paused for a bit, and then completed his sentence. "But there is only such a thing as stupid student."

In the same vein:

In my Physics undergrad, a teacher called a friend of mine to the board and asked him to write Snell's law.

He picked up the chalk and wrote "Snell's law".

This sounds like a parable for CS about the importance of quoting.

Can someone explain the introductory story? Why is it significant that the spaces were finite?

From my recollection of topology, finite spaces are mostly useful as demonstrations or counter-examples. So, to illustrate a point about why something isn't true, you might break out a finite space to provide an easy-to-understand means of grasping the counter-example (there's an entire book called Counterexamples in Topology for this purpose).

"Real work" in topology generally involves infinite spaces, though.

Reply on news.ycombinator.com