Alas, your proof by calculus is flawed. You said (several layers up):

The problem is you could also take the limit of x^2/x or x/x^2 as x->0, and get 0/0 is 0 (for the first one) or undefined (for the second). You could get any number: just take the limit of c*x/x as x->0 to get c.

Notice that the limit of x/x^2 as x->0 is NOT infinity. The limit from the right (that is, restricted to x>0) is infinity, while the limit from the left (x<0) is -infinity. What we really mean by ``the limit is infinity'' is that the function grows without bound. Start treating infinity like a number and things get much more complicated (the rules of algebra start needing exceptions, for example).

IAAM and I'm coming off a semester of explaining calc one to students (and preparing to do it again in the spring term as well).

Thanks for your posts, iluvcapra, they're really excellent and get to the heart of the matter. I think Perelman felt he'd explained enough (in his papers and talks), but you make an eloquent case that he hadn't done so to a reasonable standard.

1) you don't know me, and 2) I'm sorry for them.

I've worked or studied at a variety of places: large state schools, smaller private schools, and in between. I've worked at one of the top five math departments in the country. I've met a lot of mathematicians, from ordinary to world-class. This is just to give you an idea where I'm coming from.

Why do you think people who are smart or good at math must be emotionally or socially troubled?

The original poster said:

I'm just trying to provide a different perspective.

Yau (the mathematician, not Yao the NBA player) is, of course, the chair of the Harvard Math Department. He is a phenomenal mathematician in his own right (Fields medalist, MacArthur genius grant recipient, etc).

I'm roughly familiar with the controversy, and I think it comes down to: what does it mean to prove something? Perelman provided what for most in the field was an outline of a proof, and Cao-Zhu (among others) dotted the is and crossed the ts. Of course Perelman would say it was a complete proof, and supporters of others would say these others provided valuable details. I think Perelman worked out all the details, but he only shared what he felt was necessary.

I'm a mathematician, and I'm afraid I really don't know what you're talking about.

Mathematics is often pictured as a very isolated practice -- a person sitting alone at a desk. But it's surprisingly social, and while there is a fair amount of desk time, there's a lot of interpersonal relationships (as you put it) in the actual doing of math. Asking questions, explaining your results, mentoring students, even teaching classes -- a lot of math involves other people.

Anyway, I know lots of mathematicians, and I think generally they're pretty happy people.

Me too. That is: professor in the northeast, many students with H1N1. The university either puts them in quarantine or sends them home (and it's mostly quarantine because home is usually not close). From my sample (N=400, since I'm in charge of homework scores for a couple of courses), the infection rate seems to have slowed.

Well, no. This means "Meta-x" (which for me is esc then x) then type the command butterfly. I guess “Knowing emacs” mean “having heard all the same tired old jokes about that editor I don't use.”

Me? When I went back to grad school (early 90s), I was pleased to find I could use the same old editor I used to use in college (in the mid 80s). I still do all my work in it (used it this afternoon, and on my netbook on the bus in this morning). And version 23 is out!

Knuth already beat Python to it. Just as TeX's version is asymptotically approaching , so is Metafont's version is approaching e. I think we need more well-known constants.

(I was going to push for the Euler-Mascheroni constant, but that's =0.57721...., so it would have to be something in eternal beta. And all those Google tools are finally losing their beta tags....

It's a good alternate theory, but you're a week off:

On the week ending June 19, Goldman, for instance, was ranked first on the NYSE program trading list. But on the week of June 22, Goldman mysteriously didnâ(TM)t appear on the list of the top 15 firms at all.

So unless the Fourth of July is celebrated in June, I think that's not the issue.

Of course, I'm not checking the volume of trading either, so there could be something to your theory. (Of course, if GS bailed out for a week, wouldn't that lower the volume significantly? Weren't they the number one traders?)

Here's the choice quote I always think of when I hear Vonnegut and science fiction in the same sentence: "I have been a soreheaded occupant of a file drawer labeled 'science fiction' ever since, and I would like out, particularly since so many serious critics regularly mistake the drawer for a urinal." Found on the web, of course.

When I saw him he was wonderful. Probably 25 years ago, definitely not senile, but possibly hammered. Still very funny, though.

This ninth-grade argument crap is insightful?

Read about herd immunity. The point is that vaccines only have to be effective most of the time (someone above quotes 95%, so let me use that for the sake of argument). If a large percentage (say, 95%) of a community is immune to a disease, then it becomes difficult for this disease to spread and it dies off. This means if everyone gets vaccinated, then it only has to work for 19 out of every 20 people.

So what Duradin might be saying is: they do work, but not completely, so the vaccine deniers are endangering everyone.

This is really my perspective: Vaccines are a risk. They are a small risk (and not, I believe, from autism). The risk of the disease to the community is greater than the risk of vaccines. By refusing the vaccines, people benefit from others' immunity (and thus from other people facing the risk of vaccines) without sharing any of the cost. That's selfish.

You might argue that it's not the government's place to force these risks on us all. I see it as we the people accepting the communal risks of vaccines as better than the communal risks of disease.

I highly recommend The Shape of Space by Jeff Weeks. (He's a freelance geometer, something he can afford after winning a MacArthur Genius Grant.) I've used this book a couple of times -- once with bright high school kids and once with bright college freshman -- and even if they don't get everything, just a taste is enough.

It builds on Flatland (which someone mentioned above), but has the advantage of being more modern and not sexist. But very quickly you're learning about Klein bottles, connected sums, and all sorts of topology you typically don't see until you're well into your undergraduate (or grad!) program in math. All aimed at high school kids. Very cool stuff.

Oh, and the big punchline at the end: what is the shape of the universe? At least you'll get a good understanding of the possibilities...

Here's a taste for you from a page related to the book.