The h Bar

12:09 AM

3 hours ago, by Balarka Sen

I'm thinking, eg, how easy it is to blur the boundaries between science vs pseudoscience in social science in contrast to mathematics

Very true, especially for logic, pseudo logic will be spotted almostly instantly when you made a mistake with quantifiers

One problem of pseudoscience, is its models lack details to allow them to be testable

SigmaAlpha

1:34 AM

Hi, I was hoping someone might be able to help me understand the following statement:

"At a point p of a manifold M, a metric g has a unique signature, sig(g)=(p,n-p). Since, in terms of a chart, the components g_{ab} are continuous and since the matrix of components is invertible at each point, it follows that there is some open set O in M containing p such that sig(g)=(p,n-p) at each point in O."

I understand the first part: that the metric has a unique signature at a point follows from Sylvesters theorem. But I don't understand the logic leading to the second conclusion

Sir Cumference

@Slereah How'd you upload a vector graphic?

vzn

3:01 AM

@Secret "lack details to allow testing"? lol, what about impracticality or inaccessibility of testing, like, oh, say, string theory? extremely high energy particles? theories of black holes, or the big bang? dark matter/ energy? etc? :P

vzn

3:44 AM

re kuhnian paradigm shifts also in math, it is not widely accepted/ debated (compared to other fields), but there are many academics who take it seriously and not hard to find a few refs via googling. heres one for this audience-- university senior prj with many refs. (and who else is working on one around here?)

Paradigms and Mathematics: A Creative Perspective / shives 2012 MAA History of Mathematics student paper contest winner maa.org/press/periodicals/convergence/…

ps kuhnian paradigm shift(s) + demarcation problem intimately intertwined...

Secret

4:17 AM

snopes.com/fact-check/karl-marx-banknote-released-germany

Zero euro

@vzn it is a complicated topic. As you may aware, string theory is also quite shaky nowadays given how superstmmetric particles still failed to show up. But these models at least proposed a way to test them, thus they are testable in principle (even though it is borderline metaphysics and mathematics). Pseudosciences don't even bother doing that, which is why they are often said as not even wrong

Secret

4:42 AM

red pill blue pill -----> user list

Dawood ibn Kareem

5:36 AM

@Blue You overran your buffer, because strcat includes a terminating zero. So no, your C code is NOT OK.

Secret

6:07 AM

Should Space be Privatized? | Space Time

►

Some rocket science and economics

Mockingbird360

6:20 AM

Hello, guys. Can anyone tell me what universities or research institutions are doing great research on topological condensed matter physics

Anonymous

@DawoodibnKareem Yeah I know. I wrote that 20 initially without thinking much because I was in a hurry.

Dawood ibn Kareem

6:49 AM

31

Q: Does the International Math Olympiad help research mathematics?

I was reading a note of Hojoo Lee on inequality which is written for International Math Olympiad (IMO) participants. Although he writes that “target readers are challenging high schools students and undergraduate students“, it appears to be quite advanced. It occurred to me to ask, do these IMO ...

Wasn't there someone in here a day or two ago claiming that Motl must be one of the smartest mathematicians on SE because he earned an IMO bronze?

Anonymous

@DawoodibnKareem IMO is a school level examination. Although it requires lots of practice and some bit of ingenuity to get through, it surely isn't related to actual research. The topics are just Euclidean geometry, Combinatorics, Number theory, and some bit of Algebra.

Dawood ibn Kareem

It's hardly school level.

Anonymous

@DawoodibnKareem The topics are school level. I know, because I had solved a few papers.

Dawood ibn Kareem

I strongly disagree.

Anonymous

The problems are not school level, but the topics are.

Anonymous

7:01 AM

If you disagree, you need to show proof

Dawood ibn Kareem

There's no such thing as a "school level topic". You can study any topic you like to any level you like. Topics and levels are orthogonal.

Anonymous

While preparing for JEE, in our test series papers we almost always had a few hand-picked problems from previous IMO papers

Anonymous

Yes, you need to study some extra things

Anonymous

@DawoodibnKareem I don't even understand what your claim is

Anonymous

Euclidean geometry, Combinatorics, etc were taught to us in school

Dawood ibn Kareem

7:03 AM

I am disputing your assertion that "IMO is a school level examination". It is not.

Anonymous

@DawoodibnKareem Well, college students aren't allowed to appear for it. Only school students are.

Anonymous

Upto grade 12

Dawood ibn Kareem

Most academic mathematicians with PhDs would struggle to score 42/42 in 9 hours on an IMO paper.

Anonymous

@DawoodibnKareem Sure. I'm not disputing that.

Dawood ibn Kareem

@Blue Yes, I know that. That doesn't mean it's school level.

Anonymous

7:05 AM

It's mainly because they're out of touch with those type of problems

Anonymous

It needs practice

Anonymous

@DawoodibnKareem Your and my definition of school level are different.

Anonymous

By "school level" I meant school students appear for it

Dawood ibn Kareem

OK.

Anyway, my point is, the person who was in here glorifying Professor Motl had it wrong.

It would be interesting to know how many Stack Exchange users hold IMO medals. An absolutely impossible statistic to obtain.

I'm certain Motl is not alone.

Anonymous

Anyhow, my point is, PhD mathematicians not being able to score 42/42 on an IMO paper, is not because they are incompetent, but rather because they haven't been practicing those kind of problems for a long time. Here, students prepare for nearly 4 years for appearing for JEE/Olympiads etc. So they are better equipped for handling those type of problems.

Anonymous

7:10 AM

And almost every year 2-3 people from our institute would go to the IMOs. It wasn't an irregular feat

Anonymous

Out of them, not more than 5% would grow up to be professional mathematicians

Anonymous

One of them even went on to take up a medical degree

Anonymous

@DawoodibnKareem Sure

Anonymous

@DawoodibnKareem We concur on that.

Dawood ibn Kareem

I don't think there is a single academic mathematician in my country who has participated at an IMO. I certainly can't think of one.

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