Mathematics - 2015-06-11 (page 1 of 3)

iluso

1:15 AM

@Ashwin I made some additions if you're interested ;)

Mary Star

2:17 AM

Could someone take a look at my question:

0

Q: Apply Pohling-Hellman to calculate the discrete logarithm

I am looking at the following example of calculating the discrete logarithm with Pohli-Hellman. The group is $\mathbb{F}_{29}^{\times}$ and we given $y=10$ and $g=3$. We want to find $0 \leq x \leq 28$ such that $y=g^x \pmod {29}$. I have done the following: The order of the group is $28=2^2 ...

cryptography

?

Soham Chowdhury

2:58 AM

@Balarka, after you got offline, I had nothing to do so I skimmed the second groups chapter. There are all sorts of things with SESes in there. I had no idea you could do problems like "classify all groups of order 400 / 1024" with those (and the three Sylows)!

when are you going to tell me about that theorem?

Paul Plummer

3:09 AM

Why don't you just read the chapter, most of that chapter is fairly independent from the rings and module chapter @SohamChowdhury

Soham Chowdhury

I'll finish most of the exercises in this chapter first, @Paul.

Don't want to shoot myself in the foot.

I just wanted to see "what was coming up".

Paul Plummer

Yes, but you don't need Balarka to tell you what is going on when you can just look for yourself

Anonymous

@iluso I think you should now go for MO.

iluso

@Ashwin Haha, my last edit just kill my brain

Anonymous

@iluso I just know one or two theorems in Combinatorics,that's all :p

iluso

3:14 AM

I'm starting to think it would be better to ask my question with the factorization point of view

@Ashwin I don't know much about it either

Dave

is a(b)(c)(d) the same as saying a * b * c * d

iluso

@Dave Yep

Dave

ah okay thanks :)

Soham Chowdhury

@PaulPlummer no, he said he'd tell me about a certain theorem.

Anonymous

@iluso maybe yes,I do not know xD

Dave

3:31 AM

is there an online website which can list alternative ways to write a given expression

Clarinetist

Purely out of curiosity, anyone know where Jasper's been?

Masacroso

Jasper the philosopher?

Clarinetist

Nah, there's some guy on this site with that user name

Masacroso

haha

Clarinetist

Or at least it used to be that username

skill patrol

3:53 AM

You could use wolfram, but to be honest @Dave that is a skill that everybody works on :-)

Btw what did you think of the link?

Remember me

4:36 AM

Ha ha All 200 questions done and dusted with

skill patrol

200n

Nobody does that many?

Soham Chowdhury

5:56 AM

@Rememberme of?

Balarka Sen

6:47 AM

@SohamChowdhury yes, you could.

and I'll tell you about the theorem only after you play with short exact sequences more.

You told me last night that $V_4$ and $\Bbb Z_4$ fit into the sequence. How do they? I.e., what are the maps, if they do?

Agawa001

HAIL MATHS , hey folks

Chris's sis the artist

7:11 AM

@BalarkaSen Prove that

$$\sum_{n=1}^{\infty} \frac{H_n^3}{(n+1)^6}=\frac{197}{24}\zeta(9)-\frac{33}{4}\zeta(4)\zeta(5)-\frac{37}{8}\zeta(3)\zeta(6)+\zeta(3)^3+3 \zeta(2)\zeta(7)$$

Balarka Sen

Not in the least interested.

Chris's sis the artist

@BalarkaSen No worry. You have the possibility to buy my book (and learn).

Balarka Sen

I won't, believe me.

Why would I spend money on something I don't even care about?

3

Chris's sis the artist

BBL

Remember me

7:31 AM

Hello@Balarka

Agawa001

@BalarkaSen u must show the least interest about someone asking u to be

Balarka Sen

@Rememberme hi

Remember me

@Balarka Are you free..... I want the intuition behind subspace topology

Agawa001

thats rude + lot of people are just fended off loads of algebra u r talkin about daily .

Balarka Sen

@Agawa001 who told you we talk about algebra?

Remember me

7:34 AM

sorry if I am annoying you@Balarka

Agawa001

i just see masses of algebra daily here

Balarka Sen

I wasn't being rude : I have told Chris to not to ping me with her stuff because I don't find anything interesting about them. But she still does it. It's irritating.

@Agawa001 well, what you call algebra is actually called "topology" :P

Remember me

hahaha

Balarka Sen

It's true that I like algebra, but I don't think I have been talking anything other than topology lately.

Remember me

@Balarka Can I get some intuition behind it ... pls

Balarka Sen

7:38 AM

@Remember What kind of intuition do you want? It's a natural way to equip subsets with a topology.

Agawa001

it s still abstract algebra

Balarka Sen

No, it's not.

Topology is a branch in it's own.

And what's wrong with algebra? It's a beautiful branch of mathematics.

Remember me

Sorry I got momentarily disconnected...

I want a picture

I am doing it from simmons and simmons doesnt show a diagram for how a topology on a set might look....

Balarka Sen

Draw a set $X$, and a subset $A$. Draw a bunch of open sets inside $X$. Now chuck out everything other than $A$.

The (bits) of the open sets lying in $A$ defines the subspace topology.

Remember me

Okay....

SO we can imply from this right any subspace of a topological space is a topological space

Balarka Sen

7:45 AM

Sure, but note that there are a buckload of other topologies you can give to a subset of a topological space.

Remember me

Yes....

Balarka Sen

It's just that the subspace topology is a natural way to do it.

Remember me

Okay so in mathematical terms ...
Extending the topology to the subspace

@Balarka I also wanted to know....
How do I show that two spaces are not homeomeorphic? @AlexC gave me a question on it and I have gone nowhere in it

Balarka Sen

exercise : prove that the subspace topology on subset of a metric space is equivalent to the topology induced by the metric.

@Remember There is no generic algorithm to do it.

What are the spaces Alex gave you?

Remember me

2 days ago, by Alex Clark

@Rememberme Show that $\Bbb R^2$ and $S^2$ aren't homeomorphic

@Balarka

Balarka Sen

7:50 AM

It's a good question. Are you familiar with compactness?

Remember me

Yes a bit....

Did it from Rudin

Balarka Sen

Is $\Bbb R^2$ compact?

Rudin does sequential compactness, that's not what I want.

Do you know the covering-definition of compactness?

Remember me

Open cover one..?

Balarka Sen

yeah.

Remember me

There exists open covers $A_\alpha_i$ such that the union of these is the set.....

Sorry if it is wrong

I have to check my notes

Balarka Sen

7:53 AM

no, that's not it. learn compactness from somewhere.

anyway, $\Bbb R^2$ is not compact, whereas $S^2$ is (why and why?), and compactness is a homeomorphism invariant.

a better question for you to figure out would be this : show that $\Bbb R$ and $\Bbb R^2$ are not homeomorphic.

Remember me

SO homeomorphic has this huge relation with compactness...

Balarka Sen

that's not huge.

Remember me

A subset K of a metric space X is compact if every open cover of K contains a finite subcover

Balarka Sen

wouldn't you expect "similar looking" spaces to have "similar" properties? that's the whole point of homeomorphisms.

Remember me

Thats the definition of compact I know

Balarka Sen

7:57 AM

@Rememberme If you forgot the definition of compactness, do those from Rudin again. No point in trying to figure out the problem Alex gave you.

Try to solve my problem on $\Bbb R$ and $\Bbb R^2$ instead.

Remember me

Okay using the compactness idea?

Balarka Sen

No, no compactness whatsoever is needed (both are compact, so it's not useful either).

Use connectedness instead.

Remember me

Ahh.. Okay try my best

@SohamChowdhury Well I wanted to check that what I have learned till now do i remember it or not ... So I did 50 questions from algebra,50 questions from calculus , 100 questions from linear algebra

skill patrol

:O

Remember me

That took me two days...

And now back to topology

Hi@skill

skill patrol

8:07 AM

Hi pal :-)

Sounds like a great way to build-up your stamina for calculations.

Like a marathon runner.

Remember me

Yes it is especially in linear algebra

skill patrol

Do calculations, draw sketches, and take notes.

Anonymous

hey huys

skill patrol

Hi

@Ashwin if you want to get Huy's attention use the @ :-)

Anonymous

damn it was supposed to be guys lol

Remember me

8:13 AM

Okay @Balarka I got it till this much (with your hint)
lets assume a homeomorphism does exist between $\Bbb{R} \to \Bbb{R^2}$So it should preserve connectedness.
Now if i remove a point from $x$ from $\Bbb{R}$ and respectively $f(x)$ from $\Bbb{R^2}$ it should still be connected( which I feel but stilll thinking for its proof) after this I cant get anything.....
Am I going the right way... ?

skill patrol

np pal @Ashwin

Anonymous

@Huy hows Studien gehen?

Huy

Busy, studying some DiffGeo and teaching today.

Remember me

Hello@Ashwin

Anonymous

@Rememberme @skillpatrol hello

Anonymous

8:15 AM

@Huy You must be teaching high school math,right?

Huy

Exactly, integration right now. Today gonna teach some rules like the factor rule and sum rule.

Anonymous

You used to tell us how smart your students were :D

Remember me

It so nice to see high school teachers trying to learn diffgeo ... If I go to my math teacher and ask him a doubt in top he will be like"what on earth are you speaking!!"@Huy

Anonymous

@Rememberme Huy is a Grad student if you didn't know :D

Huy

@Rememberme: If you didn't know, in Switzerland to become a maths teacher you need a MSc in maths.

Remember me

8:19 AM

thats the thing @Huy

Huy

Yeah, just finishing my MSc right now asap. :D$

Remember me

Here you need BEd@Huy

and MEd I suppose

Huy

@Rememberme: Plus a diploma to teach, which takes 2 additional years after the MSc, I forgot.

Remember me

Why did you remove that @Ashwin...
Are you fearing someone here is your teacher :D

@Huy Does diffgeo involve PDE??

Anonymous

@Rememberme haage summane.....

Remember me

8:23 AM

Wha??

Anonymous

So,you don't speak Kannada

Remember me

Nope I dont know Kannada

Huy

sorry need to go teaching

Anonymous

@Huy cya mate

Remember me

Ba Bye@huy

skill patrol

8:30 AM

Later pal

Balarka Sen

@Rememberme yes, that's the right way to go about this.

iluso

@Ashwin Haha, still no answers but an upvote again

Anonymous

8:45 AM

@iluso Ask it in MO xD

iluso

I'll wait 7 days as recommended by some meta post
And I'll have to rework it a bit to merge my edits

Anonymous

@iluso cool

Anonymous

@iluso do you have any other problems of such type?:D

iluso

@Ashwin Not really, I'm in CS and usually don't kill myself on maths :p

Anonymous

@iluso I am in Mech. Engg. and look at me haha

iluso

8:50 AM

@Ashwin Haha. Hard to survive surrounded by so much maths

Agawa001

@Ashwin i was in math faculty before i do CS too

iluso

Isn't it sad for Math.SE that "hard" questions have to migrate to MO ? That's killing the level

@Agawa001 My first undergradute year was in math too. But that wasn't half the level needed to answer one question here :p

Mary Star

9:28 AM

How can we find $e$ such that $ed \equiv \pmod {143}$ where $d=23$?

iluso

@MaryStar Isn't there a missing part on the right off your congruence ?

Mary Star

I meant $ed \equiv 1 \pmod {143}$ We are looking for the inverse of d modulo n @iluso

Agawa001

@iluso in my faculty , u rnt qualified to do CS unless u major in analysis and n.theory + cinematics + algorithmic of course , i did , and i switched to cs by my own will , now i have a strong nostalgy for the precious domain i left back :(

in fact , the real cs (not database craps and officeworks) requires alot of maths , the measure taken in faculty was fair , despite the arguing and refuting of most students

iluso

Whoa. Don't you mix some of them with CS ?
I'm in France and here you're doing a lot of maths during a CS bachelor's degree. A lot of student choose instead to go in "Higher School Preparatory Classes" where they literally eat maths :p

Agawa001

@iluso algorithmic is an initiating part of cs

skill patrol

9:39 AM

ROTFL

iluso

@Agawa001 Agree. But since a lot of students (here in FR) are doing a CS degree only to become programmer, the maths are strongly rejected

Agawa001

@iluso u r one of "arguing students" then , no maths are strongly required , see cryptography and AI and graph teory

iluso

@Agawa001 I'm not ! I won't be here if I was

Agawa001

"the maths are strongly rejected" : iluso

iluso

@Agawa001 By a large majority of the students, but not everyone of them
(sorry if my English wasn't clear enough)

Agawa001

9:43 AM

tu peux parler en fr ?

no it was clear

iluso

@Agawa001 Oui je peux tout à fait ;)

Agawa001

bbl

iluso

@Agawa001 bye

Andrew Thompson

9:56 AM

Is the norm $I$ or $\mathfrak{i}$ when denoting the ideal of a Lie algebra?

Mary Star

How can we find the inverse of $23$ modulo $143$ ? @DanielFischer Is there an algorithm that we can apply?

iluso

@MaryStar en.wikipedia.org/wiki/…

Mary Star

10:16 AM

So, applying the extended eucliden algorithm we get the following:
$$1=-9 \cdot 143+56 \cdot 23$$
So, $$1 \pmod {143} \equiv 56 \cdot 23 \pmod {143}$$
That means that the inverse of $23$ modulo $143$ is $56$, right?

@iluso

Agawa001

hey soham

@MaryStar are u trying to solve any RSA system ;)

Mary Star

@Agawa001 Yes!! :-)

Soham Chowdhury

@Rememberme not an MEd.

@Agawa001 hey.

iwriteonbananas

hey soham

lol chris keeps pinging balarka to evaluate some sums/integrals

iluso

Yes, I think it's right
You can check your answer with http://www.wolframalpha.com/input/?i=PowerMod[23%2C+-1%2C+143]

Mary Star

10:30 AM

Ok... Thank you!! :-) @iluso

Balarka Sen

10:43 AM

hey @iwriteonbananas, @Soham

darn, we got another star-war on.

iluso

11:11 AM

Does anyone has an advice about how I could reword the first two sentences of this question to put them in a more "formal" way ?
http://math.stackexchange.com/q/1315109/108062

iwriteonbananas

11:22 AM

hey balarka

Balarka Sen

been doing any math?

iwriteonbananas

yep, some probability theory, complex analysis and forms

Balarka Sen

oh cool, so they're finally onto forms?

iwriteonbananas

it has been slightly boring

yes, we started yday

Balarka Sen

nice.

iwriteonbananas

11:30 AM

what have u been studying?

Balarka Sen

multivariable, but am ill right now.

so not doing much.

iwriteonbananas

sigh, that's no good

Balarka Sen

indeed, it isn't :(

hullo, @Alizter

Alizter

Hi @BalarkaSen

Balarka Sen

@iwriteonbananas make sure you learn the proof of excision theorem at some point, though. it's fun.

iwriteonbananas

11:41 AM

ok, i will. the barycentric subdivision stuff looks a bit messy though. i never felt very inclined to dive into it

next week we're going to prove the axioms for singular homology in my course, im curious to see how we prove excision there

Balarka Sen

it's raining over here. after days of heatwaves. woo.

iwriteonbananas

in any case, im sure it will be the least geometric, and most abstract-nonsense way possible

Balarka Sen

@iwriteonbananas bah, i don't care about the whole rigor of barycentric subdivisions either. it's just a systematic way to break your simplices into smaller simplices.

iwriteonbananas

nice

ok fair enough

btw. i feel like i always make some mistake when i apply excision lol

e.g.

say we wanna compute $H_*(D^2, S^1)$ w/ excision ( i know it's easy w/ LES but whatever )

Balarka Sen

as you'll learn later on, proving excision is equivalent to proving that $\{C_\bullet(X)\}$ is chain homotopy equivalent to $\{C_\bullet^{\mathfrak{U}}(X)\}$ where the latter is the chain complex consisting of abelian group generated by simplices sitting inside some open set of a chose open cover. that's where breaking of simplices comes into the play

iwriteonbananas

11:45 AM

then $H_*(D^2, S^1) \approx H_*(D^2\setminus p, S^1 \setminus p)$

$S^1\setminus p$ is contractible

Balarka Sen

uh-huh, you'll land into trouble in there :P

iwriteonbananas

yeah, i know...

Balarka Sen

it happened to me too. excision is not really helpful for computing things.

unless, of course, you combine it with LES to get the M-V sequence.

iwriteonbananas

right

is $(D^2\setminus p, S^1\setminus p) \simeq (S^2, p)$?

Balarka Sen

the drawback of excision is that once you excise something from $(X, Y)$ to get $(X - A, Y - A)$, while the latter maybe an easy pair upto homotopy equivalent, you have to keep track of where $Y - A$ goes after homotoping $X - A$

iwriteonbananas

11:48 AM

yeah

i've fallen into that trap many times

Balarka Sen

@iwriteonbananas yeah, i think so. the homotopy equivalence would be wacky :P

yeah, that's it. (D^2 - p, S^1 - p) is indeed (S^2, p).

iwriteonbananas

@BalarkaSen $\{C_*(X)\}$ is a chain homotopy? that doesn't parse

Balarka Sen

is chain homotopy equivalent to

iwriteonbananas

oh i misread sry :P

Balarka Sen

a chain homotopy equivalent between chains are chain maps $f, g$ going in the opposite direction, such that compositions are chain homotopy equivalent to identity (for both order, with different identities)

iwriteonbananas

11:53 AM

right, it's analogous to homotopy equivalence

Alizter

What happened to Jasper?

Balarka Sen

yes. homotopy theory with chain complexes is something interesting. i guess those abstract homotopy theorists generalize these to model categories, kan complexes, etc.

about which i know nothing of.

@Alizter he left, apparently.

iwriteonbananas

i see

btw. i suggest you start studying chapter 3 of hatcher's book

since it won't be long until i start

:P

Balarka Sen

haha

ok, maybe i will.

felipa

hi @robjohn

Balarka Sen

11:56 AM

cup product intrigues me.

felipa

I think I have an exact formula for the probability question

in case it's of interest

iwriteonbananas

i dont have the slightest clue what it is

Balarka Sen

me neither. i just know that it gives cohomology a ring structure.

iwriteonbananas

"gives it a ring structure" ?

oh

Balarka Sen

yeah, cup product is something which makes $\bigoplus_i H^i(X; R)$ a graded ring

iwriteonbananas

11:59 AM

right

Tobias Kildetoft

@BalarkaSen Commutative graded even

(or is it graded commutative)

Balarka Sen

surely, as every ring is commutative.

:P

interesting, on a serious note.

Tobias Kildetoft

@BalarkaSen Ohh, it is definitely not commutative in general, just the graded version

i.e., it is commutative up to a sign depending on the grading

Balarka Sen

oh, yikes.

i am only familiar with the H-space homological version of this : if $X$ is an $H$-space, then $\bigoplus H_i(X)$ is a graded ring.

Tobias Kildetoft

@BalarkaSen I am not even that comfortable with the cup product, though as I recall it is a bit easier to see how it appears when one considers Hochschild cohomology (which is really just a nice way to get the usual cohomology by choosing a neat complex)

felipa

12:29 PM

anyone got any ideas how to approach math.stackexchange.com/questions/1321242/… ?

Agawa001

^ show some effort within question body before ur post would be closed as (whatever irelevant reason)

felipa

@Agawa001 oh... the numerical work is not enough?

@Agawa001 ok some more effort added :)

Agawa001

@felipa just a proposition , to avoid tragic holding

that would be harder to unhold :D

felipa

12:44 PM

@Agawa001 thanks. I hope what I have added is enough

Balarka Sen

@TobiasKildetoft interesting. i have heard that differential topologists visualize cup product by the dual intersection product in homology for low dimensions.

Tobias Kildetoft

@BalarkaSen My topological understanding of (co)homology is very limited

Balarka Sen

yeah, I understand that you're not onto topology.

Tobias Kildetoft

nor into :)

Balarka Sen

haha

iluso

12:54 PM

Is there a link between a number $n$, his number of divisors $\tau(n)$ and his total number of prime factors $\Omega(n)$ ?

Tobias Kildetoft

@iluso Well, $n$ obviously determines the number of divisors and the number of prime divisors

and the number of divisors is easy to describe given the prime factorization of $n$.

iluso

@TobiasKildetoft Yeah, stupid question... Wrong idea

felipa

1:20 PM

I hope this isn't too obvious but what is the largest term in the sum $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$ ?

assuming $n$ is large

is it when i = n/4 for example?

Alec Teal

1:48 PM

@AlexClark you here?

Ted Shifrin

@Alec: No one is here.

Oh, goody. Hi @DanielF

You'll be proud of me, @Daniel: I just answered two (easy) analysis questions :D

Daniel Fischer

Hi @Ted.

Alec Teal

@TedShifrin thanks, I do love it when you try to be funny using stuff that was original waaaay back when you were my age.

Daniel Fischer

Good. I suppose you answered them well, @Ted.

Ted Shifrin

No, it was not original then, either. It goes back earlier than Winnie the Pooh.

Nah, @DanielF.

hi bananas

Daniel Fischer

1:54 PM

@TedShifrin There is no "earlier than Winnie the Pooh".

2

iwriteonbananas

hello ted

Ted Shifrin

Shakespeare will be annoyed to hear that, Daniel.

iwriteonbananas

hmm i shouldnt have come into this chat, i need to do this exercise

bye ted

Ted Shifrin

bye, bananas

Daniel Fischer

@TedShifrin Shakespeare is dead. Dead and deaf.

Ted Shifrin

1:58 PM

Well, Alec has pointed out I'm almost dead. :)

Daniel Fischer

@TedShifrin Rumours of your death have been slightly exaggerated.

4

Ted Shifrin

Only slightly, yes. So, you doing ok?

Daniel Fischer

@TedShifrin More or less. I don't get enough sleep these days, have to get up way too early.

Alec Teal

I never said you were almost dead. I... I was just trying to hold banter looks away

Ted Shifrin

Daniel: I certainly hope this place isn't making you lose sleep.

More or less, Alec.

Alec Teal

2:03 PM

I honestly thought you fed off of that stuff.

I feel like a bit of a penis now.

iluso

Does someone think that this answer can be generalized to solve this question ?

Daniel Fischer

@TedShifrin Nah, I'm nephew-sitting for a couple of days, and he has to be in school at 8 a.m.

So I have to get up in the middle of the night (6:30) to make breakfast.

Speaking of nephews, I have to pick him up in a couple of minutes. bbl, pml.

Semiclassical

2:53 PM

Hi chat

iluso

@Semiclassical Hi

Fargle

Hello @Semiclassical!

robjohn

@felipa good morning (or whatever)

felipa

3:21 PM

hi @robjohn

@robjohn it looks like the answer is $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} / P\left(\sum_{i=1}^n v_i w_i = 0\right)$

which is quite surprising :)

the numerator is the probability that both inner products are zero

@robjohn is it clear what I am talking about? :)

robjohn

@felipa I know what problem you are talking about

@felipa It definitely does not work out as simply as the other problem

Ted Shifrin

heya @robjohn

robjohn

@TedShifrin Hey, Ted... The weather here is cloudy with drizzle... Great summer weather :-)

We had rain here two days ago

felipa

@robjohn the formula I gave is numerically exact for n up to 300

@robjohn so it seems hard to imagine it is wrong.. I just don't have a proof :(

robjohn

@felipa How do you know it is exact?

felipa

3:34 PM

@robjohn I wrote some code to work out the probabilities that both inner products are zero exactly for small n

@robjohn it's a fun exercise in dynamic programming it turns out

if you use python I can give you the code to try

Agawa001

3:45 PM

hey @Masacroso & @Chris'ssistheartist

Chris's sis the artist

@Agawa001 Hey

Agawa001

have u dismantled that harmonica

Ted Shifrin

@robjohn: You (we, soon) need lots more rain. I'll be a Californian again by July 24.

Hippalectryon

:22138812 murderer

Chris's sis the artist

@Hippalectryon :D

www.youtube.com/watch?v=KuptPgLoFyc

@Hippalectryon ^^^

@Agawa001 Do you refer to some specific series? I killed all I had in terms of series with harmonic numbers. There is no one alive. :-)

Soham Chowdhury

3:47 PM

@Ted we need rain too :)
What happens is that there's a lot of thunder and everything, a very dusty wind and then barely 15 minutes of rain. And then the next day is horrible, as if to make up for those 15 minutes.

Ted Shifrin

Yeah, you guys need it too, @Soham.

Agawa001

@Chris'ssistheartist ur latest

Chris's sis the artist

@Agawa001 It requires much work, but it works elementarily.

Agawa001

@TedShifrin global warming , we ll make all rain come to our sahara

Ted Shifrin

Well, most of our politicians think global warming is a liberal myth. ...

2

Agawa001

3:50 PM

global warming is just a result of people messing alot with mothernature

Ted Shifrin

Lots of people and lots of industry, yes.

Hippalectryon

Don't worry, according to a recent study by Marlboro and British Petroleum, the principal cause for oil spills, global warming and lung cancer is maths :3

Fargle

Even a lot of the people who think it legitimately exists fervently deny that we are the cause.

Agawa001

u wont touch any changes until u see the disaster made by ur own hand in a very unfortunate time in a very horrible way

thats the human nature

Fargle

Earth is big, therefore it's too big for us to affect. QED.

Ted Shifrin

3:54 PM

Well, and you're particularly tiny, right, @Fargle?

Agawa001

@Fargle nuclear dust is enough big

Fargle

@TedShifrin I don't know what "particularly" is supposed to mean, haha.

@Agawa001 Microplastic is big enough, too. We're handily screwing over this planet.

Chris's sis the artist

"The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished." Thus wrote Alfred Adler in an article "Mathematics and Creativity" in The New Yorker Magazine (1972) echoing a common belief that mathematicians tend to do their best work before the age of 30, physicists before the age of 40, and biologists before the age of 50 (though there are exceptions!).

2

I totally disagree ...

felipa

@Chris'ssistheartist I think what really happens is that mathematicians do their best work in the first decade or so of their professional life

@Chris'ssistheartist people who start later, do good work later

Ted Shifrin

There are lots of counterexamples to that, @felipa.

felipa

3:58 PM

@TedShifrin really?

I believe there are some...but lots?

Hippalectryon