The h Bar

> Since we’re discussing style, this is a good place to apologize for the use of the plural first person throughout this thesis. This is relatively awkward, but the singular first person is even worse, and passive constructions are the bane of readability. The author invites the reader to include his or herself in this scientific ‘we’, or (if that is uncomfortable) to include the immortal F.D.C. Willard in that plural first person.

=P

Slereah

The me equation

Lozansky

Hello

Can I solve $-\Delta u = f(x,y)$ with homogenous Dirichlet conditions on semi-infinite strip using Fourier's method or would I have to use some integral transform?

Fourier's method is colloquial for series solution

Tanuj

5:27 PM

@JohnRennie Are you around ?

Lozansky

Homogenous Dirichlet on the unbounded boundaries and nonhomogenous on the bounded boundary

John Rennie

@Tanuj No, I'm a long and thin ...

Tanuj

@JohnRennie ;D haha

John Rennie

I'm kind of here but I probably don't have time for any in depth discussions.

Tanuj

@JohnRennie how "long" are you ?

John Rennie

5:29 PM

178cm I think. I can't remember when my height was last measured

Balarka Sen

@JohnRennie really redefining humor here are we

groundbreaking

John Rennie

Someone on the IPS SE just asked how to stop their dad telling dad jokes. It can't be done.

that's brutal tho

you're not a dad tho

papa rennie

5:32 PM

Uncle jokes then

Tanuj

Uncle Rennie and his jokes ;)

Anonymous

5:46 PM

A dad who tells "dad jokes" must be a fun person to be with (albeit embarrassing at times). Rare to find people who can laugh and enjoy their own jokes, and are content with themselves without giving a damn about other's reaction. :P

Anonymous

Not a good idea to try to stop them (not that I'm saying they can be stopped ;)).

CooperCape

my physics teachers a bit of a dad joke kinda guy

Balarka Sen

Number theorists are weird

I don't really have a panoramic understanding of the fundamental goal of number theory

CooperCape

intehgerrs

John Rennie

@BalarkaSen does it have a fundamental goal?

Anonymous

5:51 PM

@CooperCape The closest person who fits that description would have been my grandfather. He had this almost magical quality to be able to strike up a conversation with almost anybody and almost bore them to death with his childish jokes and annoy them with questions about their family, etc. However, my grandma used to say that he was a very silent, serious and short-tempered type of guy earlier. With time he totally changed! (In his older years). Time can do weird things to people. :P

Anonymous

@BalarkaSen Why should it have one?

Anonymous

Other than the goal being...you know...."understanding numbers"

Emilio Pisanty

Consumption of Tide Pods

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Balarka Sen

@JohnRennie Well, a chunk of mathematics does. For example I think of geometry & topology really as a program to understand shapes. But number theory seems more than just studying patterns in integers, somehow. I don't really get it.

Emilio Pisanty

^ apparently that is a thing now?

Balarka Sen

5:53 PM

@EmilioPisanty lmao

Anonymous

Learning about something is a goal in itself, tbh.

Balarka Sen

they made a wiki page on this?

@Blue That's a metaphilosophical babble

Tanuj

@Blue Can you help me with a question ?

Anonymous

@BalarkaSen I don't agree

Balarka Sen

It's an ok point of view but not really helpful

Ok

Emilio Pisanty

5:54 PM

@BalarkaSen this maybe? dpmms.cam.ac.uk/~wtg10/2cultures.pdf

Anonymous

We do a lot of things in life, without caring about what the goal is, if you look carefully

Balarka Sen

@EmilioPisanty Ah, I have heard of that article. I should read it

Anonymous

But then, maybe you were making a different point

Anonymous

Go on

Emilio Pisanty

@BalarkaSen if you haven't, then you should

ditto for the one on mathematical morality

CooperCape

5:55 PM

@Blue Heh Grandads can be cool like that seomtimes.

Balarka Sen

Thanks, I think I'mma do that right now while having dinner

Emilio Pisanty

cheng.staff.shef.ac.uk/morality/morality.pdf

CooperCape

Pretty sure mine sent back a slow cooker after measuring the different resistances between the slow and medium cook options.

Tanuj

@Blue bro ?

Emilio Pisanty

@BalarkaSen that's a weird way to apostrophize imma

Anonymous

5:56 PM

@Tanuj You can ask your question

Anonymous

Unless it is a long one...

Tanuj

there ?

chat.stackexchange.com/rooms/73598/room-for-tanuj-and-blue

CooperCape

Oh yeah, @Blue how'd your test go? (If you had a test - If my memory works)

Anonymous

@CooperCape Not bad. Except that I forgot the value of $\epsilon_0$ during the exam. ;_;

Balarka Sen

@Blue Well you're making a philosophical standpoint. What I am saying is more practical: How does someone who's not a number theory (or any other field for that matter) enthusiast understand the essence of the field, which is absolutely necessary to be interested in that field?

Anonymous

5:57 PM

I left the answer in form of $\sqrt{\epsilon_0}$ m

Anonymous

Not sure how much marks I'd lose for that. But otherwise it was okay

Balarka Sen

I can readily explain the essence of geometry & topology to someone in an hour(?), and better people can do it more clearly and in an engaging way. What's the analogue for that in number theory?

That is my question

CooperCape

Hehhh

Anonymous

@BalarkaSen Why doesn't cryptography suit your purpose for that?

CooperCape

8. something x10^- something

Balarka Sen

6:00 PM

@Blue ... you just gave me a field (of applied mathematics dare I say) which intersects number theory. How does that even answer my question in the slightest?

bolbteppa

There's absolutely no fundamental goal of number theory or combinatorics, they are just a bunch of insane problems with simple statements that people think up :p

CooperCape

Although sometimes memorising constants isn't helpful (for me) cause I'll always be a fool and mindlessly type in like $6.62607004081\times 10^{-34}$ and get the answer wrong cause too precise.

Balarka Sen

It just gives a vague answer to "number theory might be useful in the real world mumble mumble"

Tanuj

@bolbteppa completely agree !

Balarka Sen

That's an answer to a different question

Anonymous

6:01 PM

@bolbteppa You surely can't say that about combinatorics. A large portion of CS is based on combinatorics

bolbteppa

CS uses baby combinatorics

John Rennie

@BalarkaSen not everyone is goal oriented. Some people enjoy just wandering round picking up interesting things (i.e. problems)

Anonymous

@bolbteppa "At present". In the future we might find better uses. We live on hope (that's what pushes us forward)

bolbteppa

The guy who wrote that article does insane combintorics

Yeah

Balarka Sen

@JohnRennie That's true. It's just sort of counterintuitive

I'm going to have dinner and read that article now

Cya folks

bolbteppa

6:02 PM

As that article goes into, it's a question of theory building vs ???

Just genius thinking, clever thoughts, noticing interesting patterns, etc...

Anonymous

@BalarkaSen My point is just because most parts of number theory doesn't have an application in the real world, now, we can't say that it will never have. Look at my reply to bolteppa. Even major portion of euclidean geometry doesn't have much use in real life (think: nine point circle)

Anonymous

New uses of topology are being found almost every now and then for example

Anonymous

But if you notice, most of the mathematical foundation for that was laid long ago!

bolbteppa

As you see in that article, a lot of it is about graphs, sphere packing, all this stuff that could really have applications in some form and probably do but we don't see it

Anonymous

The mathematicians at that time didn't even know if their work will ever be useful in the future (useful in the sense you're talking about)

3

Emilio Pisanty

6:08 PM

@bolbteppa that's... kind of missing the point

if you're referring to the Tim Gowers article I linked above

bolbteppa

"The “two cultures” I wish to discuss will be familiar to all professional mathematicians. Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories."
How is it missing the point when he says this is his point

Anonymous

@BalarkaSen By the way, I'm quite surprised hearing this question from you. I thought you didn't believe in goals. :P

Balarka Sen

@EmilioPisanty I'm 5 pages in; it's intensely gripping!

Emilio Pisanty

toldja

Balarka Sen

@Blue I do not see how this has any correlation with my question. I did not ask for "real world applications" of number theory (I am aware and have superficially studied some of them in the past, but I also don't think I have to give a hoot about applications of mathematics to appreciate it)

I don't disbelieve in "goals". I think they constitute a consistency for various thoughts

bolbteppa

6:18 PM

The holy grail is probably the Riemann hypothesis if that's any kind of a goal

Balarka Sen

I believe, for example, that the periodic table was one of the conceptual breakthroughs in chemistry

bolbteppa

But then there's all those silly problems that have existed for longer

Is 6,5409283843829193948342323423 prime when multiplied by 44 and then exponentiated by a logarithm and then plugged into a function which turns it into an integer mod 6

These are the only kinds of people I have seen taking determinants mod n though so there is much to learn

John Rennie

Does the Langlands program count as number theory? That's a long term goal.

Balarka Sen

I think it does but I know very little about it

bolbteppa

Yeah the algebraic version is, the geometric version has already been physicsized and solved in some form (hmm)

John Rennie

6:21 PM

The Fermat proof was done by relating elliptic curves to modular forms.

bolbteppa

arxiv.org/abs/hep-th/0512172

It's just so crazy tbh

Balarka Sen

good ol' eddie

2

the first to shoot a mathematical porno

ArtOfCode

sfw please...

bolbteppa

'At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will not get anywhere in graph theory by sitting in an armchair and trying to understand graphs better. Neither is it particularly necessary to read much of the literature before tackling a problem:

it is of course helpful to be aware of some of the most important techniques, but the interesting problems tend to be open precisely because the established techniques cannot easily be applied.'

This is encouraging to many apparently :p

Balarka Sen

@ArtOfCode he really did!

its called "rites of love and math"

2

ArtOfCode

6:28 PM

@BalarkaSen whether he did or not it's still not SFW :P

John Rennie

Mathematicians having sex? Are they allowed to do that? Doesn't it compromise the purity of their discipline?

4

Anonymous

@BalarkaSen If your question is how to explain to someone the essence of number theory, I don't know. You can't explain someone the essence of music or literature. One has to hear music read literature to understand its essence.

Anonymous

If you are attempting to explain a layman why number theory is beautiful perhaps start with some facts about the primes (maybe Euler's proof), Fermat's little theorem and then move on to some current problems like the Riemann hypothesis.

Anonymous

In fact, there are several popular mathematics books aimed at the general population, which do a good job at that

Balarka Sen

@Blue You have misunderstood my question totally and you're using a terribad analogy there.

Nevertheless I think the article I was linked constitutes a very good answer to what I was asking so I'm satisfied

Anonymous

6:32 PM

@BalarkaSen Maybe I haven't understood your question, yes.

Anonymous

You haven't made it clear what you mean by "essence"

Anonymous

Your notions and my notion of that, might be completely different

Balarka Sen

That's ok

@JohnRennie yeah we're a christian field. it's outrageous

John Rennie

Insert jokes about Cox ring and Cox-Zucker machine here ...

Balarka Sen

Tits buildings are my favorite

Emilio Pisanty

6:38 PM

@ArtOfCode for clarity, you're stating that the discussion of whether someone did or did not direct a pornographic film should be classed as nsfw?

ArtOfCode

rolls eyes

I'm giving y'all a gentle reminder to keep it SFW. Discussing porn, whether mathematical or not, isn't.

That is all I'll say on the matter, because discussing it further is going to turn into an argument.

Balarka Sen

Tits buildings are sfw unless you do not know how to spell French names, you cultureless heathen

ArtOfCode

...neither are insults appropriate, in jest or not

Emilio Pisanty

is that the sound of a point being missed that I hear?

2

Balarka Sen

Supa hot fire ohhhhhhh!!!!

►

I mean I would normally not make snide messages like this but this is too ridiculous. Anyhow, I'll desist.

ArtOfCode

6:43 PM

yup

totally missed

Anonymous

People talking past one another, has become a common thing in the hbar. :) (At least it shows that hbar is quite popular now, and doesn't need anymore biweekly chat sessions to attract users :P)

vzn

7:22 PM

@BalarkaSen lol @ trying to find applications of number theory (try this) math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf (ps rats missed all the @#%& great topic/ dialog while my windows box rebooted with updates over 30m)

Semiclassical

@vzn well, tbf there's at least one big application of number theory i.e. RSA cryptography

though physics applications of number theory seem pretty unlikely to me

vzn

@Semiclassical RSA is one of the great/ superb examples of a field thought to be completely applicationless changing the world. lol anyone heard of bitcoin? yes there are physics applications of number theory also, it does actually have "not narrow" applications... actually riemann hypothesis now thought to have some deep connections with QM etc... old dialog in here from long ways back...

Semiclassical

uh

I know what connection you're referring to, and I wouldn't call it deep by any means

vzn

← lol think anything connected to riemann hypothesis is deep :)

Semiclassical

QM uses self-adjoint operators as formalism, and (per the Bender paper) the Riemann hypothesis would follow if a certain operator were self-adjoint, except it's not

Moreover, the direction there is entirely one way, from the formalism of self-adjoint operators to the Riemann hypothesis

regardless of whether you learn something about the Riemann hypothesis that way, you don't learn anything about QM that way

vzn

7:38 PM

there are quite a few papers on this subj, have not studied it myself ("deeply"), but doubt any of the (some elite) authors would agree with you on it being merely superficial

Semiclassical

[citation needed]

bolbteppa

@Semiclassical what Bender paper

Semiclassical

@bolbteppa math.stackexchange.com/questions/2211278/…

vzn

@Semiclassical lol =D vzn1.wordpress.com/2016/04/01/…

Balarka Sen

linking to your blog is usually not what citation means

vzn

7:41 PM

@BalarkaSen yeah move the goalposts as always. it has refs on the pg.

Semiclassical

tbf, it links to a lists of citations

bolbteppa

@Semiclassical incredible

Semiclassical

but given how many there are and their varied topics, that really tells me nothing

HsMjstyMstdn

@vzn I do, too. I think the RH is terribly fascinating, though haven't had much time to read up on it

Lozansky

Is $\delta(\textbf{x}-\textbf{a}) = \dfrac{1}{L}\sum_{k=1}^{\infty} \sin(\dfrac{\pi k \textbf{x}}{L}) \sin (\dfrac{\pi k \textbf{a}}{L})$?

Balarka Sen

7:42 PM

directly link to a specific citation instead of getting us to click on your blog to get you more traffic

Semiclassical

@bolbteppa ehh. I have a bit a "consider the source" reaction to Bender tbh

vzn

@Semiclassical ahem sorry that was not what was intended anyway. had a bunch of QM + riemann refs not sure where they are, maybe my bookmarks. its in the chat history of this room a few yrs back too. (tbf2 other physicists were equally skeptical at the time.)

bolbteppa

@Semiclassical he is incredible, have you seen his lectures or his book, what's wrong with him?

Semiclassical

as someone who isn't afraid to make novel claims, he's interesting

but I don't trust his rigor, and RH lives and dies on rigor.

bolbteppa

He teaches a course on approximation on youtube, he wrote a book on approximations, rigor is the folly of pedants :p

vzn

7:44 PM

@HsMjstyMstdn want to attack it after solving collatz lol :) ... there is a discrete version of RH that think would be fascinating to study empirically. there is maybe some less resistance/ bias against RH empirical work.

Semiclassical

for some things, yes.

if you want to compute stuff and see how well it works, I trust it

but the RH is not like that, since the places where you'd experimentally be able to see possible violations are faaaar beyond our technical abilities

vzn

@Semiclassical progress can be made short of a proof.

bolbteppa

The sense I've gotten from him from those lectures is he will do things a different way all the time, creative, really cool, I wouldn't be surprised that he was doing some approximations to get info on the problem and came up with something close to exact or something

Semiclassical

yes, and skepticism is part of progress

vzn

@Semiclassical dont think anyone has proven that "violations far beyond computers". mathematicians tend to have that bias. think its not (always) justified. bordering on folklore. just got in epic fight on reddit over that with phd math prof... yikes still reeling

Balarka Sen

7:46 PM

#keyboardwarriors

Semiclassical

for reference, I have in mind the following comment by Paul Garrett (who incidentally is a prof at my uni, so I guess I"m not unbiased there)

"About the spacing, I do not pretend to have any sort of definitive answer, but we do know that certain behaviors don't kick in until log log T is large, which is probably forever beyond numerical experimentation. That is, there is some precedent for meaningful phenomena occurring beyond our sight. It might be silly to "bet" in that direction, but it'd be possible, etc. " comment from mathoverflow.net/questions/266935/…

vzn

agreed computational work is not likely to lead to a proof... but think it can be supportive. computational work has indeed led to some epic proofs in a few cases. eg 4 color thm some more recent etc

Semiclassical

it's a bit like people hoping that superpartners of particles would be discovered at the LHC. even if they exist, there's no way to say how high in energy we'd have to look to find them. for that reason it's very hard to rule out such scenarios generically

vzn

@Semiclassical aha! try this one instead. better refs. meant to find this one. vzn1.wordpress.com/2016/04/22/…

Semiclassical

i'll look. but I'd be surprised if the influence was "Riemann hypothesis -> QM" rather than the reverse.

Balarka Sen

7:51 PM

People have still been working on finding more insightful and less algorithmic approaches to prove the 4CT after Appel and Haken's work, and large swaths of mathematics are coming out of it

Semiclassical

(Random matrix theory, on the other hand, is a big deal IMO)

vzn

@Semiclassical its probably deeper than you realize. theres a bunch of refs/ connections. agree that skepticism on both sides of the rather big/ crosscutting/ interdisciplinary divide math + physics is justified.

Balarka Sen

I have in mind the Krohnheimer-Mrowka program

vzn

@BalarkaSen defn worthwhile, and yet dont think it really downplays the significance of the decades old proof either, in fact maybe further confirms it.

bolbteppa

I have no idea about the problem but the idea that the source would cause questions, when you're talking about someone this famous with hundreds of papers, multiple prizes, famous book, etc... is a bit shocking tbh

Carl M. Bender

Carl M. Bender (born 1943) is an American applied mathematician and mathematical physicist. He currently holds the Wilfred R. and Ann Lee Konneker Distinguished Professorship of Physics at Washington University in St. Louis. He also has joint positions as Professor of Physics at the University of Heidelberg and as Visiting Professor of Applied Mathematics and Mathematical Physics at Imperial College, London. Bender achieved initial prominence in the sciences for his work on perturbative and nonperturbative methods in quantum field theory. At the turn of the millennium, Bender discovered the...

Balarka Sen

7:54 PM

I wasn't trying to downplay the Appel-Haken work

Semiclassical

I'll grant that random matrix theory has a lot to do with physics, and that random matrix theory has interesting connections to the Riemann hypothesis (e.g. Dyson-Montgomery pair correlations)

vzn

@BalarkaSen ok. yet precisely that happened at the time. some attitudes have slowly shifted, some persist. just ran into near bigotry wrt the topic by (very hi karma!) "crazymaker" phd math prof on reddit. (long story, in my latest blog.) o_O

Balarka Sen

Strange, I thought there were nontrivial combinatorial ideas involved in that proof

vzn

@BalarkaSen have you seen the hardy-ramanujan movie yet? highly recommend it esp if youre wondering about the "point" of number theory. (surprised to hear you question that... thought you were knee deep in pure math...)

Balarka Sen

I think a chunk of you people thought I was asking a shallow question somehow questioning the purpose of number theory as a branch of mathematics. I really wasn't.

The article Emillio linked is exactly what I was looking for

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