serious-discussion

[last oxide]

but notice that if v=0, then u has to be constant

so that wouldnt be useful

(cause CR)

[mint patio]

yup I figured it must've been wrong cause of that lol

what's real analytic then? just locally = taylor series?

[last oxide]

that said, theyre both writing in power series, but not only is being complex differentiable so strong the criteria gives you only constants, but also the power series has to be complex

[last oxide]

they both are

but complex analytic is a complex power series

[mint patio]

only constants?

[last oxide]

yeah
the CR equations over there give you only constants

thats necessary for complex differentiable

(mistyped the complex at the end too)

[jovial ember]

You can prove that an entire function is either constant or has dense image

You can even go further and show it misses at most 1 point lmfao

[last oxide]

ah true

picard

[jovial ember]

Yeah

I think Picard’s small theorem?

[last oxide]

yeah

picard big is like

[jovial ember]

It’s some hurb shit

[last oxide]

every point infinite times

[jovial ember]

Yeah

For uh

I forgor 💀

[last oxide]

essential singularities?

[jovial ember]

Yeah

But I thought that’s casorati-Weierstrass

Which says that

The infinite times thing

[last oxide]

cassoratti is dense yeah

cassoratti proof is easy and great picard proof is annoying

[jovial ember]

Ah okay

[last oxide]

thats why cassoratti is better

[jovial ember]

great Picard uses Arzela-Ascoli?

Idk I just remember we introduced that

[last oxide]

the usual one?
Im not sure

[jovial ember]

Right before doing like Picard theorems and Riemann mapping I think

[last oxide]

have to see it again

[mint patio]

what's a dense image?

[jovial ember]

Uhh

[mint patio]

doesnt density require like you to refer to density in another set

[jovial ember]

Take any point

[mint patio]

so q is dense in r

[last oxide]

every little disk intercepts the image

[jovial ember]

Yeah dense in C

A complex analytic function on C has dense image in C

[last oxide]

just like every little interval intercepts Q

[jovial ember]

This is very easy to prove if you have access to Liouville’s theorem

Basically not-dense means some point z in C where the image is at least epsilon away

Then look at 1/(f - z)

This is a bounded function

So constant

Thus f is constant

[mint patio]

Oh ok so for any entire function then its image is dense in C (in between any two complex numbers we can find a number in the image of the function) yeah?

[jovial ember]

Wel

Not “in between@

It’s in terms of open balls

So like

[last oxide]

every little disk intercepts it

[jovial ember]

Take any epsilon > 0

Any z in C

You can find a point that’s within epsilon of z

“Within” here just means distance using the Euclidean metric

You know how it works in R^2

Just do that

[mint patio]

this is like

a completely different world

lolol

[last oxide]

just take any disk with positive radius

it will intercept the dense set

[mint patio]

like with real analysis it's like explaining the things you already knew better

but here I feel like I"m exploring a new universe 😂

[jovial ember]

Complex analytic functions are

[last oxide]

dont need to worry about the metric definition too much
the open balls in C are just disks

[jovial ember]

Insanely well-behaved

The condition of being analytic is so stupid strong

That you can prove miraculous stuff

[last oxide]

yeah
you want your differential to be a complex number
the field structure makes R^2 super strong

[mint patio]

yeah everyone says it every time and I'm just here like "...sure" cause I don't know CA well enough to appreciate it except for like obviously some of the results like you emtnion here

[jovial ember]

I mean honestly

A lot of it comes down to the fact that power series is strong

Like, think of it this way

Real functions, smooth doesn’t even mean there’s a Taylor function

Every complex analytic function is basically just a power series

And a power series is almost a polynomial

And we know polynomials are like the most well-behaved functions on the planet

[mint patio]

yup

[last oxide]

a common result illustrates this
analytic functions locally look like polynomials (up to analytic diffeomorphism is what I mean by looks like)

[jovial ember]

Yeah

[last oxide]

so they are in a very rough sense collages of polynomials

[jovial ember]

Like analytic functions so strong

To make it interesting you gotta let em be not analytic at some points to spice it up

Meromorphic moment

[last oxide]

I mean

[jovial ember]

This is not really accurate but I wanted to say it

[last oxide]

isnt that analytic on the sphere

or am I tripping

[jovial ember]

Uhh

[last oxide]

oh nvm
that would only be for the poles

[jovial ember]

Yeah

Wel I mean

[last oxide]

forgot meromorphic is more general

[jovial ember]

Fuck an essential singularity bro

[last oxide]

youre just taking out points yeah

actual nerf

[neat lintel]

ah yes complex ANAL

[deep mango]

By the way essential sings are basically necessary (at least at infinity). Every analytic function on the Riemann sphere is just rational.

Oh that was from hours ago

Oh well

[neat lintel]

wait ryc I thought you were a mod

[deep mango]

i have never been a mod

[pale orchid]

kanga gang drug mod ryc

[charred ocean]

Does anyone here like R programming?

[stray kite]

whats working in academia, researching in mathematics like?

[pale orchid]

you beg for money to survive and keep your job (and if you're a foreigner, to keep your visa)

[leaden skiff]

ya know unironically, i have no clue why anyone would wanna become a mathematician

[surreal sapphire]

to do math

[leaden skiff]

well yeah but like, idk to me doing new math has never really interested me that much

i'd rather just learn stuff other people have done

the difficulty and like uhh economic unviability of being a mathematician just made me even more sure that i didn't wanna become a pure mathematician lol

[surreal sapphire]

well, its the same in all of academia

[leaden skiff]

well, discovering new physics definitely appeals to me in a way discovering new math doesn't

but im planning on going into engineering anyway lol

[pale orchid]

what i said is my current position doing a phd in engineering

it applies there too

[surreal sapphire]

working in academia isnt great unless you have tenure

[pale orchid]

at some point it became socially acceptable to enslave people as part of their coming of age in higher education

[surreal sapphire]

i wonder how new german government plans to make it more viable 🤔

[crystal stone]

yA teach a bit, then you go try and get some papers out, and apply for tenure or do some other shit. Going to conferences is a big part of it

[surreal sapphire]

they claimed they will

[pale orchid]

academia? or what exactly? i didn't catch that part loch

[crystal stone]

You might think like "oh going to conferences takes away time from research", but if you want a new job

[surreal sapphire]

academia, yes

[crystal stone]

It's important to network around so people are familiar with your work

[pale orchid]

harassing people at poster sessions is the best networking you can do

[leaden skiff]

poster sessions?

[pale orchid]

yeah

[crystal stone]

Sometimes you'll be pulled into academic/departmental meetings about curricula or committees

[pale orchid]

presenting in front of 50 strangers is useless for networking

[crystal stone]

Usually this is a voluntold type thing

[leaden skiff]

is networking in academia different from normal? like, theres no normal people in academia so it can't be, right?

[pale orchid]

posters are where it's at

[leaden skiff]

also what is a poster session?

[crystal stone]

It's technically "volunteering" but you're told to volunteer

[crystal stone]

It's a bit different, than in the real world. Letters of recommendation are a regular thing to get hired at a research university

You want evidence that you're not dogshit at teaching

and you're somewhat decent at research or show promise

e.g. grants

[surreal sapphire]

posters huh

we had this crypto wtv summer class recently

[crystal stone]

Disclaimer: I'm not a professor, nor do I have a PhD

[surreal sapphire]

and people made posters

[crystal stone]

I just work in higher ed for now, within a math setting

[surreal sapphire]

i remember when i was preparing a room for an exam with a prof and we stood in front of a poster reading it

and suddenly he gets supper angry about how all posters are shit but this one especially

[leaden skiff]

what was the poster?

[crystal stone]

Yeah most posters are bad

[leaden skiff]

also wdym poster? like why are you making posters?

[crystal stone]

To advertise your research

Never been to a room full of math posters while mathematicians try to give you an elevator pitch on their research?

[surreal sapphire]

present what you did during the summer school

but like

it just full of trivial information if you know the field a bit

and random pictures

for some reason of a flower

[pale orchid]

😌

[leaden skiff]

this feels like one of those dumb projects they make you do in HS

do you have any pictures?

[pale orchid]

that's exactly it

like those dumbass trifolds for the science fair

it's exactly like that

[leaden skiff]

but it's like, people a decade older?

[pale orchid]

like 1~5 decades older

[leaden skiff]

bruh

i thought decade was highballing it

[surreal sapphire]

i still dont get the flower

there was a graph on there

and the flower looked vaguely like it i guess

[leaden skiff]

i really wanna see this now

[surreal sapphire]

dont think i have a picture

and it would doxx me anyway

[pale orchid]

📰

[stray kite]

why are all portrayals of academia so horrifying

[pale orchid]

cuz it's shit

it's only good when you hit tenure

the rest of the time you're eating dick or feeding it down the ladder

[stray kite]

so you're telling me there isn't much of a point to just not studying software and becoming a developer at some random company huh

[leaden skiff]

you eat dick so in the future you can get your dick eaten

[pale orchid]

for whatever reason i thought i'd enjoy it, but i was mistaken

i grow bitter and jaded by the minute

but i'm already half way in, so

[surreal sapphire]

also throwback to when my advisor printed dozens of posters from his own money and put them up in universities all over the world to attract foreign students

and then corona happened and nobody came

[leaden skiff]

any field that people join because of a "passion" is always dogshit

[pale orchid]

[pale orchid]

it's not even that

i barely work on the actual shit

[leaden skiff]

that's actually really sad

[surreal sapphire]

passionate people are easily exploited

[pale orchid]

i'm always in meetings or supervising students

the only time i actually had time to do research was when i was working on my master thesis

[surreal sapphire]

and academia is highly competitive which doesnt make it easier

[stray kite]

tbh im doubting if i should even continue studying mathematics at this point
if theres no point id rather just go into cs and make money in the future at least lmao

[leaden skiff]

i mean, there's reasons to learn things other than just money

im not planning on being a mathematician or physicist but still wanna be learning that shit till im dead

[pale orchid]

you can do that without suffering

[surreal sapphire]

studying anything with "academia or bust" mindset is probably not a good idea

but you can study math and learn enough CS to be employable

and then see what happens

[leaden skiff]

is there any way you could actually do any research without going into academia and dick eating?

[pale orchid]

at a company

[surreal sapphire]

ye, but not in mathematics

[leaden skiff]

physics?

[pale orchid]

sure

[stray kite]

i mean its like
uninteresting job + money > uninteresting job

[surreal sapphire]

unless you are like one of a handful of people

[pale orchid]

at a company for like 5x the salary

[leaden skiff]

well how'd you do physics

[pale orchid]

usually for physical modeling of stuff

[surreal sapphire]

mathematicians have pretty good job prospects

[deep mango]

I think math people have a tendency to project a bleaker image of math academia than actually exists

It's still kinda bad but so is anything

[devout nacelle]

What are other reasonable alternatives to CS for employability as a mathematician?

[surreal sapphire]

finance

[pale orchid]

let be clear that i'm projecting a bleak image of engineering academia

[devout nacelle]

Finance stuff looks cool

Ye

[surreal sapphire]

but it probably boils down to similar stuff

you have to learn wtv your boss tells you for a project

and you have to know how to write code either way

[deep mango]

Electrical/computer engineering have a different flavor from normal CS stuff

Working on the architecture/hardware side of things has a lot of interesting math in it

[devout nacelle]

I think there's more frustration piling up after years of investment

[crystal stone]

how tragic

[devout nacelle]

Employment seems like a pain

Why can't I get lifelong patronage from some rich lad on a throne

[leaden skiff]

i mean, this definitely feels bleaker than anything ive heard any SE say lol

[deep mango]

I feel like investing super heavily in anything is going to have a similar outcome

[surreal sapphire]

the german mathematical society has this interview section "studied math ... what now?" in their monthly notices

i probably read a few dozen by now

[deep mango]

That's bleak in a different way

[devout nacelle]

"death, devastation, despair"

[surreal sapphire]

and the connecting thing is that almost nobody needs the math from uni

[crystal stone]

You can run a math education company, like Khan Academy, Proof School in San Francisco, Russian School of Math

[surreal sapphire]

but the jobs are mostly "here is a problem, learn about it and solve it"

[leaden skiff]

well ok, game devs have definitely said worse. but other than that

[surreal sapphire]

and thats what mathematicians are good it

[devout nacelle]

This sounds more promising

[surreal sapphire]

especially if they went through a phd

[crystal stone]

That's kind of the world that I'm in right now

It has its issues

[devout nacelle]

It can't be all smooth sailing certainly

But it's a start

[crystal stone]

There's also consultant work at companies like Pearson

[crystal stone]

So if you think mymathlab is shit

Go work for them and give them feedback on how to make it better

[devout nacelle]

Hmmmm

[crystal stone]

Math IXL is another big one

[leaden skiff]

i feel like that might be easier said than done...

[devout nacelle]

Aren't these stagnated/not really used platforms?

[crystal stone]

It's better than sitting on your ass and complaining

[deep mango]

Lol

[crystal stone]

MyMathLab is the most popular online software module for math education

[devout nacelle]

OwO

[crystal stone]

In k-12, and in the higher education

[leaden skiff]

what abt kahoot

[crystal stone]

They even have similar things for calc 3

WebAssign

etc.

[deep mango]

Work for Pearson and then demolish from the inside

[crystal stone]

There you go

You know what's hilarious? MyMathLab actually raises grades & pass-rates

When used properly

[deep mango]

Clown world

[crystal stone]

It's one of the single most effective ways of getting students through remediation

[leaden skiff]

is it cause they're cheating

[crystal stone]

No

It's because insta-feedback on you got this wrong

You can't move on till you get it right

[leaden skiff]

oh that's actually sick

[crystal stone]

etc.

[leaden skiff]

holy shit that's actually even sicker

[deep mango]

[leaden skiff]

that's actually the way of the future

[crystal stone]

Yeah, and also professors/instructors can let you redo assignments

Without them devoting more time to you

So they can focus on other things

[stray kite]

what else are you supposed to do exactly lol

[crystal stone]

Although, I fucking hate Pearson and MyMathLab

I can't argue against its efficacy

[leaden skiff]

it seems like good idea awful execution

[deep mango]

At least some kind of plan B

[leaden skiff]

altho i haven't use MML so i can't say how the execution is

[crystal stone]

The executing isn't awful, it's ok

There's a lot of room for improvement

Looking at you graphing tool that only accepts integer points

[surreal sapphire]

i dont worry about employment at all tbh

[crystal stone]

yeah y = 0.37x - 0.58

[stray kite]

i on the other hand
live in a third world country

[crystal stone]

But you need integer points to graph!

[leaden skiff]

me neither except for the occasional panic attack

[surreal sapphire]

mood

[leaden skiff]

when are the devs gonna drop the 4th world anyway

[surreal sapphire]

i will talk to the unemployment agency here soon

"hello, i graduate soon, pls help find job"

[crystal stone]

You're unemployed loch?

[surreal sapphire]

probably not

[crystal stone]

Are you finishing PhD?

MS?

Life?

[surreal sapphire]

masters

[crystal stone]

My condolences

[surreal sapphire]

but i will very, very likely smooth transition into phd

but i want to see where i stand on the job market

[crystal stone]

I graduated with my MS a year ago, and found a full time job

but now I'm quitting

To go do research

[leaden skiff]

what's ur plan for a job?

[surreal sapphire]

i know how to program a bit and not much else

[crystal stone]

You can work in math ed

Are there private education companies in germany?

Or can you teach the little ones?

[surreal sapphire]

probably but i dont think i want to do that

[crystal stone]

Understandable

[surreal sapphire]

i will use contacts to siemens to scout

siemens likes mathematicians

[devout nacelle]

Siemens does heavy electricals and stuff like that?

[surreal sapphire]

they do everything

[crystal stone]

9-5 jobs are soul sucking

[surreal sapphire]

my contact is building railways

[crystal stone]

I see why some people like working 9-5

[devout nacelle]

Christ they really do everything

[surreal sapphire]

well, overseeing multi million dollar projects all over the world

but the end goal is railways stuff

they built the bullet trains in japan etc

or were heavily involved at least

[devout nacelle]

Has a Toshiba/Hitachi/Mitsubishi like vibe to it

[surreal sapphire]

i think big companies are good for mathematicians since you can move a lot within the company

and you might be able to add value to multiple teams

[crystal stone]

I don't think I'll ever do SWE

It looks awful

but the paychecks are nice

[devout nacelle]

Oh btw, is anyone here familiar with the "Chartered Mathematician" designation?

[leaden skiff]

how so?

[crystal stone]

I don't like programming

[leaden skiff]

really? why not

[surreal sapphire]

,calc .9/1.8

[fathom swallow]

Result:

0.5

[neat lintel]

Oops

Yeha bsjwjwjjw

0.5

[fair mural]

what does your question even mean

[surreal sapphire]

(i dont even see the connection either way)

[leaden skiff]

because 0.9 is half of 1.8

also yeah what even is the connection between your 2 statements?

[neat lintel]

Nevermind

[crystal stone]

It's frustrating and I prefer doing math on pen & paper

or a board

[leaden skiff]

huh i find regular math way more frustrating than coding

[crystal stone]

I'm also relatively uninterested in the applications of coding that aren't math

Creating a website, doing data-base stuff, or even security or debugging

Isn't fun to me

[neat lintel]

then you might like cryptography stuff

since a lot of that is math

and it's also coding

[crystal stone]

Nope, not that interested in it

The only thing that I might find interesting is Computational Fluid Dynamics

Cuz fluid flow is cool

As of right now at least

[neat lintel]

or computational physics in general?

[crystal stone]

I even gave quantum computing a try

And it was still meh

[neat lintel]

haha navier stokes go brrrr

it is cool

[crystal stone]

Maybe my point of view will change

but I don't wanna be a software engineer

[neat lintel]

what about computational magnetohydrodynamics?

[crystal stone]

sounds like stoke's

[neat lintel]

maybe you'd be interested in that

[crystal stone]

🤷‍♂️

Doesn't keep me up at night

[neat lintel]

but cfd does?

oh wait

you should check out this paper in cfd

it's awesome

https://www.researchgate.net/publication/322530755_Analysis_and_Qualitative_Effects_of_Large_Breasts_on_Aerodynamic_Performance_and_Wake_of_a_Miss_Kobayashi's_Dragon_Maid_Character

"Analysis and Qualitative Effects of Large Breasts on Aerodynamic Performance and Wake of a “Miss Kobayashi’s Dragon Maid” Character"

[crystal stone]

No thanks

[cold needle]

#chill

[real sigil]

whats a nice fact/exception/paradox/secret/rule about linear functions that not many people know

[compact tartan]

are we talking linear algebra linear functions, or middle school linear functions

[leaden torrent]

all linear functions are nonzero except the zero function

[sick burrow]

Holy shit 🗿 from Pink Floyd????

[delicate steeple]

all functions are linear except the zero function

[last oxide]

all zero functions are linear except the nonzero function

[wild jay]

False a circle isn't lineair

[delicate steeple]

exactly, zero is a circle: 0

not linear

[wild jay]

oh sorry

you're right

but

0 looks more elliptic

than circlish

[neat lintel]

cryptography is awesome

shame people automatically think of cryptocoin when the word crypto comes up though

[sick burrow]

Yeah

Blockchain and its consequences have been a disaster for the human race

[neat lintel]

Blockchain society and it's future by Ted Kanga

Anyone interesting in developing good habits or something like that together? DM me i guess.

[vagrant kestrel]

Fractals.

[wild jay]

weierstrass function

upside down

[vagrant kestrel]

it's for this

[fair mural]

hmm floor function

[wild jay]

floor weierstrass

[sick burrow]

Ok I'll actually stop now

[spring wyvern]

the best fractal i've ever generated yet

[ancient flame]

is that an ostrich

[neat lintel]

it's a dog

[neat lintel]

How do you guys have motivated to do math tbh

[placid quartz]

math is cute

[toxic schooner]

[placid quartz]

[ancient flame]

oh right, another thing my calc teacher did that was stupid was when she was trying to show that you can switch the bounds of the integral and make it negative... she proved it by showing an example, because we all know that proof by example is a valid form of a proof

[toxic schooner]

ofc

thats how proofs should be in an ideal world

non of this axiomatic bs

just show that it can be true

[fair mural]

is that really stupid though

[toxic schooner]

and it is

[ancient flame]

lol

like it's fine to show an example

but to then say "so we proved this" is dumb

because that's not proving that it works in all cases

[crystal stone]

I don't think it's that dumb of a thing to say

It's how most people think

[placid quartz]

if the same technique works in proving, then it's okie ig

[crystal stone]

Because it's the same trick when you prove it

[ancient flame]

yeah

ig I'm just being nitpicky lol

[crystal stone]

maybe I'm too sympathetic

[ancient flame]

lmao

[spring wyvern]

wow

(also, that is literally how every proof works at my place - luckily i get my info from the internet)

[ancient flame]

lmfao

proof by example

[placid quartz]

disproof by counterexample
proof by example

[spring wyvern]

welp

also, technically, in physics, every theory were proved by examples?
(tons of examples, yes, but that's still proof by example)

[toxic schooner]

I mean, they do have mathematical reasons for the theories
but they also have to be true in real life, not just on paper

so its a mix of both ig

[spring wyvern]

i know
but real life situations are examples

[spring wyvern]

the proof for this is literally so simple

[toxic schooner]

then yeah they do use those to show a theory is correct

[vivid halo]

Proof by example can be fine in some cases

[toxic schooner]

[ancient flame]

bonk

[spring wyvern]

no, it's a snail

[ancient flame]

ohhhhhh

alright

I see it now actually

[vivid halo]

Some books do this like “we illustrate the proof in this particular case, the general proof is exactly the same except notationally difficult”

[ancient flame]

oh

alright

ty

[neat lintel]

that's called engineering

[vivid halo]

Nah

[light needle]

Proof by example is fine when the statement is “there exists” so true

[primal crater]

@light needle The answer of that question was true indeed

[vivid halo]

theorem: every differential operator with constant coefficients has a Green’s function
Proof: bullshit involving holonomic D modules

[primal crater]

$\textcolor{green}{Function}$

[jovial ember]

I am just totally fine with “for any blah blah” and it’s like “okay for simplicity assume it’s x1”

Like usually there’s some automorpjism taking anything to x1

But even if not like

It’s literally just the same shit, just way more annoying to write down

[vivid halo]

Yea

[jovial ember]

Convince yourself it works for anything

Also it’s funny you like

Told me about perfectoid stuff yesterday or whatever

Cuz Yon told me about this direct summand conjecture which was proven a few years ago using them

[vivid halo]

[neat lintel]

lmao

[compact tartan]

you can prove things by example

if it's an existential statement

[leaden skiff]

are there any famous existential conjectures?

[compact tartan]

yeah

the negation of the riemann hypothesis

[leaden skiff]

[compact tartan]

navier-stokes blow up

[leaden skiff]

but usually most of those conjectures are phrased in terms of all right?

also what was the navier stokes blow up again?

[compact tartan]

there exists a smooth initial/boundary condition for navier-stokes that does not extend infinitely into the future

given recent advancements in that area I'd think we have compelling reasons to believe it does blow up

i.e. the conjecture is "there exists BVP that blows up" rather than "forall BVP it doesn't blow up"

[leaden skiff]

wait really? what would that mean physically tho?

[compact tartan]

depends on the nature of the blow up

most likely it would mean that in certain conditions the particle reality of liquids can be amplified which would mean navier-stokes are not an appropriate model of real liquids

[torpid plover]

Navier-Stokes leading to discontinuity is well known in physics. It was studied very extensively for 1-dimentional turbulence

Burgers Equation if I remember correctly

and it's derivative models

A.Polyakov works in Math.Ph.

[leaden torrent]

P = NP and P ≠ NP are both frequently phrased with existentials

P = NP is "there exists an NP complete problem in P", P ≠ NP is "there exists an NP problem not in P"

this isnt a matter of a "cheaty" negation like the RH example, its the typical way both of these forms are thought of

but really, forall and exists are dual, and the forall phrasing usually makes more sense

as it typically suggests some deep, as-yet-not-understood connection between a set of assumptions and a given property

ie that connection is the "conjectural" bit

whereas the other side of the duality, the existential, is just saying that there is no connection

which, uh... cool

doesnt really "feel" like a conjecturable theorem really

if we found one and put it in a textbook, you wouldnt label it "theorem 7.1", youd label it "example 1"

[leaden skiff]

i just meant conjectures where the expected theorem is an existential one rather than a forall one

[leaden torrent]

yes

the point is that mathematical theorems are almost always universals

[compact tartan]

hmmm

[leaden torrent]

existential theorems are rare

[torpid plover]

just be careful, in existence of solutions works for 2D in 1960s they consider ideal NS liquid: non-compressible and with zero viscosity, then they worked out viscosity things; it is not even close to real liquids

[compact tartan]

I guess inhabitedness of a fibration is less exciting than existence of a section

[leaden torrent]

this isnt a matter of conjectures often being foralls, its a matter of theorems often being

[torpid plover]

all real liquids are compressible and their viscosity is never linear

[leaden torrent]

obviously thats an arbitrary metalinguistic choice rather than a mathematical one

[torpid plover]

if liquid is incompressible, it would have infinite speed of sound

[leaden torrent]

though i do think it makes more sense than the opposite convention

(but perhaps im biased towards the status quo)

[compact tartan]

all real liquids are not continuous either

approximations exist for a reason

incompressible liquids are fine in quasistationary processes

[torpid plover]

also people call "liquid" even things with non-zero shear stress, like Lennard-Jones Liquid 🙂

"Liquid Crystal" is even more troll from physical viewpoint 🙂

I was reading NS stuff, generally its a presentation of solution in form of convergent series, properly proving that it (1) converge, (2) it's components are good

[compact tartan]

the liquidity of bitcoin gives me sheer stress

[leaden torrent]

what liquidity

[real sigil]

eh? both i guess

[real sigil]

what do you mean nonzero?

oh

yeah thats about right

lol

[stray kite]

what are "connected spaces" wrt vector spaces?

[distant vortex]

Are you sure it's not a topological vector space?

e.g. do you have a norm which defines a topology?

[sick burrow]

Are any normed vector spaces not connected?

[neat lintel]

one would really hope straight line paths are continuous

[cold needle]

lmao

[jovial ember]

Mandrip?

Or Pimpanzee

[gilded hedge]

Why are no physicists or mathematicians interested in formalizing biology !?
Don't you guys realize those people are struggling?
They have no formal language to describe, say, how a cancer might form or how a disease will spread, so they lack a great deal of predictive power.

[leaden torrent]

[gilded hedge]

You guys can describe how a radio transmits signals or how a plane flies with extreme precision. You all can predict if the rocket will reach the ISS exactly or be off by a few millimeters, and you can tell me when all the planets will be aligned again a few thousand years from now.

Where are all the cross disciplinary biophysicists at, or biomathematicians (is that a thing?)

[leaden torrent]

biomathematics is a thing

its a very large field, in fact

our failures to "solve" biology are not due to lack of trying.

[gilded hedge]

okay so at the very least people are trying to formalize it

[leaden torrent]

great progress has been made on, e.g., protein folding

[gilded hedge]

I'm certainly not suggesting biologists are lazy or incompetent, but I read this article recently and it really illuminated the difference between how biologists approach problems vs how engineers do - https://www.cell.com/cancer-cell/fulltext/S1535-6108(02)00133-2#relatedArticles

I mean just look how a biologist would attempt to repair a radio vs how an engineer would

[leaden torrent]

the thing is that we do know how cancers form, its when random mutations cause cell growth to exceed safe constraints (whether by vastly increasing reproductive rate, decreasing death rate, or both)

the problem is that theres a lot of ways for this to happen

since its just a random DNA screwup, which happens literally thousands of times in every cell

if you asked physicists to predict physical outcomes in a system of millions of nonnegligible gravitational bodies, they wouldnt be able to do it either

theres just too much data

(this is the n-body problem)

and its a lot easier to "see" data about planetary systems than cells, for obvious reasons

dna is small and expensive to sequence

and time consuming

thats why a biologist's approach is necessarily based on casewise experimentation, eg "does exposure to this increase cancer rates in a population?"

obviously, thats not gonna be perfect

[surreal sapphire]

always in awe how much work you put into this

[leaden torrent]

but its the best we can feasibly do

[surreal sapphire]

at some point i will trick you into explaining me stuff i need to know

[gilded hedge]

But the number of data points shouldn't be a limitation. Microchips these days contain half a billion transistors, and yet it's performance can be reasonable predicted. The formal language in circuit schematics make even the most complex electrical system understandable in a highly precise way.

[leaden torrent]

those systems are designed to be human comprehensible

[gilded hedge]

I don't see why cellular systems are any different though

[leaden torrent]

i mean, if you think you can viably revolutionize biology like this

go and do it.

[gilded hedge]

They abide by rules and laws of physics

[frosty zinc]

There is yet another reason why half - billion transistor systems are easy.

It's because of our absurdly powerful tool to linearize

[gilded hedge]

Oh no, I'm certainly not smart enough to do it, but it's just a thought I had after reading that article

[frosty zinc]

And most digital systems only care about steady state values

[leaden torrent]

also yeah lmao that shit works based on threads and linear processes

[gilded hedge]

And I've been asking the physicists, mathematicians, and the biologists what they they thought of this issue

[frosty zinc]

All dynamics is abstracted with a few delays that is assumed to be constant

[leaden torrent]

like there are minor considerations like random electron movement, solar radiation, thermals, and random mechanical imperfections

but for the most part, shit in a circuit happens in order

you only need to look at where the current is travelling

[frosty zinc]

(Systems) Biology is a hard problem that is subject to discussions related to application of complex systems

[leaden torrent]

you dont have to consider literally every transistor at once

but you do in biology because of how crammed and cobbled-together the interior of a cell is

there are like 5 layers of "mutation checks" and they still manage to miss shit

(which isnt exactly a bad thing, its what makes evolution possible)

which is why the comparison to the n-body problem is more apt

hell, we know more about the physics behind the n-body problem (relativity) than we do about the mechanics of cell reproduction and the mechanics of electron movement (in a circuit or otherwise)

doesnt make it any easier

[tiny marten]

"what if we do biology but actually it's just math now"

you could email a professor this question

in some sense that is exactly what stuff like neural networks mathematics is

you can't formalize one big mathematical theory of biology any time soon, it's hard to do that with physics at times

also lots of biological processes have to be modeled by totally different systems

or the processes may be modeled by a lot of different systems

it's hard to imagine what that would even look like, a formalized theory of human biology

[serene parrot]

that field needs to become more popular

[sick burrow]

We can talk about the Putnam in 25 minutes right

[wooden flax]

putnam

[sick burrow]

11 minutes

[wooden flax]

gl

[sick burrow]

Well I took the exam

But I can rant about it in 10 minutes

[mild pebble]

holy shit that exam was brutal. really went into that thinking i'd solve 2 or 3. ended up getting one of them and flailing around for the rest of the test

[sick burrow]

Got 2 on A side, got none on B side

[mild pebble]

i was kicking myself for not getting A2. and geometric probability is just kinda gross

[sick burrow]

I got A1 and A6

[mild pebble]

and for B2 i spent 2 hrs thinking the max was 1/2 and trying to prove it

[sick burrow]

Started A2 and then remembered I'm shit at analysis

[jovial ember]

I was gonna do Putnam 2 years ago

[sick burrow]

The max is morally 1/2

[jovial ember]

I slept through it :)

When I looked at the test later I’m glad I slept instead of going

[sick burrow]

It's greater than 1/2, but it's 1/2 morally

[mild pebble]

yeah bcuz intuitively you maximize it by lumping the big stuff together. unfortunately my intuition for bigness is shite

and there's like this deceptive AM-GM bound that makes everything look so nice but ends up giving you nothing useful and the lesson is that one shouldnt hope for anything good in this life

[sick burrow]

My best guess is the max was given by like 3/4, 3/16, 3/64...

But it's probably a series with first term 1-1/e or something stupid like that

I was so hopeful going into B side

Since I got 2 on A and I was like "if I can keep this up I'll get 4"

[jovial ember]

Is it 3 hours each side?

[sick burrow]

Yes

[jovial ember]

Oof

[sick burrow]

3 hours of potatoing

[mild pebble]

so seems like a bunch of ppl at my school had something for A6 but their claims all seem to be really shaky. like saying the factors of the polynomial all have coeffs 0 or 1 etc

[mild pebble]

same, i thought i woulda gotten B1 and had some chance on B2

[sick burrow]

I said look at the smallest degree nonconstant term

For each the two factors f(x) and g(x)

Say a_k and b_j

Then a_k b_j x^(k+j) is a term in P

So a_k and b_ j must both be 1 or -1

Then you see that both terms have to have degree 1 since f(2) and g(-2) both need to be 1 or -1 for their product to be prime

Which you brute force to get 2 possibilities for f and g and then you check that none of them give a binary polynomial as their product

So you conclude that the product is composite

A1 was actually just trivial though

Solved it in like 15 minutes but took a while to come up with proof

It works out really nicely though since 288*7+5=2021

[mild pebble]

yeah number 1 on first glance looked hard but then after finding the intuitively shortest path, the greedy thing just works

did you also end up wih 578?

[sick burrow]

And you get trivially that it's a lower bound since ceiling(4021/7)=578

That problem felt more fitting for an intro combinatorics class extra credit problem

[mild pebble]

i'm really angry bcuz i should have gotten A2. apparently you compose with log and e and do lhopital and ur good

[sick burrow]

mnip I see you're lurking how did you on the Putnam

[sick burrow]

Lmao actually

[compact tartan]

didn't

[sick burrow]

mnip why

[mild pebble]

i was trying to do some dumb taylor series thing but i had forgotten everything nontrivial about analysis so yah

[sick burrow]

Wait how do you do A2 with log

log((x+1)^(r+1) - x^(r+1))^(1/r)

Pull out the 1/r

Wait and then can you actually L'hopital

No fucking way that works for a Putnam problem

What

The fuck

[mild pebble]

yeah i was completely not expecting the solution to be that easy so i just didnt try

angery

[sick burrow]

How did that slip through QA

If a problem could fit on a challenging calc 1 final

It probably doesn't belong in the Putnam

Angery

Fucking what

[mild pebble]

In retrospect i'm glad it doesn't seem like B2 was similar in that it's hard on the test then has an obvious solution that you think of in the shower later that might. or maybe it is like that

I hope someone better than me miswrites their pin and i get credit for their solution

i'm kidding but damn that was a brutal exam

[sick burrow]

Wait no are you sure l'hoptial's works?

[mild pebble]

my bones ache

[sick burrow]

I'm not sure how l'hopital's gives you that

[mild pebble]

i haven't actually gone through the details but according to my friend it works. lemme see

[sick burrow]

Wait this is giving me contradictory answers

Or wait hold on

[mild pebble]

make sure ur differentiating the numerator wrt r, not with x

[sick burrow]

Wait nope it works

It's just nasty

Fucking excuse me then

How

Is "take the log then l'hopital's rule" the solution to a Putnam problem

That's like

The naive calc 1 student's default approach

Did the exam get easier or something

What

[wooden flax]

Lmao

when you overcomplicate

[odd sail]

How did you prove it

[sick burrow]

Note that each move changes taxicab metric by at most 7

Note that ceiling(4042/7)=578

Demonstrate an explicit solution in 578 moves

Which also happens to be the obvious greedy thing

[wild jay]

so was Putnam fun :)

[odd sail]

What does this mean

[icy flower]

what obvious greedy tihing?

[sick burrow]

Run along diagonal

Hop by 5 along x then y to finish

[mild pebble]

basically consider |2021-x|+|2021-y| which is at least |4042-(x+y)|

and see how quickly you can get to 0

[sick burrow]

Ok I'm actually tilt

[odd sail]

Thanks, I get it now

What did y'all plug into the integral for B1?

[sick burrow]

$$\int_{\text{if}}^{\text{fuck}} \text{I know}$$

[mild pebble]

blegh i had a headache trying to even set this problem up and just went to B2

[fathom swallow]

Kanga Gang Mole (sleepy agent)

[ancient flame]

if to fuck I know dx

[sick burrow]

B1 was pain

[icy flower]

can someone expalin how to use L'hopitals for A2? i stared at that thing for too long this morning

[ancient flame]

imagine taking the putnam

[icy flower]

also for B2 how is AM-GM used?

[sick burrow]

Just take the log

Pull out the 1/r

Wait a minute

Do you get an indeterminate

[ancient flame]

was anyone able to complete every question

[wild jay]

I was

[sick burrow]

Ok yes

[odd sail]

But did you solve the secret B7

[wild jay]

when will the questions get online?

[icy flower]

wait i get log of limit is 1

that cant be right

[mild pebble]

you want e^log of the limit

oops i meant to respond to a different comment

[icy flower]

$$\lim_{r \rightarrow 0} (1/r \ln \frac{(x+1)^{r+1} - x^{r+1}}{1/r} )$$

[fathom swallow]

Optimism

[icy flower]

oops theres atypo

hmmmm ok

[sick burrow]

I'm actually on 16 levels of tilt right now

And 1729 levels of cope

Because like my first thought upon seeing that problem was like "this looks like you might be able to use l'hopital's rule"

And then was like "hmm I don't see it right away and there's no way a Putnam problem would be that easy"

AND THEN IT FUCKING WAS????

[mild pebble]

same. and part B was just straight garbagio like holy fuck

[sick burrow]

How many questions did your friend get algebraic

[mild pebble]

which made me even sadder that i didnt get A2

my friend got 3 probs

A1, A2, and B1

apparently very shaky on B1

[sick burrow]

B1 moment

Damn I should have gotten A2

[mild pebble]

i was screaming down the halls "I shoulda gotten A2!" for the whole time during the break

[sick burrow]

Wait hold fucking on

Does l'hopital's even work

I don't think it does

Wait no it does

[vague lion]

it looks a bit like a derivative??

[wild jay]

1 second later 'nvm it doesn't'

[fair mural]

@vague lion the more you look at it the less it does

[vague lion]

yeah

[icy flower]

does anyuone have a written out solutions they did lol? i keep thinking l'hopitals doesnt work or at least doenst give me the right anser

[mild pebble]

lemme go and scibble something down rly fast

[sick burrow]

Or wait does l'hopital's rule even work

Or is the point that some subtle condition fails

Wait ohh right because is the function defined on an open interval containing 0

Oh yeah it is

I actually

I don't even

[icy flower]

Ye idk how to do it lmao

[sick burrow]

Call me
$\begin{bmatrix} 0 & 1 \ -1 & 0 \end{bmatrix}$ because I'm tilted as fuck

[fathom swallow]

Kanga Gang Mole (sleepy agent)

[sick burrow]

This is it

I've finally snapped

[mortal igloo]

Hi -i

[fair mural]

icy of course you immediately knew that

[mild pebble]

so i didnt write any words here but yeah hopefully this is readable

[sick burrow]

Sorta came out to myself as a lesbian yesterday, have a final paper due tomorrow, and missed the world's easiest Putnam problem today

I may have missed the limit problem but I am now past my limit

[mild pebble]

dammit there goes top 500 😦

[sick burrow]

https://tenor.com/view/going-insane-cat-gif-22428080

[wild jay]

Ye, then u get like 80% for total

[mild pebble]

actually i was at the point in the academic term where i had zero fucks left to give but after this i have negative fucks left to give. and i still have 2 finals

damn how am i gonna sell out to finance with this putnam performance

i was sooooo certain coming into it that i'd get at least 2 ahhhhhhhhh

[sick burrow]

Why?

[mild pebble]

because that's generally how i did with the practice tests

[sick burrow]

Bruhh

[mild pebble]

but all the practice tests were from like 2005 or earlier so ahhhhhh

[sick burrow]

I feel like the exam was lower quality this year

Like A1 and A2 were basically freebies

(I say despite having missed A2)

[mortal igloo]

I haven't looked at the problems yet 👀

[sick burrow]

But then B1 was a fucking nightmare

[light needle]

I got B1 wrong

[sick burrow]

A2 was literally just

[light needle]

we ran a monte carlo simulation after class

test

i was wrong bleak

I got A1 A2 and B4

[sick burrow]

What did you get?

[light needle]

A3 was impossibly hard

[mild pebble]

part B in general was just completely insane in my opinion

[sick burrow]

For the monte carlo

[light needle]

spend like an hour on it

[mortal igloo]

Is there a place I can see problems?

[light needle]

and then missed other problems bc of it

[sick burrow]

Not yet but I think I can tell you

[light needle]

i could have done A5 if i had time

rip

[mild pebble]

anyone get B2?

[light needle]

i didnt

that was really hard

i only got an upper bound of 1

idk how else to even think about approaching tbh

also about 9% for simulation

gammy

[mild pebble]

really seriously thought the max was 1/2 but someone after the exam had a counterexample lel

[sick burrow]

A2 was evaluate
$lim_{r\to0} ((x+1)^{r+1} + x^{r+1})^{1/r}$

[fathom swallow]

Kanga Gang Mole (sleepy agent)

[light needle]

I am proud of getting B4 tho

that one took a long time but

and was the only thing i solved on B oof

[mild pebble]

no a2 was to evaluate the limit as x goes to infinity of that above limit over x

[light needle]

that one was just e right

[sick burrow]

Ok actually A2 was call that g(x) and evaluate $lim_{x\to \infty} g(x)/x$

[fathom swallow]

Kanga Gang Mole (sleepy agent)

[sick burrow]

But that follows instantly once you get the first part

Icy look

[mild pebble]

the thing with 1 is that it's a strict upper bound so can't be a max

[sick burrow]

Look upon that

And wonder

[light needle]

yeah it cant

[sick burrow]

"How the FUCK did that get onto the Putnam"

[light needle]

but idk what else to do for that

[sick burrow]

I'm proud I got A6

[light needle]

the poly one? nice

[sick burrow]

Since that one was nontrivial

So I basically got a 30

I got a 30 morally

[mortal igloo]

Morally...

[light needle]

I think i got lower than what i did last time

[sick burrow]

Just like the answer to B2 was 1/2 morally

[light needle]

which was a 31 in 2019

[mortal igloo]

I have never solved a #6

[light needle]

which to be fair i didnt prepare this time at all

[sick burrow]

A6 wasn't even that hard

Ok but Icy look at that A2

Please

Validate my anger

[light needle]

I literally wasted all my time on A3 didnt get to solve anything else on A

A3 was so hard no one in my school solved it

[mortal igloo]

Is the problem copied wrong?

[light needle]

bleak

[sick burrow]

no?

[light needle]

yeah A2 was fairly easy

[sick burrow]

I simplified it a bit

but like not actually

[mortal igloo]

When I take log of what's inside the first limit, the denominator goes to 0 but the numerator goes to log(2x+1)

[sick burrow]

oh right that +

was a -

I dumb

[mortal igloo]

lol

[light needle]

yeah u copied it wrong

its -

[sick burrow]

[light needle]

oh u fixed

smh

[sick burrow]

A1 was easy too

it was like

[mild pebble]

A1 seemed like it would be super hard but then the easy thing worked

[sick burrow]

a grasshopper is trying to make it from (0,0) to (2021,2021) in the minimum possible moves

each move it jumps 5 units in any direction but lands on a point with integer coordinates

[light needle]

A3 was finding Ns for which there are lattice points on x^2+y^2+z^2= N which are also vertices of a regular tetrahedron

Best i could do was narrow down to 3|N

[sick burrow]

so either 5 along an axis or along a 3-4-5 triangle

A6 was fun though

it was "let P(x) be a polynomial where each coefficient is either 0 and 1 and P(x) = f(x)g(x) with f,g nonconstant polynomials with integer coefficients. Is P(2) always composite?"

[mild pebble]

my anxiety was through the roof today

[sick burrow]

my solution honestly wasn't that complex for a 6

I don't understand though

do problems as easy as A2 usually make it onto the exam?

[mortal igloo]

What was your mistake on A2?

[sick burrow]

not recognizing I could just use l'hoptials

[light needle]

tbh B1 was really heard for a 1

maybe compensating for A1/A2 was so easy

[mortal igloo]

Not sure if A2 is objectively easy, taking typical college math students in mind

Well obviously it's easy compared to Putnam standards

Okay

[sick burrow]

my intuition said it felt like a l'hopital problem but I ignored it since that felt way too easy for Putnam

[sick burrow]

is it?

like sure if your frame of reference is your intro calc students

but consider the average person who takes the Putnam

if you handed each Putnam participant this year A2 yesterday

[mortal igloo]

I heard from the honors linear algebra professor that (a) the class can be said to consist of the top math students in this school and (b) most of the class has never written a proof before

Well, top math freshmen

[sick burrow]

and was like "this was a particularly hard problem on a calc 1 exam. Can you solve it?"

[mortal igloo]

Maybe 50% of the Putnam takers would get it

Which makes it on the easy side for sure

0% of a calc 1 class though

[brave hollow]

What problem was this one?

[sick burrow]

A1

[sick burrow]

really?

not 0%

it's literally just l'hopital's rule

[mortal igloo]

Yeah and there was a problem on my first exam that was literally u-substitution and symmetry and 0% of the class of 87 students solved it

[brave hollow]

so like are all problems worth equal points?

[sick burrow]

just a particularly difficult derivative and a bunch of notation that requires you know how to read math to be able to parse the problem

[mortal igloo]

Yes

requires you know how to read math to be able to parse the problem
Only 40% of the class has this skill

🤣

[sick burrow]

sure sure

[mortal igloo]

It was like 10% at the start of the term

[sick burrow]

my point is

take an out of touch math professor who hasn't taught intro classes in 5 years

take who they imagine a very good calc 1 student to be

that person has a 90% chance of solving this problem

[mortal igloo]

Hmm...

That's a funny way to say it

[sick burrow]

I could have gotten this problem back in highschool

it's waaaay to easy for a Putnam problem

[mortal igloo]

What was the easiest reasonable problem on there?

[sick burrow]

I remember a funny one from a practice test I did

actually let me remember it

it was like a basketball player is shooting free throws

[mortal igloo]

Actually I just had a nice thought

If you keep the copying error and have the + there

It could be a reasonable calc 1 problem

to show the limit diverges

inb4 protests of "now it's way too easy"

[sick burrow]

wait let me solve it

*find it

here

I feel like this is a reasonable example of the easiest a Putnam problem should be

or maybe a bit over that line

like you could reasonably get a bit easier but not much

[deep mango]

is the putnam out

finally

i want to look at the prblems

[sick burrow]

half your class: "acktually it converges because as x goes to 0, the limit does also"

[mortal igloo]

That's way too coherent for half my class

[deep mango]

WHERE IS THE NEW PUTNAM PROBLEMS

[mortal igloo]

It should be more like "for $x=\bR$ the limit is equal to the value of the function which converges because x is greater than or equal to 0"

[fathom swallow]

Icy001

[deep mango]

x = R

[mortal igloo]

I kid you not, they write things like this

[deep mango]

i'm a fan of it

[primal crater]

mathematical physicists write forces as X, Y, Z

[sick burrow]

Ryu

ryc's lost brother???

[mortal igloo]

Sullier has competition

[primal crater]

[deep mango]

hi ryu

[primal crater]

hello Ryc

[deep mango]

i had wine tonight 😋

[sick burrow]

I don't think they're online yet

but we can tell you

eryc do you want to hear the mean problem

[deep mango]

thank you

yes

[sick burrow]

it was awful

[deep mango]

i want ot hear a problem

[sick burrow]

and terrible

and bad

[deep mango]

it was probably the most fun one

[sick burrow]

and I spent 3 hours on it and got nowhere

[mortal igloo]

One student writes this on the latest homework:
[f(x,y):x{\bR,\text{ except }x=0, y{\bR}]
This is verbatim

[sick burrow]

and it was B1

[fathom swallow]

Icy001

[deep mango]

i heard the first one was a frog hopping problem

that's so funny

those are the problems i always meme on

[sick burrow]

ok so eyrc

it was like

tile the plane with unit squares

drop another unit square on it at a random point with random rotation

what is the probability it misses all the corners

that was B1

A1 was "frog hopping problem except the greedy solution is trivially optimal so you don't actually have to think"

A2 was l'hopital's rule

B1 was that

[deep mango]

that's so fun gamma

omg

the B1

[light needle]

B4 was the best imo

[sick burrow]

B4 was Fibonacci right

[deep mango]

[sick burrow]

that one was weird

[deep mango]

stop spoiling them all!

i want to do them

[sick burrow]

bruh

[light needle]

show the remainder of prod_1^(F_m-1) k^k mod F_m is also fibanocci

[sick burrow]

that was in the problem statement

not the solution

[deep mango]

oh ok

[light needle]

dw john doesnt spoil