/sci/ - Science & Math

Will Scholze refute Joshi's abc conjecture proof?

>>16089127
Heh-heh. He’ll have to get through me first!

So the method to generate Pythagorean primitive triplets I can understand.

[math]a = m^2 - n^2,\ b = 2mn,\ c = m^2 + n^2[/math], where [math]m > n,\ \gcd(m,n) = 1[/math] and one of m or n is even. I can follow how this works by simple substitution.

I already know this does not generate every triplet, you can multiply primitive triplets by some scaling integer k to do that. However everywhere I read up on this it also states this method generates *every* primitive triple but I cannot find a proof. Anyone know how to show that?

Optimized my mandelbrot set generator, this took me 6 minutes to render, a few days ago this would've taken all day lol

>>16089185
https://en.wikipedia.org/wiki/Pythagorean_triple#Proof_of_Euclid's_formula

I had a dream that somebody proved that there are exactly [math]\aleph_1[/math] large sets. After a series of terrorist attacks on biggest universities Unified Abrahamic Theocracy took over the Earth and plunged it into a millennium of darkness.

>>16089185
>multiply primitive triplets by some scaling integer k
I don't think that's possible with some single integer (maybe I'm wrong its almost 2am here) but you can totally do that with matrices.
https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples

>>16089190
6 minutes?? That is incredibly slow.

What are some unsolved problems in calculus

>>16089204
kino

Do you guys know of any good probability and combinatorics textbook that makes heavy use of set theory?

Does studying/learning math basically come down to reading a lot of books and papers, doing the exercises in the books, and thinking a lot about what you read? If I am doing just that, am I on the right track? I feel like I could be missing something. And doing research is basically just writing your own papers after you have acquired enough knowledge?

>>16089612
I do not

Do any of you think, that the fact that [math]R^4[/math] is the only Euclidian space which doesn't have a unique smooth structure up to diffeomorphism and instead has uncountably many nondiffeomorphic ones, has any implications on fundamental physics?

>>16089460
That's actually an interesting question. I'm not immediately finding anything from google

>>16089460
Navier-stokes existence and smoothness

>>16089460
Calculus is not an area of mathematics, and as a concept it doesn't really exist outside of the US. As for real analysis, there are plenty of unsolved problems which are one google search away.

>>16089853
big if true

>>16089119
>i will never have enough schizophrenia to do cool pure math like op's
why live

>>16089641
I mean pretty much more or less. Doing research in pure math though isn't as straightforward as always just applying knowledge. Sometimes you spend hours staring at things until something comes to mind or you have to really be creative in your method of approach. I absolutely love math research but it's not for everyone and sometimes can lead to dead ends or failures. The key is to autistically be obsessed with finding an answer and being consumed by it in your waking hours.

>>16089119
Does this function have a polynomial expansion? How can I find it?

it's's the end of chapter 3 of godel escher bach.

can someone show me an example of how to produce primes with his system?

>>16089853
I only understood about three of those words and two of them were R and 4

I’m a midwit or worse with likely an 117IQ at most based off online tests I’ve done. I’ve always had a shallow interest in math with mostly superficial thoughts on the subject. I’ve always enjoyed doing math, though I’m not very proficient: i.e. I could never learn new concepts as well or in the same way as other kids in high school or solve questions as fast. However I realized last week in a mandatory geometry class for a tradeI’m entering that now I get high off solving math questions especially if I’ve calculated the answers only in my head. This high is a euphoric high similar to aderal, greatly improving my concentration.
I have no drive or control over myself to go back to community college at this point yet, even though my pipe dream has always been to be a research mathematician since my senior year. In order to do anything I want to do in life it always take mass amounts of effort to start towards it.
Besides killing myself of course, what would you do if you were me Anon? I’m hoping perhaps I can try to become addicted to math and achieve my dream.

>>16090538
It's not that complicated, just look up the definition of a smooth manifold and a diffeomorphism on between manifolds. Roughly speaking the case for Euclidian spaces of any dimension except 4 is that no matter how you define their coordinates locally, their calculus will always be equivalent to the one on the usual Euclidian coordinates, 4 is the only dimension where it's not the case.

>>16090561
Learn German -> Enroll at online Fernuni Hagen -> Transfer to Bonn, ideally 3rd semester of the bachelor program -> Master at Bonn -> Realize you can't even get a phd position under good profs, especially not Scholze -> Stuck in Germany for a few months with a useless degree before deportation -> kys

>>16089460
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Analysis
http://www.openproblemgarden.org/category/analysis
Don't mind inaccuracies; I am mere peasant as to verify integrity of my own opinions

>>16089127
i doubt he will try. better question is why mochizuki refuses to acknowledge joshis attempts to un-autism all his papers

>>16090701
The real autists are you guys who don't seem to understand Mochizuki doesn't need to engage people who keep insulting his work. Especially a Pajeet who tries to take credit of your innovations.

All topological spaces should be Hausdorff.

>>16090812
read a book

>>16090832
I should note I don't know much about algebraic geometry.
What's interesting, however, is that Grothendieck was not content with the state of topology at his time (which hasn't changed much).

To quote his `esquisse d'un programme':
"After some ten years, I would now say, with hindsight, that 'general
topology' was developed (during the thirties and forties) by analysts and in
order to meet the needs of analysis, not for topology per se, i.e. the study
of the topological properties of the various geometrical shapes. That the
foundations of topology are inadequate is manifest from the very beginning,
in the form of 'false problems' such as the 'invariance of domains' [...].
Even now, just as in the heroic times when one anxiously witnessed
for the first time curves cheerfully filling squares and cubes, when one tries
to do topological geometry in the technical context of topological spaces, one
is confronted at each step with spurious difficulties related to wild phenom-
ena. [...] This situation, like so often already in the history of our science,
simply reveals the almost insurmountable inertia of the mind, burdened by
a heavy weight of conditioning, which makes it difficult to take a real look
at a foundational question, thus at the context in which we live, breathe,
work – accepting it, rather, as immutable data. It is certainly this inertia
which explains why it took millenia before such childish ideas as that of
zero, of a group, of a topological shape found their place in mathematics.
It is this again which explains why the rigid framework of general topology
is patiently dragged along by generation after generation of topologists for
whom 'wildness' is a fatal necessity, rooted in the nature of things."

Sure, the issues were different, but the sentiment not so much.
Why shouldn't the geometers, then, use a subtly different setup for their theory, so that the rest of us can put all the needless generality to rest?

https://www.youtube.com/watch?v=KV2ssT8lzj8

>>16089119
Has anyone argued against counting or number sets? Curious to see what happens once you question them. Is that a topic for philosophy of mathematics?

Why is 7 significant compared to the first 6 integers?

>>16091444
It's the smallest prime that isn't 2, 3, or 5

>>16091448
It precedes a cube, too...

>go to my local hodge theater to see DUNE
Feels good

>This general still exists
Neat, is the touhou poster still around as well?

>>16091487
Derp. I'm retarded.

>>16091444
First long period prime in base 10. (well, technically 2 is firstest long period prime since 1/2=0.5(0) )

>>16089119

I got your Frobenius-like Kummer detachment right here, now make yourself useful. It's a Hodge theater so there's lots of people watching just fyi

>>16091444

It's a prime which is one less than a power of two. These primes can be used to construct perfect numbers by multiplying them by the next lesser power of two. In this case the result is 28, the number of teeth in my head following the loss of children's teeth and the surgical extraction of four so-called "wisdom" teeth.

>>16089460
does Zeta(3) have a closed form. If yes, what does it look like

I literally live like pic related. I'm poor, don't work (welfare and in subsidized housing), mostly crazy, live in the ghetto surrounded by addicts and criminals, and take 4th year math classes at a local university (pretty big name actually). All I do is math. Doing math and not worrying about anything else is pure kino. Sometimes I have the odd thought of "What if I got a regular job?", "What if I got a girlfriend?", but it all seems so pointless and meaningless.

Guy's I spent up to a year of trying to find some nonstandard (non analytical) proofs to infinitude of primes in good irreducible polynomials (or at least linear functions!) or even a topological proof but I just can't wrap my head around it...
Other that number theory I see no other way to handle primes

>>16091787

I also live in a shitty neighborhood in the middle of the city. Have the Go board spiral laid out on the kitchen table.

>>16091787
Sad but true, it's only the recognized genius level Einstein's that get the nice neighbourhoods and normal people, if you are just a bit slightly below great yet you get the bad treatment ughh

>>16091787
I wish my government would give me welfare for being a NEET as well, I wouldn't even mind living in a ghetto.

>>16091793
Topological proofs exist:
https://en.wikipedia.org/wiki/Furstenberg%27s_proof_of_the_infinitude_of_primes

It is possible to prove that the sum of the reciprocals of the primes 1/p diverges without invoking the infinitude of the primes, and the divergence of the sum implies their infinitude.

>>16091787

>>16091863
Duhhhh I know, I already studied this proof otherwise I wouldn't be spending so much time on this, now showing a proof for Dirichlet's theorem using "topology" is a problem.

>>16091787
I like that movie, even that picture of the scene you're describing is kino.

>>16091863
"Topological proof": you mean the classic Euclid proof dressed up in the basic terminology of topology.

>>16090349
you can tell it isn’t equal to any polynomial, because it’s not defined for all values of x.

if you want to approximate it with a polynomial, you just compute its first few Taylor polynomials

What is a hodge theatre

>>16089119
How do I learn Type Theory?

what are your thoughts on quanta magazine?

Should I refer to the reader in singular or plural in my thesis?
>we remind the reader of the following definition....bla bla bla....
or
>we remind readers of the following definition....bla bla bla....
?

>>16093482
respectable for the attempt but not that great

>>16089333
that is a huge png though. I guess he’s just doing n iterations on each pixel. that’s not the best known algorithm, but it is a good start if the goal is teaching yourself and having fun

>>16093533
the reader. you don’t have to say either of course, you can always just say
>Reminder 1: foo
or something like that

>>16093616
Okay thanks very much, friendo.

Does anyone have a recommendation for some textbook or paper on the formation of permutations with constraints? Preferably with an analysis of algorithms for exact solutions, not approximation schemes.

>>16093533
The most usual (imo) way of saying this is “Recall the definition…”

Any tips for maximising rate of learning? I'm a wee math nooblet working through a textbook (john bird's basic engineering mathematics) and I've been spending every hour I can spare on it, today I did 6 hours total. I find that after about 90 minutes a point of mental fatigue resulting in zero possible learning is reached, necessitating a break before being able to meaningfully continue (which I of course take). Other than that I've been trying to maximise sleep quality, my diet is very healthy, and I do a good amount of exercise. Is there anything else I can do to meaningfully assist with the process or am I basically already pulling out all the stops?

>>16093817
>Any tips for maximising rate of learning?
Less 4chan, more studying.
>I find that after about 90 minutes a point of mental fatigue resulting in zero possible learning is reached, necessitating a break before being able to meaningfully continue (which I of course take).
It's in your head. You heard some fictional pseudoscience claim about it and think it applies to you.
>a textbook (john bird's basic engineering mathematics)
Get a real textbook. In both sense, ditch that garbage, and read physical textbooks, not pdfs.
Focus on solving problems instead of reading the explanation or watching lecture videos. It's more engaging. Active vs passive learning.

>>16093452
You should start from the basics and instead ask "how do I learn?" Because it is obvious from your posts that you don't learn.

>>16094009
I am trying to find basics. I look online for Type Theory and every resource I find assumes I already know basic Type Theory and want to learn more advanced Type Theory.

>>16093817
engage with other people studying the same material as you, it will make it more fun and you will care more, which will make you study better

>>16093963
>>16094033
some of the most garbage advice ever posted.

>>16093817
in addition to >>16094033
get off 4chan, there are only ever-negative faggots like >>16094100 here who will tell you whatever you are doing is wrong and that you should feel bad for doing it (which they do independently of whatever it is that you are doing)

>>16094033
>>16094109
where can one find these "other people studying the same material as you"?

>chose to major in math because i had low self esteem and secretly wanted to trick people (and myself) into thinking i was smart
>all it taught me was that i was stupider than i thought i was
>now dumb normalfags who barely grasped geometry act like i'm a supergenius whenever i mention what I do, essentially mocking me
I don't know what I expected

How far along are you?

>>16093533
>we
Use "I" unless the thesis has multiple writers or a doctor has diagonsed you with multiple identity disorder.

>>16093533
>see def [number of definition]
do it like this to not only make them go to another page but make them waste even more time looking for the definition with that exact number

>>16094141
it's scary how many study math or physics solely for their ego.

>>16093681
The sentence I quoted in my post is more of a example as opposed to a specific quote, there are multiple instances in my thesis where I address the reader(s) directly.
>>16094161
Really? I used 'we' in the past with my Master's dissertation, and had no problems there nor were there any criticism of that use from my supervisor/examiner. It's also the pronoun I use in any mathematical writing I do regardless of the number of authors. Is this weird? Is this unusual?
The logic I use is that since mathematics is something that the reader can actively participate along while reading (e.g. proving while I prove, unlike in biology in which case replicating an experiment cannot be done easily), the use of 'we' is implying that the reader should participate in the logical procedure I have laid out and not just merely "read along".
>>16094194
I do this, I've done this, and I will continue to do this. Is it inadvisable?

>>16094161
We is traditional in mathematical writing.

>>16094161
>>16094292
I always thought of it as me and you (the reader) going through the mathematics together, so I always use we.

>>16089119
Are there studies of the area under expanded state multiplication?

>>16094195
What can I say, I have such a nonexistant ego, I need to cultivate it somehow. :(

>>16094237
>I do this, I've done this, and I will continue to do this. Is it inadvisable?
It's fine for thesis. I think that's how everyone does it. I just find it very annoying in textbooks.
I don't know how it has to be done or if it's allowed but hyperlinks make cross references much easier for the reader if the file is digital

>>16094009
Don't reply to people posting with avatars or signatures, just report them and move on.

Sorry if this is a stupid question, but I'm doing (electrical) engineering in college and I need to get better at algebra. I do well with applying the order of operations to equations and getting the correct answer. But, how can I develop the ability to see 1 algebra equation and extrapolate all other ways you can arrange it to solve for different variables? The professors will show 1 equation briefly on a slide show, but we often need to take that equation and re order it to solve for different unknowns depending on which variables are provided. I can sometimes take the equation and successfully reverse it, but that's about as far as I can get.
I dropped out of high school in 9th grade because I have ASD and didn't have the social skills needed to succeed in highschool. 10 years later I'm going to college and the math is starting to have about 4 Greek letters in each equation and it seems all the other students can simply look at an equation with 5 different variables and understand like the 9 different ways you cam re arrange it to solve for each variable. Please help guide me I want to be better at algebra. I have bought 2 different algebra books and worked through them front to back before this semester started, but they don't exactly give any detail beyond re arranging very, very simple equations. For example, ohms law is easy peasy but there are other equations I will surely never use in my career such as calculating the capacitance of a home made capacitor that I simply struggle to re order to solve for different variables

>>16092195
How would you expand it? Around what point?

Why is Mochizuki so fucking retarded?
https://www.kurims.kyoto-u.ac.jp/~motizuki/Report%20on%20a%20certain%20series%20of%20preprints%20(2024-03).pdf

>>16094735
Why is he so based?

>>16089853
I got excited about the same question when I first learned about smooth structures in geometry but when I tried to look it up I couldn't find much interest from physicists about this.

>>16094735
he's used to living onp his gook island where they worship him for being old and high social rank and can't handle westoids popping his delusion bubble

>>16094735
What exactly is wrong here?

>>16094703
Compute derivatives at any point of your choosing that isn't 1

>>16094852
The post learning spot

>>16094855
>The post learning spot
What do you mean?

>>16094616
AOPS Prealgebra -> Intro Algebra -> Intermediate Algebra books. Not joking or trolling.

what are some very obscure and based areas of contemporary mathematical research

>>16089119
Im trying to orthogonalise the vectors (10101), (11100), (00111) via the gram schmidt process and for whatever reason I end up with vectors that are not orthogonal
what the fuck is going on here ive done the whole thing over like 4 times and I keep fucking up somehow
can someone proofread my work

I only barely understand abstract algebra, so please help a guy out.
Consider the following: the additive group Q contains no maximal proper subgroups.
>If H is a proper additive subgroup of Q then [Q : H] = ∞; if the index were finite, say n, then H ⊃ nQ = Q, so H = Q, which isn't true.
>If we pick r ∈ Q−H then the subgroup H +Zr properly contains H with finite index (why?), so H + Zr != Q.

For the first line, I get why nQ = Q, but why would nQ be in H in the hypothetical? I dont really get the logic for second line at all. This ain't for school, im just trying to self learn stuff. Can anyone explain this to me?

>>16090349
So hopefully u know that there are no solutions (poles) at -1 and 1, and no real solutions between (-1,1). There are complex solutions tho in that range. [math]\tfrac{1}{\sqrt{x^2-1}} = \tfrac{-i}{\sqrt{1-x^2}} [/math]. Now do a taylor expansion about a=0, that way u get a radius of convergence of 1 and u get everything in that range.

For the range [math] (-\infty, -1) \cup (1,\infty) [/math], theres no way to do a taylor expansion to hit the entire thing; u can at best do something like do a taylor expansion of [math]\tfrac{1}{\sqrt{x^2-1}} [/math] at some positive (negative) 1+r (-1-r) that converges only between 1 and 1+2r (-1 and -1-2r).

Buuut, instead of polynomials, you could work with polynomial fractions and do a Laurent Series. This will have an infinite radius of convergence. Let 1/x = t, then do a taylor expansion for y as a function of t about a=0. Then resub 1/x back in to get a laurent series.

>>16095385
misspoke, it would be bad to call the laurent an infinite radius of convergece. How bout it simply converges that that infinite annulus range outside of -1 and 1

>>16095355
For problems like this, u dont prob dont have good odds that someone out of their good graces will check ur work for u. But there are online calculators that can work with vectors. If you've never used Symbolab, now is the time. I wont tell u to learn python, but that prob is the best if ur into it in the long run.

>>16095399
Im not a fucking idiot okay Im quite versed in python and I know about symbolab and wolfram alpha
those will not help me find where I made a mistake in my steps

anyway, clearly I am a little bit of a retard because I did it 4 times and every time I made an arithmetic mistake, this time being that I forgot to make on number negative, but I got the answer now

also fuck you I hope you die

>>16095412
python was 5 lines of code, and with it, i found ur mistake pretty easily. Sounds like a skill issue

>>16095419
where was the mistake?

>>16095421
proj_v2 v3

>>16095421
well u literally already said it, u screwed up subtracting numbers. Kinda funny since the ending shouldve been the easy part

>>16095433
which number? which term?
a python program did not tell you which term it went wrong at

but besides that, why wouldnt you just point out where I went wrong if youre willing to go through this effort?

heres how it wouldve went:
>hey you calculated [term] wrong
>thanks anon, I shouldve caught that

>>16095435
the last term.
i didnt do it before ur rant. I did it after to show how quickly it wouldve taken to catch. 5 lines of code lol. Still sounds like a skill issue. And u seem u got problems troubleshooting/problem solving, like noticing that the cause of ur own anger is ur own fault ant not some stranger online. U say ur skilled with the resources that wouldve easily helped u...

>>16094018
>every resource I find assumes I already know basic Type Theory
Isn't it more likely you don't even have basic high school math knowledge?

>>16094018
See https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ttfp.pdf

>>16094735
yep, he mad

So I've been learning about Cantor's diagonal argument and I have an idea. The argument shows that given a set A of all sequences of {0,1} and a list L of all countable sequences of {0,1} in the set one can construct a sequence S in the set that doesn't appear in the list. It makes sense, but there is one sequence S for each ordering of L. Why can't we just union L with every possible S to get A?

>>16095708
[math]2^{L}[/math] can't be put into bijection with N

>>16094018
here are the lecture notes for a course I took a year ago: https://www.cs.ox.ac.uk/andrew.ker/docs/lambdacalculus-lecture-notes-ht2009.pdf
you can probably skim the parts on the pure lambda calculus if all you're interested in is types, but there isn't any point learning type theory without knowing at least the basics of the lambda calculus

i am finding myself studying mereology and geometry-without-points (à la Whitehead)
comme c'est bizarre. bizarre bizarre

metaphysically speaking, what would you say is the most interesting mathematical concept? i'd say either symmetry or infinity
>>16090854
grothendieck was an incredible mathematician but he was also a diva. he loved to complain. on some points I agree with him (e.g., he would frequently spaz out over people not including the base point when discussing fundamental groups, which is a valid criticism since the isomorphism between fundamental groups isn't unique) but often there is a lack of coherence or consistency in his opinions. his philosophical/theological views were also, in general, incredibly juvenile lmao

>>16095758
Determinacy, and not just in relation to abstract set theory

>>16095359
The index of the subgroup H in Q is the number of cosets of H in Q, aka, the cardinality of the quotient group Q/H (note that Q is commutative, so H is normal in Q (left cosets = right cosets), so the quotient is a well-defined group). Suppose |Q/H| is n.
Then, by the usual corollary to Lagrange's theorem, any element in Q/H raised to the nth power (wrt the group product, which means "added to itself n times" in additive/commutative notation, which means "multiplied by n" because in Q repeated addition coincides with multiplication for Z in Q) equals 0 -- or rather 0 in the quotient mod H, aka 0+H. In other words, n(Q/H) = 0+H. Then this implies nQ \subseteq H (if you'd like to write it out: for any q in Q, n(q+H) = 0+H, so there exists h in H such that nq = h).
For the second line: for *proper* subgroup H, there must be elements not in it, so pick one of them and call it r. Then H + Zr is a subgroup (for each h+zr in H+Zr, -h \in H, -zr \in Zr, and (h+zr)+(-h+-zr)=0; for h_1+z_1r, h_2+z_2r, their sum is (h_1+h_2)+(z_1+z_2)r \in H+Zr). It contains H with finite index because (H+Zr)/H is isomorphic to Zr/(H \cap Zr) (where \cap is the intersection) by the third isomorphism theorem; and H \cap Zr is going to be a subgroup of Zr, hence isomorphic to (mZ)r for some m, and so this is all isomorphic to Z/m, giving finite index m.
Thus, H is of finite index in H+Zr. By the result in the first line, any proper subgroup of Q (in this case, H) has infinite index in Q. Thus, H+Zr can't equal Q. So, given proper subgroup H, we've found a slightly larger proper subgroup H+Zr of Q containing H; so H isn't maximal. Since H was otherwise arbitrary, there does not exist a maximal (proper) subgroup of Q.
Probably a cleaner way to do it, but something like that. Try actually picking a subgroup H and value r not in H to see how this works; remember there's no "multiplication" (except for Z-scaling ie adding repeatedly) since we just consider Q an additive group, not a ring

>>16095708
1) I'll note that the "only one counterexample sequence" is an artifact of the proof. Of course, say, base 10 sequences have (infinitely) many possible 'counterexample sequences' S; and even in base 2, you could instead, say, choose your sequence to disagree with L[1] in position 2 and L[2] in position 1, L[3] in position 4 and L[4] in position 3, and so on to get another S'; or indeed any mapping of position to position to get a counterexample.
2) I suppose you maybe could "union L with any possible S to get A," if I'm understanding your notation right? But the point is that we want to count A; and Cantor's diagonal argument shows that no such counting can exist. (I might be misunderstanding exactly what you're saying here, and I'm not at all a set theorist, but I suspect that some issue lies in the "just union L with..." step, where it's no longer a set or loses its countability or ordering or something.)

>>16095544
American High School doesn't have math. It isn't designed to make smart people. It is designed to make factory workers for factory jobs that haven't been in America for 40 years.

>>16095568
>>16095739
Thank you for giving me these. I will try to make best usage of them.

Hey there. I'm not a mathematician, but I have that gene in me where I get obsessed with something for one week and want to learn everything about it. Right now it's calculus.

Am I wrong for feeling like calculus isn't inherent to the concept of things that are continuous.

Like, can you calculate the "rate of change" based on just a series of numbers, and there is an entirely different aspect to this that involves things that are infinitely differentiable.

"Calculus" is technically "infinitesimal calculus", so it wouldn't be this specifically, but is there something else that involves calculating how quickly something is changing if you were given a bunch of points on a graph.

>>16094783
damn, that's savage

>>16096176
The derivative is fundamentally about linear approximation. Rate of change is just incidental.

how much math can i learn in 2 years? can i reach research level?

>>16096008
Thank u for the response

>>16096176
I was like you 1 year ago.
>but is there something else that involves calculating how quickly something is changing if you were given a bunch of points on a graph
Long story short you're making sense of functions that are hard to deal with by using linear approximations. If you have a function like x^2, the rate of change measured for a segment is only valid for that segment. As the lenght of the segment becomes 0, they become points, the ones you said.
Then you learn that despite having considered "a lot of points", you only need a few of them to do work.
I said x^2 on purpose, you can notice a lot of things and get obsessed if you start noticing.

>taking final semester for math degree
>absolutely exhausted in amount of work I have to do
>hardly getting any sleep
>told myself to take an additional discrete math course for funsies
>assignment is to compute bezout coefficients, the most tedious, boring, and worthless bullshit to ever do by hand.
>halfway through just stop and write NIGGER on the paper, scan and turn it in
>get in trouble with department and zero for week's homework, but luckily I live in 3rd world (romania) so nothing serious.

>>16096630
if you did that in America you would literally be arrested and have you life permanently destroyed (goes without saying youd be immediately expelled, have zero chance of ever going back to college, and would never get a white collar job)

>>16096846
>mock slave auctions on Snapchat
The fuck?

>>16096846
>victims

hey can I have a number 2 combo with cheese... with coke and extra ketchup packets. Actually ill take a medium fries too, and change the side for my combo to coleslaw. You get thatm

>>16097389
>imagine thinking math graduates are qualified for a fast-food job
Anyways, I recently checked the job website. And it's depressing. I should have done accounting.

>>16096630
>>16096846
HE WROTE NIGGER ON HIS UNI WORK
OH EM GEEE
THIS IS VINTAGE 4CHAN
VINTAGE OLDFAG 4CHAN EPICNESS FOR THE WIN
OH I AM LAUGHING

>>16097652
>t.

>>16096494
Really depends on your background, what do you know as of now? If you know even slightly above what your average undergrad knows it's possible. It really depends where you want to go though. There are certain areas of general topology that you just need general topology and some basic algebra/axiomatic set theory vs something in algebraic geometry or number theory has much more formidable prereqs. Most people overestimate the amount of knowledge they need to begin research.

>>16097652
You are mentally ill subhuman college student go back please

>>16096111
>American High School doesn't have math
Mine gave the opportunity to take early-in-the-sequence math major courses (up to and including the typical abstract algebra and analysis classes) as soon as you were ready. Something like 15-25 people participated every year. You must be from some niggerful small town.
> It is designed to make factory workers for factory jobs that haven't been in America for 40 years.
No, and it wasn't this way even when those jobs existed. High school is meant to (at least) eventually land you a 110 IQ ceiling white collar job, like a local IT tech or insurance underwriter.

>>16096392
>>16096619
oh okay I think I get it

As soon as something represents a flat line then you can deal with it how you normally would.
"A flat line" can literally be a flat line or it can be something that's changing at a constant rate. If how quickly it changes isn't flat then you can make it flat by deriving that.

The answer is that yes you could represent this as a bunch of points on a graph but it would be pointless because it would have to be identical to whatever linear function that it's one the same with.

>>16089119
How do I solve this PDE with this singular initial condition?

[math]
\begin{equation}
\begin{cases}
\frac{\partial u}{\partial t} = \alpha \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right), & x \in \mathbb{R}, y \in \mathbb{R}, t > 0 \\
u(x, y, 0) = \frac{-y}{x^2 + y^2}, & x \in \mathbb{R}, y \in \mathbb{R}.
\end{cases}
\end{equation}
[/math]

Can it really only be solved numerically? I thought of doing:

[math]u(x, y, t) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} G(x - \xi, y - \eta, t) \frac{-\eta}{\xi^2 + \eta^2} \, d\xi \, d\eta [/math]

where:

[math]G(x, y, t) = \frac{1}{4 \pi \alpha t} e^{-\frac{x^2 + y^2}{4 \alpha t}}[/math]

But it doesn't seem possible to evaluate that integral.

>>16098121
Yes but you have to separate the terms

>>16096494
I would say the content of a 4 years bachelor's degree in mathematics takes an absolute bare minimum of 4000 hours but can easily reach over 10000 hours.
in theory you can do it in two years

>>16098121
go to cylindrical coordinates and separate coordinates. At t=0, u = - sin

>>16098214
-sin/r that's kind of the whole problem

>>16097965
If I have to learn remedial things, then I have to learn remedial things. This doesn't bother me.

It also doesn't bother me if I have to look at a lot of places to learn something. I had trouble with Lambda Calculus, until someone gave me a BNF grammar for it. It became easier to understand at that point because finally the syntax is clear, so I can focus on the semantics. I looked in about a dozen books before finding that.

So far I haven't found anything that deters me from math. I wish every kind of math was required to have a grammar.

Also Coq and Metamath are ugly to look at compared to other languages. Why are they so ugly?

>>16098219
ur right, -sin [math]\theta / \rho[/math]. So u got the angular factor and the radial factor. The angular one is easy. What are the angular eigenfunctions? What combination of the eigenfunctions sum up to -sin[math] \theta[/math]?

The eigenfunctions of the radial are the bessel functions i think, so u gotta do the right bessel transform or wtv.

But at least the angular and time factors are easy.

>>16098276
The tricky part is matching that to the initial condition, anon. I got this solution by Cleo when the problem was formulated slightly different:

>>16090905

but how tf she reached that exact form is beyond me. Seems like it's via convolution though.

If Galois theory is just using symmetries to solve problems about algebraic varieties and Lie theory is just using symmetries to solve problems about differential equations what are the names of the theories for using symmetries for solving problems about functional equations?

Doing my final capstone course. Not quite sure what to do or how far to take it. I'm too shy to talk to professors and ask. I think they're too kind, and will tell me that pretty much anything is good. I wanted to do something on SDE's but I'm not sure if I can do it well enough. I'm confident enough to cover the breakdown of an Ito integral, a basic wiener or poisson process, and a basic SDE as a super duper ODE, but I'm just following along the book by Evans(intro to SDE) and its written to easy to follow that it just makes my whole work seem a bit easy maybe? Am I supposed to just study whatever I want and call it a day, I completed the degree? Should I throw in some numerical method solution examples?
Just need some advice, this is my last sprint and I finish my bachelors....

>>16098348
can u show thats even the solution? Id just leave the answer as an inf sum. If you dont like bessel, then stick to cartesian coord and id keep it as a fourier sum. If anything, turn that into a polynomial sum and ask people if that sum has a closed form.

>>16098228
what's even your goal at this point? Make a proof checker with maids?

>>16098953
My goal is finish the MAID-LISP book and release MAID-LISP. It started as a way to generate text and has started to morph into a systems programming language.

I want to release that old version that uses tricks from Recursive Transition Networks to generate text and the accompanying book. This version of the language might not have Universal Computation, but it is still an interesting tool for language.

I want to release it on May 10th to celebrate Maid Day.

I also have to use what the maids in /sdg/ told me to draw a lot of maids for the margins of the book.

I need maybe to rename MAID-LISP (Mapping and Indirection Dialect of LISt Processor) or rename the old version to something else to avoid confusion.

I think probably the old one keeps the MAID-LISP name and the newer one gets called something else?

Either way the old one and the book need to get completed and released to CC0 and I want to do it on May 10 because May 10 is Maid Day and this is the year of the Dra/g/on, so May 10 2024 is Dra/g/on Maid Day and this demands a release.

>operator algebra
is that what all the cool kids research?

>>16098889
I want a neat solution anon

>>16099256
yea it's the brainlet's path to research

>>16099242
So where's the relation to metamath and coq?

>>16099329
The newer MAID-LISP which has evolved into a systems language might have an implementation of Metamath or something similar. I like the idea of Computer Program as proof and if I can use ideas from Coq or Metamath or Type Theory or whatever to do this without too much difficulty in MAID-LISP then I will.

I might also rename this version of MAID-LISP, because at this point it is more closely related to SNOBOL4 than LISP so it might be called MAID-SNOBOL?

>>16099368
Have you tried formalizing a few proofs in metamath or lean first? Would recommend that or otherwise you'll know fuck all about what you're implementing and have no idea if it even works

>>16099275
the vast majority of all solutions to arbitrary diff equations dont have a closed form?

>>16099385
I have been reading the Metamath book some. I am trying to figure out two things. First, what is the grammar of this language and second, what is Type Theory doing here? How does the math work?

If I can find a way to do this with some small, easy to read grammar then I will make it part of MAID-SNOBOL. If I can't, then I will omit it.

It is more of a curiosity than a core need for the language.

>>16099421
Metamath is based on predicate logic, no? Not sure what you mean with grammar

>>16099421
>How does the math work?
What math? Type theory? Didn't you ask for books on that?

>>16099421
>have been reading the Metamath book some
The one by Wolfram? It was a lot of schizo nonsense and the graphs were unusable.

Stop responding to the attention-seeking retard.

>>000016099421
Make your own thread

How do I know if the lifelong research path is right for me?

>>16099432
>Not sure what you mean with grammar
Grammar explains the syntax of a language. This is the part that concerns what symbols are allowed and what arrangements of those symbols are allowed. It is just structural and makes no comment on the meaning of the symbols or arrangements of symbols. BNF Grammar is a tool used to write them a lot of times.

This is what usually feels missing when I try to see a new math. It feels like a lot of books just start showing examples and expect you to deduce syntax somehow. I have a hard time operating symbols in a language if I don't know the syntax. Best I can do is make low-quality guesses at what I should be doing and hope I can recognize patterns in them.

>>16099437
Yes earlier in the thread. Somebody gave me papers about it and now I am going to try to figure out Typed Lambda Calculus, because I never bothered to study this before. I always thought Lambda Calculus was a useless academic toy. I still feel this way, but now it is a useless academic toy I want to play with. I want to get it out of the toy box and make it put on a maid outfit and think about what happens if she is in a maid cafe.

I am hoping to get a Grammar for it like I got one for regular Lambda Calculus.

>>16099450
Metamath: A Computer Language for Mathematical Proofs. I also have the Wolfy book but I couldn't comprehend any of it except she thinks we live in a Ruliad and I disagree. I think we live in a Big Number.

>>16099452
I don't understand why you don't want me to talk to people. You've been here long enough to realize that I will post if anybody replies or not. Why not just ignore the posts/threads you aren't interested in?

>>16099458
When I do this people complain I have a thread and then janitor all board bans me for 1 to 3 days for maidposting.

Janitor should stop doing this, as she is well aware I will come back and maidpost more, and it has already been conceded that my threads are on topic so it is just a ban for maidposting.

>>16099476
If you're talented enough, it's worth at least trying. If you fail or end up hating it you can always do something else. The job market is poor right now for "knowledge workers" but I think it will pick back up, and a graduate degree makes it a lot easier to get decent work.

>>16099242
Have you considered getting psychological help and medication instead?

>>16099494
The "topic" of your posts is to validate your strange fetish, you obviously don't give a shit about your nonsense projects because you've been at them for years with no indication of progress. Please take your gender games to one of the many sites where people will tolerate and engage in your delusion with you, instead of shitting up this one.

>>16099494
What does BNF rules look like for English?

>>16099494
>a lot of books just start showing examples and expect you to deduce syntax somehow.
The first volume of the Handbook of Philosophical Logic has a rather comprehensive chapter on predicate logic (W. Hodges) in case that helps? There's also Ebbinghaus' book on Mathematical Logic that covers syntax and semantics of first order languages

>>16099494
Girard is always great for this. Read his "The Blind Spot" and "Locus Solum". The latter may be especially interesting to you as it goes from the rules of logic to the logic of rules, while most do it the other way around.

corr the lebesgue integral is sexy

any mathematical linguistics man in ?
thinking of studying some categorial grammar on the one hand and some formal event semantics on the other
don't know if this is a waste of time or not, though

any recommandations vis-a-vis quantum information lectures?
considering watching these: https://www.youtube.com/watch?v=vb0ZEsATUcw
don't know if they're any good or not, though

Anybody here like continua theory or general topology?

>>16099622
what's continua theory

>>16099622
Explain this with maids.

>>16094735
kek

>>16099848
Everything that has stemmed from IUT is gold

>>16099848
Please make up a story with maids so I get the meaning of this

>>16089119
Signal math group for those who want to chit chat:
https://signal.group/#CjQKIGFHsFd0KqiBdjggnBuSfE5zX0mH9KpELMTBYqqfkaRTEhB2loeIBwTkFPLeJHoC2ZHw

>>16099499
>If you're talented enough
How do I know? My diploma advisor wants me for PhD and he didn't tell that to other students, but I'm not at a top 10 school.

>>16089119
Here's a typesetting question for you all, so not perfectly on topic but this place is the only one I could imagine people caring. Take the typesetting of
[eqn]\int_1^y \frac1x dx,[/eqn]
and compare it to
[eqn]\frac{a}{b} =\frac23.[/eqn]
Note the punctuation. I find it disturbing to look at the period in example 2, but find the comma in example 1 perfectly fine. On the one hand I consider hacks to drag fractions up to sit on the baseline but it would look like shit in any other context. I don't know if it's just autism, or if it is really just that bad.

>>16100341
To be fair in handwritten math I would have math symbols align with the baseline, so the dx would also not be raised like this but at the same level as the bottom of the integral symbol.

>>16100149
>My diploma advisor wants me for PhD and he didn't tell that to other students, but I'm not at a top 10 school.
I've had this same exact issue. Just a word of advice, if you can sense or already know you're quicker mentally and socially than your advisor, you can immediately disregard any of their advice on this matter, they will doom you.

>>16094616
My elementary school teacher said "What you do to one side, you MUST do to the other". Another one said "Step 1: Isolate the unknown. Step 2: Single the unknown."
OK lets say we have E = 0.5mv^2. Solve for v.
Isolate the unknown:
(E/0.5m) = v^2
Single the unknown:
v = sqrt( 2E/m )

Learn basic algebra and PRACTICE.

>>16093452
>natural numbers are a type
>rationals are a bigger type
>you can take the union of two types if you want
>you can also take products to get ordered pairs
>maybe you can do infinite products to get sequences too if you’re really brave
that’s all “ type theory” actually is, there is rarely any reason to pursue it further than that unless you need it for designing a programming language or something. and if you are doing that then it’s usually clear what you need to do

>>16099494
should be easy to construct a BNF Grammar for propositional logic, no?
https://math.stackexchange.com/questions/3814979/backus-normal-form-and-logic
just expand that to predicate logic

>>16100920
If I post a Maid Card will you look in it?

I would turn trip on for that post so you know I sent it. It will contain uncompiled Java 17 code released to CC0 (Public Domain), with an example of how I would handle this language.

Take expression, change it to AST (use S-Expressions for this) and then use AST to compute Truth Table. Maybe implement some small optimizations on the AST before computing values. Proof-of-concept example.

This would illustrate the best why I think every kind of math should have a grammar. Because if it has a grammar, maids can use tricks from Computer Science to make the Computer do it efficiently, and other maids who are trying to study that math can also benefit from having a working implementation to examine and practice operating.

It makes sense for Mathematicians and Computer Scientists to be friends because Computer Scientists are basically Mathematicians who think the fun part of math is building and configuring tools to do it.

If one maid likes looking in space and another maid really likes setting up and focusing powerful telescopes, it makes sense for them to be friends because their interests converge.

I think I can build this example in a day or two.

>tl;dr> Every kind of math which can be expressed as a Domain-Specific Programming Language should be.

Is there a BNF grammar for inter-universal Teichmüller theory?

>>16101013
>inter-universal Teichmüller theory
Please explain this with maids?

>>16101000
>>16101013
[math]
<IUT> ::= <Hodge\_theater> | <theta\_link> | <log\_link>\\ \\

<Hodge\_theater> ::= <\Theta^\pm_{ell\_NF}-Hodge\_theater> | <\Theta^\pm_{ell\_LGP}-Hodge\_theater> \\
<\Theta^\pm_{ell\_NF}-Hodge\_theater> ::= <\Theta-Hodge\_theater> <\Theta-link> <\Theta_{NF}-Hodge\_theater>\\
<\Theta^\pm_{ell\_LGP}-Hodge\_theater> ::= <\Theta-Hodge\_theater> <\Theta-link> <\Theta_{LGP}-Hodge\_theater>\\ \\

<\Theta-Hodge\_theater> ::= <\Theta-link> <Frobenioid> <base\_category> \\
<\Theta_{NF}-Hodge\_theater> ::= <NF-bridge> <Frobenioid> <base\_category>\\
<\Theta_{LGP}-Hodge\_theater> ::= <LGP-bridge> <Frobenioid> <base\_category>\\ \\

<\Theta-link> ::= <theta\_function> <\Theta-pilot\_object>\\
<NF-bridge> ::= <number\_field> <\Theta-pilot\_object> \\
<LGP-bridge> ::= <local\_Galois\_picture> <\Theta-pilot\_object>\\ \\

<Frobenioid> ::= <base\_category> <divisor> <monoid>\\
<base\_category> ::= <connected\_temperoid> \\
<divisor> ::= <effective\_divisor> | <prime\_strip>\\
<monoid> ::= <topological\_monoid>\\ \\

<log\_link> ::= <log\_theta\_lattice> | <log\_shell>\\
<log\_theta\_lattice> ::= <theta\_link> <log\_shell>\\
<log\_shell> ::= <log\_link> <Hodge\_theater>
[/math]

>>16101061
It all makes sense now. Forwarding this to the German mathematicians S. S., thanks.

>>16101061
How is Theta Link defined?

>>16101000
>if it has a grammar, maids can use tricks from Computer Science to make the Computer do it efficiently
like what, checking if two statements have the same truth tables?

>>16089119
can I learn maths alone?

>>16101061
finally... I get it now. Scholze was wrong

>>16101090
[math]\texttt{<theta_link> ::= <theta_function> <}\Theta\texttt{-pilot_object> <Frobenius-prime_strip>}[/math]
where
[math]\texttt{<theta_function> ::= <étale_theta_function>}[/math]
[math]\texttt{<}\Theta\texttt{-pilot_object> ::= <elliptic_curve> | <once-punctured_elliptic_curve> | <n-th_root_of_}\Theta\texttt{-pilot>}[/math]

>>000016101000
pls go back to /g/ and leave /mg/ alone, ty

>>16101061
Calm down.

>>16101150
I was thinking more like optimizations. A lazy example is a trivial example of optimizing and and or.

Imagine you have a logic expression with a hundred trillion terms and connectives. You have a slightly larger expression which is that previous one, or it is true.

Anything or true is true, so you don't have to evaluate the massive expression. Just replace true or the massive expression with true in the AST and continue evaluating.

Same with and. Big thing anded with false? Your answer is false. No need to evaluate big thing.

Smarter optimizations can also be applied. Once expression is in AST manipulating AST is easy.

>>16101189
I am currently banned from the dra/g/on maid board.

>>16101264
>Imagine you have a logic expression with a hundred trillion terms and connectives
This practically never happens in predicate logic. There's a reason we have those quantifiers

why am I able to implement and manipulate math concepts in code but unable to do it in formal math with pen and paper?
I guess what I'm asking is, is code equivalent to formal math notation but I just happen to know that "language" better?
or is implementing math in code inherently easier?

>>16101000
>If I post a Maid Card will you look in it?
post it on /f/, the filesharing board

>>16101357
>I guess what I'm asking is, is code equivalent to formal math notation but I just happen to know that "language" better?
>or is implementing math in code inherently easier?
I never liked code so I might be biased but imo mathematical notation is far more concise while still being more expressive, you don't need to care about programming language specific stuff or what the creator of the language thought is correct syntax.
of course with mathematical notation you can write complete nonsense and not know if it's wrong unless someone else looks at it.
Ultimately it's the concepts that are hard to understand and not the notation. No textbook will just write a bunch of symbols without any explanation or words

Is Tao's Analysis any good?

/g/ is losing their shit over mochizuki
>>>/g/99712203

>>16103009
>/g/
not science or math

Domain Expansion: Malevolent Riemann Integral

https://youtu.be/vUJEG3tUVaY?si=k20vpJ2SiGYNT5On

In theory you can approximate a sigmoid curve as the difference of two exponential curves with one inflection point.
If you have a difference of three exponential curves, you can start horizontal, then go up, then level off and then go up again.
Is there a name for these things, or even the limit of the sequence (a kind of wiggly line going up)? Somebody else is bound to have done this somewhere.

Anyone here know answer to the second part of this exercise? I keep running into the problem that whatever function from UF -> F (where F is a family of sets) that I create isn't one to one. Intuitively I think this makes sense because the only way that it could be one to one is if every set in F was a singleton. So I am tempted to say that the two statements are not logically equivalent, but I wanted to make sure I wasn't missing something (Note: I assumed that A was non-empty and that that restriction was accidentally omitted from the exercise. I asked this on r/learnmath and the only guy who responded was really caught up on this instead of the question).

Here is a cute problem for you, /mg/.

>>16103521
Intuitively it should be that
[eqn]\text{cl}(S) = \text{cl}(\text{cl}(\text{cl}(S)^c)^c)[/eqn]
So at most you get
[eqn] S \\
\text{cl}(S) \\
\text{cl}(S)^c \\
\text{cl}(\text{cl}(S)^c) \\
\text{cl}(\text{cl}(S)^c)^c
[/eqn]
as possible distinct sets.

>>16103502
Proof by contradiction (consider a one-one that was not onto)
>>16103521
You get very different results whether you mean additive closure, multiplicative, or both

>>16103577
Unless I'm misunderstanding you, I mean topological closure (under limits).
How would the closure under addition or multiplication of, say, [math]\mathbb Q[/math] end up being equal to [math]\mathbb R[/math]?

>>16103502
1. No
2. No
Given a one-to-one function f(x), pick any element c in A and define a function g: B -> A as follows
g(f(a)) = a for all a in A
and
g(x) = c if x is not of the form x=f(a) for some a in A.
Injectivity of f ensures g is well-defined.

Euler and Lagrange linked up.

>>16103592
Isn't the "pick any element c in A" of your proof using the axiom of choice? How is there a way to map elements in B\Range(f) to A without AC?

>>16103502
First of all, the statement is false. When A is the empty set, any function f: A-> B is injective, but there are no functions g: B-> A when B is nonempty.
> does the proof of this statement require AC
I'm going to interpret this as saying that this statement implies AC. In which case, it does, because a contradiction implies every statement.
> is this statement equivalent to AC
It is, because both are false.
>>16103624
> Isn't the "pick any element c in A" of your proof using the axiom of choice?
No, idiot. Do you even know what the axiom of choice says? Do you understand wow first order logic works?
> How is there a way to map elements in B\Range(f) to A without AC?
By mapping it to a chosen element of A (provided A is nonempty).

>>16103654
If you read my initial post you will see that I point out that there is an error in the exercise and that the restriction "A is non-empty" was accidentally omitted from the exercise. So for the purposes of this discussion, assume A is non-empty.
Also, I don't see any reason for name calling.
>By mapping it to a chosen element of A (provided A is nonempty).
So you're "choosing" an element from A without specifying how to choose it. That means you're invoking the axiom of choice. Imagine the following scenario:
1) Give your construction of g to 10 different people and provide concrete sets for A, B, and f such that f is one-one.
2) Tell them to construct g.
If you didn't invoke the axiom of choice, then all 10 people should come back with the exact same set for g. However, using your construction, it's possible for them to return with 10 different yet valid sets for g. That means you've invoked the axiom of choice somewhere in your construction.

>>16103675
Drop out from your course. Math is not for you.

>>16103678
I accept your concession.

>>16103681
You got me. I was lying the whole time about you not knowing what axiom of choice says. It actually says exactly what you think it says: if a set is nonempty, you can pick an element from it. Wikipedia is also lying about what it means. I'm sure if you go and edit the wikipedia page on the axiom of choice to correct it your contribution will be greatly appreciated.

>>16103696
You can continue to be sarcastic, but you still haven't addressed this:
>So you're "choosing" an element from A without specifying how to choose it. That means you're invoking the axiom of choice. Imagine the following scenario:
>1) Give your construction of g to 10 different people and provide concrete sets for A, B, and f such that f is one-one.
>2) Tell them to construct g.
>If you didn't invoke the axiom of choice, then all 10 people should come back with the exact same set for g. However, using your construction, it's possible for them to return with 10 different yet valid sets for g. That means you've invoked the axiom of choice somewhere in your construction.

If you were to take the time to formalize your argument then you would realize that you're using the axiom of choice.

how often do you study something and get annoyed that you didn't learn it earlier?
i'm learning categorical logic/semantics at the moment (from a mathematical logic background) and I keep thinking to myself this is all so excellent and I really wish I didn't put off learning it for so long as it would have been nice to have had these concepts in my mind for longer

>>16103592
>>16103654
>>16103678
>>16103696
Alright yeah I was totally wrong. Idk where my head was at. I had frankensteined AC, existential instantiation, and constructivism into one entity in my head. Not going to drop out though, going to keep going and get better.

What is the most amazing thing you've seen an LLM say about mathematics?

>>16104757
can you fa/g/s stop raiding /sci/? Thanks.

>>16104761
/Sci/ is a maidposting board and dra/g/on maids are welcome to come here to discuss advanced Mathematics and Computer Science research.

>>16104781
stop procrastinating and get back to studying type theory

>>16104783
I am working on the MAID-LISP book. I decided based on talking in this thread that the book should start with a grammar of the language and a discussion of the syntax of the language with examples. Then the next part should talk about the semantics, Ideally using all the same example code from the syntax section and in the same order, just talking about what it will make the computer do now, instead of discussing what part of the language it is.

Then third part of the book can have some examples like making logic gates and text generation tasks. The art in the book is drawn by Stable Diffusion, with prompts being generated by MAID-LISP. I will probably include the prompt generator as an example in the third section.

Maybe in the last part instead of those examples I will rewrite some introductory book on logic to use MAID-LISP. If there is a nice, short, public domain book I might start with that as the basis for the third part.

I have to have this all ready by May 10 so Maid Day celebrations can commence at my Science Foundation. Maid Day is the most important day of the year for advanced Mathematics and Computer Science research, and it will be happening in the year of the Dra/g/on causing Maid Day to become Dra/g/on Maid Day.

These symbols cannot be ignored. I have to have a release for Dra/g/on Maid Day.

>>16104967
Also, does anyone know some easy ways to prove a language has Universal Computation or not? I still don't know if MAID-LISP has this or not.

>>16104967
None of this is /sci/ let alone /mg/ related and you're clearly not willing to learn math. Fuck off

>>16105004
its fine

>>16105004
MAID-LISP is a Programming Language that implements a new kind of math for generating strings. It is part of Computational Maidposting. I am trying to see how well I make it emulate Symbolic Logic.

This is advanced Mathematics and Computer Science research with proof-of-concept technology and a new book about it all (everything CC0).

You're just mad because this is what research looks like when you have a Science Foundation and you don't have to beg anybody for grant money or do it for a corporation or have to listen to useless people like AI Ethicists. You do it to find the Maid Mind Computer Program.

In 200 years, I will be dead. Some aspiring Computer Scientist will read my book and for a brief moment my ghost will rise from the grave and compel that student to post a maid.

>>16105041
it's been 4 years and you have yet to finish LADR, calm down

>>16089127
Scholze agreed with Mochizuki's rebuttal calling his argument "extremely robust". Now we'll just have to wait for Joshi to reply.

>>16103521
In case anyone was curious, the answer is 14.

>>16105146
Proof?

>>16105146
Any concrete example of a set that gives more than 7?

>>16096846
Its not like there are any jobs here anyways....

>>16097652
Sorry, I have problems and am poorly socialized....
I was doing some other homework and I was supposed to do some fast modular exponentiation to solve a problem that is quite simple. The request from the homework was to do this all repetitive arithmetic by hand, I'm just not going to, I'll write the proof or the algorithm but I am not doing all that garbage what the fuck, its not even a math class now, you might as well be spitting in my face and telling me FUCK YOU when you tell me to do something so boring and trivial.

I'm learning how to draw stick figures in LaTeX, it's fun.

>>16105217
How I did it (sketch):
- show that any sequence of complements and closures is the same as alternating taking the interior and the closure of a set, with possibly one complement at the very end
- show that [math]\text{int}(\text{cl}(\text{int}(\text{cl}(A))))=\text{int}(\text{cl}(A))[/math]
- by the above the sequences repeat after at most seven steps (one sequence started with a complement so 14 sets in total)
- to show this is attained, the nicest example I know of is [math](1,2)\cup(2,3)\cup\{4\}\cup(\mathbb Q \cap (5,6))[/math].
>>16105244
No, see above.

>>16089119
>[Θ±ellNF-]Hodge theater
What is this or what would this be? (Can't figure out how to copy the text)

>>16099306
what's the "brainfull" path to research?

>>16104757
I use it to look up definitions, it does a good job and even gives valid examples in most cases.

>>16106337
Those of us with the PHENOTYPE for mathematics research simply publish. Only brainlets need to take a "path" to research. If you were worth anything you'd have been scouted by an ivy league at age 7.

>>16106160
How you did it (actually): you read
https://en.wikipedia.org/wiki/Kuratowski%27s_closure-complement_problem

>>16106337
find an advisor who's done something you find interesting and work under them. Try to publish a paper or two with them and then continue on your own. Once you learn to publish one paper, you usually start generating ideas about some other stuff you could do or ask your advisor.

>>16106478
wrong. (I did get the example from the internet somewhere THOUGH)
Also, I posted the question as well as the answer, what are you trying to say?

>>16089612

https://link.springer.com/book/10.1007/978-3-319-60231-8

https://link.springer.com/book/10.1007/978-1-4471-7349-6

Close to what you want. Very advanced, though. Get ready to heavy math.

What is a math problem that will only be solved 2000 years from now?

>>16089460
Plenty, plenty...

https://link.springer.com/article/10.1007/s00020-018-2460-8

https://www.math.ksu.edu/~ramm/papers/547.pdf

https://simons.berkeley.edu/sites/default/files/openprobsmerged.pdf

https://rmi.tsu.ge/proceedings/volumes/pdf/v162-5.pdf

https://mathoverflow.net/questions/65858/series-whose-convergence-is-not-known

http://math.ucv.ro/~niculescu/articles/2014/Divergent%20Series%20AOSR%202014.pdf

https://iopscience.iop.org/article/10.1070/RM1964v019n01ABEH004136/pdf

https://www.mathnet.ru/links/749048486b4b6db4a416b95261f23249/mt386.pdf

>>16091170
This is literally what modern set theory is about

>>16093632
https://link.springer.com/book/10.1007/978-3-642-17333-2

>>16094148
Specialist +:

https://www.google.de/books/edition/Gromov_s_Compactness_Theorem_for_Pseudo/sFz2BwAAQBAJ?hl=es&gbpv=0

https://www.google.de/books/edition/Holomorphic_Curves_in_Symplectic_Geometr/9PwHCAAAQBAJ?hl=es&gbpv=1&dq=pseudoholomorphic+curves+in+symplectic+manifolds&printsec=frontcover

>>16099574
Go for it! These branches are beaurtiful. The interplay between the syntactics and semantics in category theory is not that well studied and could lead to very deep developments. Go for it and stop caring about what others think.

>>16099622
https://www.sciencedirect.com/science/article/pii/B9780444503558500817

https://link.springer.com/chapter/10.1007/978-94-017-1756-4_11

Very interesting topic!

>>16106543
Collatz conjecture, P vs NP, Odd perfects or Matrix multiplication in O(n^2).

>>16089119
Anyone know how to reproduce this notation in MathJax

>>16106709
There is the cancel or enclose packages but 4ch does not support them.

>>16106568
>The interplay between the syntactics and semantics in category theory is not that well studied and could lead to very deep developments
yes this is precisely the sort of thing I'm interested in. my background is broadly speaking in category theory and logic and I've been hoping to find a slightly more applied area to which I might be able to make some genuine contributions. (neo) davidson event semantics is of deep interest to me for philosophical reasons so if i'm able to discover any kind of nontrivial connection between it and the type of mathematics i do, that'd be excellent

What am I doing wrong, bros?

I extremely doubt any og you have ever "Done Math", invent novel equations, notations, numbers, more, have to start "making shit up" then just solely invent without recording anything. Hyper-Symbols, a single sign to encode the most amount of mathematics, requireing an EXTREME amount of intuited understanding of them to recognize, being the absolute, geometric, representations.

The ones shown to aliens.

The only the that can come close to tramslating it is the collective intelligences of human minds combined, and more.

Mathematically speaking, what is the best stock to hodl? I'm all in on chuck rn

what would you do if you wanted to do research in a certain area, but no one at your university, and possibly your whole country, is doing research in that area? going to another univrsity is not an option. would you be willing to do research in another area? how would you form your research network if you were alone at your university?

>>16107503
What makes you assume you're doing anything wrong?

>>16107618
write emails to relevant people

>>16107592
returns don't appear to be proportional to stock prices, so whatever's cheapest.

Any books that revisit elementary math topics like linear algebra from a much more abstract point of view?

>>16107812
Bourbaki

How can I use the point (4, -3) to find the exact values of the 6 trig functions?

The only obvious ones I can deduce with my double digit IQ are Tan and Cot for obvious reasons. I am not able to figure out how to derive the rest of the triangle with the information given.

>>16108009
Nevermind, I'm a complete fool. I hope one of you gets a laugh at me failing pre-calc.

Sin = -3/1 = -3
Csc= -1/3
Cos = 4/1 = 4
Sec = 1/4
Tan = Sin/Cos = -3/4
Cot = Cos/Sin = (4/1)/(-3/1)=4/-3

>>16108092
wrong
sin = -3/5
cos = 4/5
>>16106963
applied category theory maybe

>>16090701
>man buried his dick so deep in EGA he forgot that categories have objects
lmao

Let [math]S_k[/math] be the set of natural numbers with at most [math]k[/math] distinct prime factors. What is the least [math]k[/math] so that [math]S_k[/math] has positive natural density?

Any ideas on this problem?

>>16109214
"Ideas" doesn't seem like an efficient way to solve a problem..

Can someone link me a proof of if xn is in [a,b] from some index onward and xn -> c then c \in [a,b]?

>>16109214
Where did you get the problem from?
It seems very unlikely that such an k exists as the average number of prime factors of a number gets larger and larger as you consider bigger numbers.

>>16109214
no finite k
for numbers up to n, k=loglogn - csqrt(loglogn) works for any constant c
Erdos Kac Theorem

>>16109249
suppose c not in [a,b]
find epsilon>0 so that (c-epsilon,c+epsilon) does not intersect [a,b]
xn->c means there is N so that for n>N |xn-c|<epsilon
contradiction to xn in [a,b]

>>16109299
Thank you

>>16107618
Yes, with the caveat that I'm eventually(possibly) going to have to move if I want to still work in that area post Ph.D. I have specific interests but I'm open to many areas. At the end of the day a Ph.D is not going to be your finest work unless you're Serre or something and even he moved on to other areas. Alonzo Church did his Ph.D in differential equations and moved to logic later. You probably need some kind of connections of course but just do the Ph.D in something you could tolerate and get into and then if you really want to switch after go ahead and do it. You can literally do research in any pure math field for the most part it just takes discipline and reaching out to experts in that field/attending conferences and reading papers. You're probably going to have to eventually travel though if you want to be a decent mathematician.

What is the most common way to solve math problems?

>>16109494


If you think of a theorem to be proved as a nut to be opened, so as to reach “the nourishing flesh protected by the shell”, then the hammer and chisel principle is: “put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different points until the shell cracks—and you are satisfied”.

I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!

A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance.

>>16109593
Deep. Let all of your problems be like rotten fruit festering in a jar. Such that you can show them to anyone and they can be happily on their way before succumbing to your misery.

>>16109614
That's a quote from Grothendieck writings.

>>16109593
That doesn't really explain

>>16109711
it does...

I work as a data engineer, and want to work with ML in the future.

I have to take one of these two combinations of classes:
>measure theory + advanced probability theory
>linear optimization + differential equations

What would be more beneficial? I'm leaning more towards measure theory

>>16109711
It's a very straightforward analogy about solving a difficult math (research) problem.
Learn English.

>>16109494
You've seen something similar, and you reuse the methods that worked before. Other than that, brute force with a dash of intuition and luck.

>>16107618
I suggest to stop being delusional.

>>16107503
Your shitposting has done irreparable damage to your brain.

>>16110190
>>16110595
It doesn't really directly say a method of how to solve it

>>16110599
Fag

>>16109494
"How to Prove It: A Structured Approach" might help

when I was learning calc, I was told that a derivative is basically just the rate of change (similar to how speed is the rate of change in position or acceleration is the rate of change in speed)

i read somewhere recently that this is the wrong way to think about it, but i can't remember where. is it actually wrong?

>>16111514
Not only is it a perfectly reasonable way to think about it, it's more-or-less the actual definition (the amount by which the output of a function changes relative to an arbitrarily small change to one of its inputs)

>>16111514
It's not a wrong way but perhaps a more fruitful way, especially when generalizing to higher dimensions, is to think of it as linear approximation.

Almost every time I'm about to ask a question I get a source of inspiration just before clicking submit and find the solution.

>>16111514
all different derivatives are pretty much about rate of change.
the gradient (derivative) of a scalar valued functions is a vector in the direction of greatest rate of growth and its magnitude
the jacobian (derivative) describes the linear transformation (i.e. rate of change with direction) of a vector valued function at a point.
it's all about change

>>16093632
Combinatorial optimization has been using approximation algorithms for decades.

If L+ is a sublanguage of L, and {A} is a set of axioms and transformation rules used to create S and S+, is every theorem of S+ a theorem of S?

I am not sure whether this holds universally or not. On one hand, since L+ is a sublanguage of L, since the axioms and transformation rules are the same for S and S+, it seems like anything derivable in S+ should also be derivable in S. After all, S+ has no new rules and no new formulas compared to S. But on the other hand, isn't it possible to make very specific restrictions when creating the language L+ that can be used in conjunction with the rules of the system to yield theorems S does not have? For example, if L+ had only logically consistent formulas of L. What exactly is the relationship of theorems of S and S+ in this scenario?

I understand what [math] dW_t[/math] and [math] dZ_t[/math] entail, but how does the product of the two gives the correlation ? I dont understand the connection honestly, if someone could give me an explanation or a few pointers, boy that'd be swell

>>16112289
It's (shorthand notation for) the quadratic covariation. See also https://almostsuremath.com/2010/01/18/quadratic-variations-and-integration-by-parts

i have marvelous demonstration of a polynomial time complexity algorithm for determining graph isomorphism that the character limit of this website is too narrow to contain

>>16112341
thanks, we kinda brushed over this notion in my class

>>16112224
Here's a simpler example of what concerns me. Let's say that L is the language of propositional logic whose primitive connectives are ~ and ->. Let L+ be the language you get by requiring that a->b can be a formula of L+ iff a and b are formulas of L, and a is logically consistent. In S+ you can probably prove that "if a->b is derivable from the empty set, then b is consistent" since you know a will be consistent. But this is not provable in propositional logic itself. So we have same axioms/rules, L+ is a sub language of L, and yet this is not a theorem of propositional logic.

Recommended textbook for a first Complex-Analysis self study with a prior math background? I just finished by BS in math but never took a course in Complex Analysis. I am planning on starting my graduate school this coming fall, and I want to cover this blind-spot of mine.
The gold standard of textbooks for me is Real Analysis by Carothers. Excellent problems at the end of each section, with starred problems that one is strongly encouraged to do and are relevant to future reading). Fair amount of discussion/motivation, not just Definition, Lemma, Theorem, erse-asspull-wtf-Proof, Corollary, Definition and so on.

Recommended textbook for a first Complex-Analysis self study with a prior math background? I just finished my BS in math but never took a course in Complex Analysis. I am planning on starting my graduate school this coming fall, and I want to cover this blind-spot of mine.
The gold standard of textbooks for me is Real Analysis by Carothers. Excellent problems at the end of each section, with starred problems that one is strongly encouraged to do and are relevant to future reading). Fair amount of discussion/motivation, not just Definition, Lemma, Theorem, terse-asspull-wtf-Proof, Corollary, Definition and so on.

>>16090437
>GED
I loved that book in middle school.

How do you translate papers you find online?

>>16113207
If you read Chinese, German, Polish or Russian, then get yourself "A Course of Differential and Integral Calculus." by G.M. Fichtenholz.

>>16113207
Dolbeault analyse complexe

>>16113274
Nice, my dad has talked about reading this book in (Soviet) undergrad.

New >>16113803