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12:01 AM
According to the people who had to write set theory exercises with me on overleaf you should not follow my style advice concerning latex code
 
on overleaf?
 
An online latex editor
 
never used such things
 
It's quite handy when many people need to work on the same document at the same time
For my own stuff I always use an offline editor of course
 
The Fundamental Theorem of Algebra was rigorously proven in 1806. (Gauss's topological, but nonrigorous, proof was from 1799.)
 
12:02 AM
Yeah, either that or you use dropbox and make sure people don't forget to get the latest version. Simultaneous changes don't work, though.
 
I feel like someone should organize these things into a timeline
 
It took me several books to learn decent LaTeX skills, and a few things never did work as the manuals said they should.
There are math history books, DogAteMy. :P
And there's an online history site in Scotland.
 
@TedShifrin a few things I could mention:
- a PhD student asked me if I want to give a talk in research seminar (so one level above masters seminar) which is a bit unusual for undergrads
- after my advisor wrote a recommendation letter, I got a free membership in the EMS (the european equivalent of the AMS)
should I mention on of these?
 
The first, not the second.
 
Maybe I should read through this
This is a timeline of pure and applied mathematics history. == Rhetorical stage == === Before 1000 BC === ca. 70,000 BC – South Africa, ochre rocks adorned with scratched geometric patterns (see Blombos Cave). ca. 35,000 BC to 20,000 BC – Africa and France, earliest known prehistoric attempts to quantify time. c. 20,000 BC – Nile Valley, Ishango Bone: possibly the earliest reference to prime numbers and Egyptian multiplication. c. 3400 BC – Mesopotamia, the Sumerians invent the first numeral system, and a system of weights and measures. c. 3100 BC – Egypt, earliest known decimal system ...
> c. 1000 – Law of sines is discovered by Muslim mathematicians, but it is uncertain who discovers it first between Abu-Mahmud al-Khujandi, Abu Nasr Mansur, and Abu al-Wafa.
> [Al-Qūhī] also wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows users to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas.[7][8] It is likely that al-Qūhī invented the device.[9][10][11]
 
12:10 AM
Math history is difficult to keep track of.
The influence of the east was marginalized until recently (with regards to math history textbooks)
And mathematics in Russia vs the rest of the world is another common issue mathematical historians run into.
Another is that the notion of proof is anything but well-defined.
 
Yeah, and the Russians developed a lot of things for themselves because they banned access to "western" mathematics.
Ah, you typed about Russia while I did.
 
And it's also difficult to say whether or not someone was thinking of something in the "right" way.
Like for example, in my (unprofessional) opinion, Fermat definitely did calculus before Leibniz or Newton. This is not the wide-held scholarly opinion, mostly due to the fact that historians debate whether or not Fermat understood the concept of a limit.
@TedShifrin i got ur back
bro
 
Fermat had a different way of calculating $\int_a^b x^n\,dx$. I put his as an exercise in Spivak's book.
But I admit to ignorance on the time-line on Fermat versus Leibniz.
 
You were in charge of writing exercises for a Spivak book?
 
I contributed several hundred problems to the latter editions of Calculus, yeah.
 
12:14 AM
Wow.
Also, have you ever met Spivak? I wonder if he is as nice in person as he is in writing.
 
And some changes to the text in the fourth edition.
I took a year of grad diff geo from him at Berkeley. He taught as a visiting scholar for one year. But we are in fact friends, yes.
 
@anakhro I think the question is, who first made it a "calculus", in the other sense of the word - a systematic way of calculating with infinitesimals rather than ad hoc techniques
Hence, "infinitesimal calculus"
 
@anakhro Did you learn from that book and just realized how much Ted made you suffer? :P
 
Archimedes did limit-y things, too
 
DogAteMy, why do you say "with infinitesimals"? Newton definitely didn't think that way, although Leibniz did.
 
12:15 AM
Then why did it come to be called "infinitesimal calculus"?
 
@AlessandroCodenotti I have actually never read Spivak's calculus book. Only parts of his differential geometric saga and his physics book.
 
Yes, Archimedes and the Greeks definitely had a rigorous treatment of a lot of integration.
 
I don't know how Newton thought of it
 
@TedShifrin Do you happen to know the story behind his wikipedia picture?
 
That's super neat, Ted.
 
12:16 AM
Oh, he was infamous for that pose. I hadn't seen it on Wiki.
 
I don't know why wiki says "trying", he appears to be very successful
 
There were also semi-caricature pictures on various volumes of the 5-volume Diff Geo.
 
> Michael Spivak, Berkeley 1974, trying to smell his shoe.
Wat
 
That shows how limber he was ...
 
I must say that looks like a stretching exercise to me
 
12:18 AM
It was about limberness (he did all sorts of marshall arts stuff) ... not about shoe-sniffing.
 
Surely there's easier ways to smell your shoes if you really want to
 
Such as taking them off your feet first
and then wearing them on your hands
and then sniffing them
 
silly people
 
Or bending over backwards.
 
Also have you ever noticed how many (especially European) mathematicians have a wikipedia photo taken in front of the Boy's surface model at Oberwolfach? It's crazy
 
12:21 AM
Have someone else sniff them and then develop a standard smell communication protocol
 
@Alessandro: To make mathematicians like me, who've never been to Oberwolfach, feel inferior.
 
I applied to a conference there and got rejected
 
Makes it feel like everyone and their mom have been to Oberwolfach
 
my friend got accepted
 
Aw / Yay
 
12:23 AM
So now you're on an epic revenge, to become such a good mathematician they'll have to invite you, and then refuse their invitation?
 
LOL
 
I'll make my own Boy's surface!
 
with blackjack and hookers
 
Or I'll make the orientation double cover, with the sheets separated slightly
 
I was reading about how people are trying to preserve smells.
 
12:25 AM
and call it Man's surface
 
They basically just catalogue the composition of smells so they have a "formula".
 
so men are orientable and boys are non-orientable?
 
Or a recipe.
 
First time I've seen the word "formula" be used as a metaphor for "recipe" rather than the reverse
 
Formula does mean a list of ingredients.
Hence baby formula.
 
12:27 AM
Oh fair
I'm working on a project to make a Wiki for qualia…
that way I can get people to experience the otherwise indescribable feeling of trying to communicate qualia
 
What's qualia?
 
It's like what it feels like to perceive things
Like how you can't explain what colors are to a blind person
 
But you can.
 
You can explain the physics and how it's processed by the brain, but is that the same as them "knowing" what it's like to see red?
 
Yes. Exactly.
 
12:31 AM
You can smell red if you take drugs
so I hear
 
or if you have synesthesia
 
synesthesia or something
 
Every time I see red, I say to myself, "wow, the light hitting my eyeballs has a wave length of approximately 625–740 nanometres!"
 
sniped
 
@anakhro That's not even true
I mean for red it might be
But for, say, yellow, it's not
If you see yellow, it could be monochromatic light with the yellow wavelengths,
 
12:33 AM
Yellow is 570–590 nanometres.
 
or it could be dichromatic light - half the photons have red wavelengths and half have green wavelengths
 
Yello is rgb(255, 255, 0)
 
Our eyes can't tell them apart because they activate our three cones equally
 
to me anyway since I'm a coder
 
@ShineOnYouCrazyDiamond You know why color is 3-dimensional?
Why there are three primary colors?
 
12:34 AM
You could just use "dominant wavelength" and it solves your quip.
 
Whereas sound is essentially infinite-dimensional
despite them both being waves
 
@anakhro I think those are the peaks in our amplitude vs frequency
 
Because we have three cones in our eyes. It's because of human anatomy, nothing to do with how the world actually is
 
@ShineOnYouCrazyDiamond "In color science, the dominant wavelength (and the corresponding complementary wavelength) are ways of characterizing any light mixture in terms of the monochromatic spectral light that evokes an identical (and the corresponding opposite) perception of hue."
If that's what you were thinking of.
 
I was thinking of Qt framework, and CSS lol
 
12:35 AM
Hm I hadn't heard that term but sure
This is unrelated to the qualia thing anyway
 
Qt is world renown platform-independent (mostly) framework for doing GUIs
Can be coded in both Python, C++, and other langs
 
A subset of $\coprod_{i \in I}X_i$ is closed $\iff$ its intersection with each $X_i^*$is closed.
 
*there is a binding for those languages, but C++ is the natural lang of Qt thank god
 
That's basically how the topology of disjoint unions is defined
 
12:37 AM
What is $X_i^*$ ?
 
Well, it's done with open sets, but that's equivalent
Oh I didn't notice the star
 
@AkivaWeinberger Its not "closed in $X_i^*$
 
You wouldn't usually, because they only come out at night
^_^
Well, there is a big star right next to us. Did you notice it?
 
$X_i^*$ is the image of the canonical injection
 
Oh sure
 
12:39 AM
the question I have is that is it supposed to be closed in $X_i^*$.. right?
 
I don't see how it's different
How are you defining $\coprod_{i\in I}X_i$? Is it $\bigcup_{i\in I}X_i\times\{i\}$?
 
$\coprod_{i\in I}X_i$ $=$ $\{$ $(x,i)$ $:$ $x\in X_i$ and $i\in I$ $\}$.
 
I think that's the same, yeah
How is the topology defined on this space?
 
you identify $X_i$ with $X_i^*$ and the topology is defined by declaring a subset $U$ of the disjoint union is open $\iff$ every $U$ intersects $X_i$ for each $i\in I$ is open in $X_i$
 
12:45 AM
Why are all news logos the same stylized globe
 
where $X_i$ is treated as a subset of the disjoint union
 
Mhm
If a subset of $X_i^*$ is open in $X_i^*$, is it open in $\coprod X_i$?
By that definition
Note that most of the intersections are empty
 
$\coprod_{i\in I}X_i \cap X_j^* = X_j^*$ right?
 
yes, @ShineOnYouCrazyDiamond
 
12:47 AM
though you've used $i$ in two ways there (dummy variable and, uh, actual variable)
Never mind you fixed it
 
@AkivaWeinberger thats essentially what I'm asking
 
@topologicalmagician You can prove it using the definition you just gave
 
So your question is then the coproduct is closed iff each component is
 
Prop: If $A\subseteq X_i$ is open in $X_i$, then $A^*\subseteq X_i^*$ is open in $\coprod X_i$
Proof:
 
What's $A^*$ ?
 
12:48 AM
Hint: Use the definition of "open in $\coprod X_i$ @topologicalmagician
@ShineOnYouCrazyDiamond $A\times\{i\}=\{(a,i)\mid a\in A\}$
 
$A^*$ is $=$ $\{$ (a,i) : a \in A$\}$
@ShineOnYouCrazyDiamond
 
How do you get $i$ there?
 
From $A\subset X_i$
 
It's the same $i$ as the index of the $X$ it's in
 
12:50 AM
Thanks, @AkivaWeinberger
 
We want to prove $A^*$ is open. This means that $A^*\cap X_j^*$ is open in $X_j^*$ for all $j\in I$, right?
What if $j=i$? What if $j\ne i$?
(In fact the proposition should be an 'iff' so we should do the other direction too)
But yeah this is just chasing definitions
It might be annoying to write out but it's not particularly clever
♫ I dreamed a dream ♫
♫ I dreamt a drem ♫
English is weird
The past tense of host is haste
 
1:07 AM
Does munkres have anything on adjunction spaces?
 
Don't know
 
There are exactly three mentions of "adjunction space" in Munkres, all within exercises. There is a small chapter on adjoining two-cells as well.
 
I'm guessing you looked at the back of the book
(This is known as the Munkres Index Theorem)
Pun Jeopardy: If you get into this spaceship you can keep it
What is the Enterprise?
 
 
2 hours later…
3:30 AM
Yo, I need one or two of my algebros to save this post from downvoters:
-1
Q: A seemingly polynomial-time integer factoring algorithm. P = NP

Shine On You Crazy DiamondHere is some test code: from math import gcd, log from sympy import divisors, isprime start = 100000 end = 200000 list_of_lists = [] for m in range(start, end): if not isprime(m): sum = 0 #for e in range(1, m): for k in range(1, m): for e in range(1, i...

Downvoting without a comment should be illegal
Wow, P=NP and nobody cares
in fact they anti-care by downcasting my post
@Ultradark would you like to write a paper with me?
 
3:52 AM
@ShineOnYouCrazyDiamond why did you remove it
 
Fuckers downvoting me to death
It's still working, though the inner bounds may need adjustment
 
You think you proved P=NP?
 
Yes, that's correct, except without proof, just evidence. When you discover an algorithm the proof comes last usually
If I show you an algorithm with apparently poly-log running time, then it warrants further investigation. Try convincing these throwbacks on MSE though..
The 3 loops essentiall compute:
$(\sum_{k=1}^{?} \sum_{e=1}^{n} \sum_{i=1}^n (i^e \pmod k)) \pmod n$ where $n$ is your input integer
It stops computing the sum as soon as it finds a divisor
$?$ in this case is not a proportional to $\sqrt{n}$ as is usually the case, it looks way at or below poly-$\log(n)$.
Therefore, if proved correct, then P=NP as Donald Knuth believes
The reason it hasn't been discovered yet is so simple is because we don't normally mix the moduli in mathematics.
To a programmer though, it's trivial to do that
Are any coders here? Could we look at this together? So I'm not out here on my own like a crack pot?
Actually the summation is with $\log(n)$ bounds on the inner two not $n$.
 
@ShineOnYouCrazyDiamond If it works, factor one of these
In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that are part of the RSA Factoring Challenge. The challenge was to find the prime factors but it was declared inactive in 2007. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits. Cash prizes of varying size, up to US$200,000...
 
Yes, that comes next
 
4:04 AM
(The numbering is weird 'cause some are named by the number of digits and others by the number of bits)
 
I know that was reading up on it last night
And the sadder fact is they took the prize money away like crooks
 
If you can do it you'll gain everyone's attention easily. No words needed
 
Not necessarily. That would require them to multiply two numbers and it's just easier to hit downvote
Okay, I'll stop ranting
I'll work on my presentation and the algorithm and let you know if it doesn't work
 
By the way, prime factorization isn't known to be NP-complete
so this wouldn't prove P=NP
 
I heard the opposite
 
4:07 AM
Well you can tell why it got downvoted.
 
crap, well even if it is efficient, there's no prize money
w. t. f.
 
This is such an important problem that that really doesn't matter
You should try it by hand for small numbers @ShineOnYouCrazyDiamond
 
It does matter when you have $0 and no one hires you
 
Does it factor, say, 91?
 
@AkivaWeinberger of course
not
is 91 prime lol
 
4:10 AM
7*13
 
Oh, then yes, it returns quickly
 
Have you tried it out by hand
or run the program
 
programming
I do enough on paper
 
Doing something like this without examples is a sure way to let mistakes creep in
Always have examples
 
Example output: 1000000000006 => k loop bound of 2
1000000000007 => 34519
you're right though
I'll work on it tonight and post a related, smaller question on MSE and post a link here
It's surprising that it returns an exact factor and not just something that GCD's with input to get a factor.
So some kind of math is going on :D
 
4:14 AM
As Akiva says, factor an RSA number, get the cash prize, enjoy your fame.
 
There's no cash prize for those any longer
But as soon as I have the bounds nailed down, I'll start with RSA-100 and work my way up
I'll probably send an email to the RSA people
I'll just not share the algorithm unless they pay up
 
You don't need to share the algorithm, just the factors
 
exactly
I'll extort the world. Give me money or I keep it a secret lol
Notice that although I've shared it, I don't think any one was paying that close of attention to see what I did
Such is life
I was working in Python, but now switching to D (C++ speed) for sake of RSA challenge
RSA-100 can be factored using GNFS in 72 minutes on an overclocked machine similar to mine
I expect that if this works, it should only be a few minutes
Except I won't be enjoying my fame. I would rather stay private
 
 
2 hours later…
6:09 AM
Guten Morgen @Lukas :P
 
Guten Morgen @ÍgjøgnumMeg
 
Alles klar? :)
 
Jap. Und bei dir?
 
Jaa schon gut, ich muss glaub ich die Feb. Klausuren verschieben lol
 
sagen Deutsche auch “lol”?
 
6:22 AM
kA, ich bin halt "Mischling"
ahaha
 
6:43 AM
@LeakyNun ja
 
7:27 AM
Okay, that algorithm didn't work out, but I noticed something interesting
unrelatedly
You take a large enough composite, say $67\cdot 37 = 2479$ and try to solve for one of its non-trivial factors using and only using each digit precisely once, digit concatenation, and $\cdot, +, -$.
$79 - 42 = 37$ e.g.
@user21820 ?
Not sure how that answers the question.
:)
 
@ShineOnYouCrazyDiamond I made a stupid mistake, that's why I deleted it.
 
It's interesting isn't it?
The fastest factoring algorithm is the GNFS, perhaps we can beat it
 
You're not going to beat it by this method, because there are exponentially many expressions of the form you want.
 
Yes, true, but that's where the work comes it
*in
In other words, there may be a way to skip some of the expressions
 
I suspect the answer is that it is false because there should be arbitrarily large numbers of the form 100...01 that have factors not near a power of 10.
 
7:40 AM
Who cares about those numbers though, when's the last time you saw an RSA number that looked like 1000...01?
 
If your question is about the density of numbers with such factors, then you should edit it just to make sure to exclude such potential counter-examples.
 
$1001 = 7 \cdot 11 \cdot 13 \implies 10 + 1 + 0= 11$
 
But my point still stands; the exponential number of expressions of your form dooms the approach from the beginning, because decimal form has nothing to do with the intrinsic number-theoretic structure of factorization.
@ShineOnYouCrazyDiamond 11 is near a power of 10.
10001.
 
@user21820 you're right, 10001 fails
Let me modify my post
thanks!
 
100000001
1000000000001 also fails, but barely.
10000000000000001.
10^(4n)+1 should provide ample counter-examples.
 
7:46 AM
What if we worked in base two then?
then $100001 = 2^5 + 1$
lol, idk where I was going with that
 
It's the same in almost any base, because the easy factors are 11 and 101, which exclude those of the form 10^(2n+1) and 10^(4n+2).
 
@user21820 this method shouldn't ideally depend on the base. I.e. if we declared another base, then you could also make it work since base 10 is just arbitrary and we do have all these examples of it working
 
There are no obvious factors for 10^(4n+1), in any base.
 
What about 10?
 
10?
Lol.
+1
Forgot the +1.
 
10^(2n+1)+1 and 10^(4n+2)+1. 10^(4n+1)+1.
 
You're funny
^_^
 
I make funny careless mistakes.
Can't help it.
 
Well, if you were going to turn it into a factoring algorithm, you'd have to break it up case by case, so this doesn't rule out the usefulness of it in some cases
It's odd that it worked for the examples I just came up with randomely
 
@ShineOnYouCrazyDiamond The numbers that you pick randomly have lots of nonzero digits.
 
7:52 AM
for 10000001 wouldn't you just convert to another base with some nonzeros?
 
> “Euler proved that the set of rational points on an elliptic curve is a group. Which is funny because he didn’t know what an elliptic curve is and didn’t know what a group is.” - Várilly-Alvarado
 
@ShineOnYouCrazyDiamond Does nothing about the objection I raised earlier (exponential).
Frankly, if you want to beat the GNFS, you should actually just learn about it first.
 
Nah, that would take 3 lifetimes
I'm no Euler
 
@ShineOnYouCrazyDiamond I don't believe it would take that long. Are you an undergraduate?
 
College drop out
And I don't want to learn about an algorithm that can't be optimized any further
 
7:54 AM
But from your profile, you know type theory!
So what makes you think you can't learn other stuff too?
 
only a little. I mostly know some category theory, but just enough to implement my BananaCats app
 
Haha. So I'm not the funny one.
 
That's not my cat. It was a google image search. It's actually the splash screen to the pap
*app
 
Still... who puts cats on their app?
=P
 
Apple computer, fruit, banana; categories, cats = BananaCats
that was my thought process
I'm still in shock that a post of mine got 21 upvotes the other day, and it ain't that great
Then other posts I care more about, get no votes
Oh wells!
@user21820 thank you for your interest on the post
Do you think there will ever be an efficient integer factoring algorithm?
I think the span of things we haven't tried is a lot larger than the small fraction of stuff we know
 
8:02 AM
@ShineOnYouCrazyDiamond That is a very interesting question, but I don't know enough to give a good answer. I think the current consensus is that factorization is intermediate between P and NP.
Because factorization is also coNP, and most believe that P ≠ NP.
And most believe that NP ≠ coNP.
 
How to find the range of a linear transformation that's transforms function or matrices?
 
8:22 AM
Does anyone here agree with me that studying mathematics is a very different thing than preparing for a mathematical exam?
 
@adeshmishra JEE :P?
No, I loved the mathematics which was trendy at that time , when I prepared for that. The problem is with the method that is usually taught.
 
@AjayMishra I'm not talking about JEE specifically, I have found that a preparing for exam instills a feeling of solving a question anyhow
 
8:54 AM
A small question on this proof of the Intermediate Value Theorem: "But $|f(x)-f(c)|<\epsilon=f(c)-y$ implies $f(x)>y$ for all $x$ in that range," I don't see how this follows if $f(x)>f(c)$
 
9:51 AM
$f(c)-f(x)\le|f(x)-f(c)|<\varepsilon=f(c)-y$ implies $-f(x)<-y$, or equivalently $f(x)>y$
 
From what I've seen looking around, it appears that:
Given a relation matrix, I can find its *transitive closure* by multiplying it by itself multiple times until the multiplication ceases to change the matrix.
For example: Given the relation matrix A, calculate $A^n$ until $A^n = A^{n-1}$ and the final non-changing $A^n$ is the transitive closure of A.
Is that all correct?
 
Thanks @Thorgott
 
10:52 AM
Hey chat
More specifically, hey @Ted :). I wasn’t online anymore when you pinged me
 
Why no one has heeded on my question "Does anyone here agree with me that studying mathematics is a very different thing than preparing for a mathematical exam?" Is it because that it happens to everyone at some stage? Or because my question was senseless?
 
11:13 AM
@ShineOnYouCrazyDiamond
 
12:03 PM
@adeshmishra depends on the type of exam
 
12:33 PM
Is there a way to convert between any random coordinate system to another?
At my institute, we were first taught cartesian, then cylindrical, then spherical, now they're trying to force us to do parabolic
!
There must be some way in which we can just remember the governing rules (like x = r cos(theta) and y = r sin(theta) and z = z, and derive the rest)
If there is such a thing, please tell me what to look for, as I'm desperately lost
 
12:48 PM
@StupidQuestionsInc Exam wants me to solve 25 questions in 1 hour.
 
1:13 PM
@AbhigyanChattopadhyay remember the idea, not the formulas. The names are pretty standard
 
@LucasHenrique Okay, but what I meant was, given the idea, how would I derive, say, the volume element in the parabolic space, or the unit vectors?
 
1:35 PM
Calculus
The volume of a transform is given by the determinant of the Jacobi matrix (IDK if this is a common way to call the Jacobian)
@AbhigyanChattopadhyay what do you mean by unit vectors?
 
@LucasHenrique Unit vectors meaning an expression of the new coordinate system as a right handed coordinate system, and their relationship with the previous coordinate system. E.g. $r\hat{r} = x\hat{x}+y\hat{y}$ and $r\hat{\theta} = y\hat{x}-x\hat{y}$
 
idk if that’s always feasible
 
Ah... So in parabolic coordinates, what would I do?
No unit vectors?
 
No
If the transform is linear then obviously there’s this relation
But that’s not true for $(r,\theta,\varphi)$ for example
Even $(r,\theta)$ doesn’t have this
 
@LucasHenrique But I just wrote that above
 
1:48 PM
What’s $\hat \theta$?
 
Right, I think I get it... So that Jacobian gives a local linear transformation, but it's only valid in the infinitesimal case, right?
And the unit vectors are totally out of question
 
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