00:00 - 21:0021:00 - 00:00

12:06 AM
Appears not, else I might have some help with what I would presume is a relatively simple task for which I simply don't know how to do.
Maybe I can get something from this? desmos.com/calculator/3lqqip5uyj
Also it turns out that wolfram gives "True" because it thinks I'm asking for a verification.
But if you look at the value of b, I've been messing around with that value there, approximating by hand, but I can only get so far until all I see is floating-point error and then it is a matter of guessing which of these is what I'm looking for unless I can find a solution analytically myself or by someone else: wolframalpha.com/input/?i=closed+form+7.615818

what do you need to do?

if a person wants to get a PHD in math
with a concentration in abstract algebra ( or something like it) do elementary courses like Calculus and Differential equations really matter ?

Yes, because you must be well-rounded and pass exams on a variety of subjects, and those are basic foundations for a huge amount of mathematics.

@JoeShmo Well, I need to find the minimum and maximum values of b such that the function equals zero at $x = \pm 1$.
The particular function in question is $f(x)$ there.
It's the absolute difference (error) of my cosine approximation and the real cosine.

12:21 AM
@TedShifrin thanks

Research in algebra is getting broader and broader, too. It's not like taking an elementary undergraduate course.

I suspect an elementary undergraduate course in modern algebra is still hard
requires a lot of proofs?

Once I have the minimum and maximum values for b, I can then proceed to figure out the function which makes this error zero between [b_min, b_max].

Yes, it's mostly proofs.

thanks and good night

12:26 AM
Good night.

12:41 AM
AMDG, I'm not following. Also, "...such that the function... the particular function is $f(x)$", lol
Independently - The winner of last night's debate was Chris Wallace

Well if you mess with b, and you stretch the y axis with your mouse by holding shift and dragging until you can see the shape of the error function, you'll see there are zeroes for different values of b.

what is $f(x)$ here? and what are you trying to approximate?

It's right there in the graph on desmos. desmos.com/calculator/g0ibuinztw
(click home in the top right to reset the graph to default parameters and position)

I don't really know how to use desmos. care to explain in two words?
what are you trying to do?

Trying to analyze the error function of my cosine approximation so that I can make the error zero.

12:48 AM
I'm sorry I'm not exactly parsing, and if you're approximating anything (if you even have to approximate? and certainly on a computer) you cannot make your error exactly $0$. Only successively closer to $0$, given a "resolution" of the user's choice

Yes, I know that. However, I want to find a function of cosine that has zero error from my approximation. From there, I can create an optimal approximation of sine and cosine which is trivial to compute.

is this a homework? do you have the original problem statement?

I haven't had homework for a very long time. :)

well, good for you.. :-)

By long time I mean about two years.
I suppose this means you can't help me, or...?

1:00 AM
I would love to help, but I still don't understand what you're asking

Oh

give me an explicit function $f$, and explicitly what you want to do with it, and where you got stuck

$$f\left(x\right)=\left|\cos\left(\frac{x\pi}{2}\right)-\left(\frac{\cosh\left(\ln\left(b\right)\cos\left(1\right)\left(\sqrt{\frac{\pi^{2}}{4}-\left(\frac{x\pi}{2}\right)^{2}}\right)\right)-1}{\cosh\left(\ln\left(b\right)\cos\left(1\right)\sqrt{\frac{\pi^{2}}{4}}\right)-1}\right)\right|$$

lol

I mean I did say it was on desmos... hehehe

1:02 AM
oh dear lord

XD

and what do you want to do with it..?

Find all the points at which this function equals zero for a specific range of values for b.

OK, and what have you tried?

Asking for help because I don't know how to compute the range [b_min, b_max], and I'm just a programmer, not a mathematician. :D

1:04 AM
here's a better one, unless wolfram can give you a closed form formula for the derivative $f'$ en.wikipedia.org/wiki/Secant_method

It can

try newton then
what is this for?

For charity's sake. Contemplation and programming are my main occupation. I thought finding an exact, closed form of all the circular functions would be a fun challenge, and it would also, like I said, allow me to get an optimal approximation of the circular functions, not just any approximation. :D

you lost me again :-)

define "optimal"

1:11 AM
Ok, well then for all you need to know, I just want an optimal approximation of the circular functions. For that, I only need to find a closed form for one of them (obviously) that does not involve an infinite series in the definition, and is not expensive to compute (such as in the case of $e^{ix}$) and which is, in purely mathematical terms, free from any error whatsoever.

I don't know what you mean by optimal

noone does

AMDG, "optimal" approximation with $0$ error is not an approximation (let alone optimal)
alright, g'night fam
"optimal approximation" in the way you seem to be using the term, is an oxymoron

Optimal may be objectively defined as that which is perfectly balanced between simplicity and complexity and is perfectly just in that it has only what is necessary.
Applied to computations, it means that a given algorithm, in this case a circular function approximation in $\mathbb{Q}$ from a closed form that produces exact values for the circular functions in $\mathbb{R}$, and the accuracy or number of digits that are true for the rational approximation increases as the accuracy of the transcendental constants or closed form, transcendental functions (e.g. $e^{x}$) for which the function is composed of increases.

you're using vague and subjective terms in your definition here

1:18 AM
I don't see how...

"perfectly balanced between simplicity and complexity" is a doubly, perhaps triply subjective characterization.
alright, gotta run now forreal

Actually, it is entirely objective. Simplicity is opposed to complexity. Increasing one decreases the other and vice versa.

lmfao

...and who gets to be the judge of what is simple and what is complex?

Reason
Truth

1:20 AM
ohh
reason and truth it is, then

reason and truth, the lesser known siblings of facts and logic

haha

More like under-utilized since the Renaissance.
Balance is a matter of justice which, justice simply put, is giving what is deserved, but generally speaking, means that you have or use only what is necessary, nothing more, and nothing less.
Thus if something is just, it is perfectly balanced.

nevermind..

I'm sorry?

1:23 AM
perfectly balanced, as all things should be

Simplicity may be defined as the quality of having lesser diversity of order present in a system without regards to the magnitude or quantity of orders of a particular kind.
Complexity may be defined as the quality of having more diversity of order present in a system without regards to the magnitude or quantity of orders of a particular kind.
$x^3$ is less complex than $abc$ and is therefore more simple than $abc$
It therefore follows that simplicity and complexity are quantifiable objects, though the values are purely abstract and represent purely abstract qualities inherent to all things in existence.
So does what I just said about "optimal approximation" make sense now given these definitions?

get help

That is not a very reasonable response whatsoever.
For someone so inclined to exercising his intellect and will on abstract things, you seem to have no care for philosophy whatsoever. How very odd and paradoxical.
But my whole purpose for being here is to get help--help with my analytic problem, not get help for what you perceive to be defects of the truth or be told what I ought to do.
Now, you suggested Newton's method for one possible solution.
> produces successively better approximations to the roots (or zeroes)
Does that mean I can't obtain a closed form for the minimum and maximum values for those zeroes for the variable $b$ using Newton's method?

1:38 AM
nope. it gives you a numerical approximation

Well, thank you for giving me this technique, but it isn't what I'm looking for.

there are also algebraic algorithms out there that might give you what youre looking for

There's two values for which b approaches from negative or positive infinity which yields two zeroes at $x = 1$ and $x = -1$. I want to know what the exact value of b is at those points.

but having nice, closed form solutions are the exception to the rule

Exception!?

1:41 AM
yeah, you would typically only be able to find approximations

Well, I suppose I really shouldn't have any sort of surprise. I guess my algebra classes gave me the wrong impression of mathematics.
Up to algebra 2, everything is closed form solutions.

the plight of the engineer

Well up to and thru pre calc at least I think.
Hm, well then I suppose I have something worthwhile to study: make finding closed forms for everything that much easier :tm:
I mean for me, the difference between an approximation and a closed form is to me like going from a high-end pair of headphones to a low-end pair of headphones, or decreasing the digital quality of the audio signal using the same pair of headphones: I notice every defect, and the difference between them.
Or perhaps you might know what it's like to go from a high refresh rate monitor to a 60Hz monitor? Once you've gone beyond, you always see tearing in anything less.
I don't know... if you know that it exists out there and you just have to find it... well why be complacent and settle for less than the best?

2:31 AM
Oh wow, this seems to describe exactly what I posted earlier today: mathworld.wolfram.com/ShallitConstant.html
Well, almost. It describes a sum of a sum and a product. I had asked if there might be some form that has a finite product equal to an infinite sum (with the finite product having terms that would have to be transcendental or something to be able to do so).
Also far more generalized than what is displayed in that page: $$\forall \alpha \in \mathbb{N},\forall \omega \in \mathbb{N}, f(x)=\sum_{\alpha}^{N}{\delta_{\alpha}(x)},(\exists g(x)=\prod_{\omega}^{1}\delta_{\omega}(x) : f(x) = g(x))$$
Oh, I copied the wrong latex
should be \sum_{\alpha}^{\infty} and \prod_{\omega}^{\alpha} respectively for f(x) and g(x).

Is the equation $\frac{3}{x}+3=-1$ a linear equation? I am getting $x=-\frac{3}{4}$ Hence it is of the form $x+\frac{3}{4}=0$. So, it is linear.
Am I correct?

no. plot it

2:50 AM
@Unknownx $x^3+1=0$ has the solution $x=-1$, but just because that solution can be written as $x+1=0$, does not make $x^3+1=0$ a linear equation.

@robjohn but when we multiply the entre equation with $x$, we can transform to a linear equation.right?
$x^3+1=0$ But we can not make this equation like that.

@Unknownx $3+3x=-x$ might be a linear equation depending on how things are defined.
We can take the cube root of $x^3=-1$. what operations are we to consider legal when manipulating an equation to verify linearity?
according to Wikipedia, a linear equation of one variable is an equation that can be written as $ax+b=0$

@robjohn yes, you are correct. But how can we check the linearity of the equation?

what "can be written as" means is I guess what you are asking.

3:06 AM
But the $x^3=-1$. has more than one solution in complex plane.

I think that linearity is a property of a relation between two bound variables. Asking if an equation is linear is beset with the kinds of problems we are encountering here

But $\frac{3}{x}+3=-1$ has only one root.

But $\frac3x+3=y$ is NOT a linear relation

yes
you are correct

You can manipulate many things into $x=a$, but that doesn't make that equation linear
This is why I think of relations as linear, not equations
$ax+b=y$ says that $x$ and $y$ are linearly related
equations can be manipulated to be in many forms. relations are not so easily transmogrified

3:11 AM
I searched for the definition of the In mathematics, a linear equation is an equation that may be put in the form

${\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0,}{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0,}$ then equation is said to be linear

@Unknownx That is what I said, but reduced to one variable
I would thing that if you think of a linear equation, you don't want to do ANYTHING to it and get that form. Otherwise, too many things might be considered a linear equation
I would not have thought that $\frac3x+4=0$ was a linear equation either

@robjohn I don't understand

I don't think $\frac3x+4=0$ is linear, even though we can manipulate it into $3+4x=0$
which is a linear equation

In mathematics, a linear equation is an equation that may be put in the form $ax+b=0$.
It was the definition in wikipedia. But the didn't mentioned any operation.

@Unknownx "may be put in the form" is ambiguous to me

3:21 AM
yes

relations don't suffer as much from amibiguity
an equation has solutions and one can rewrite equations into different forms, and one of those forms might be $ax+b=0$. Does that make it a linear equation?
this is unclear

$\frac{3}{x}+3=-1$ is non linear. right? Since, power of unknown variable is $-1$.

yes

@JoeShmo Thank you very much

How did bombelli derive this "\sqrt[3]{\sqrt{2+\sqrt{-121}}}=2+\sqrt{-1}" assuming you know nothing about complex number and please don't tell me by taking cube power since it's not verification. Just curious about this.

3:32 AM
I think I figured out what the minimum and maximum values of b must be for my function... $f(\pm{1})=e^{1/2(\arcosh(1) + i\pi)} - 1$
Not even real lol

@robjohn thank you very much for spending time with me.

@Unknownx pleasure.

That's interesting, though... my cosine approximation accepts this complex input, so does that imply that I can compute $e^{ix}$, or at least a subset of it, with my approximation (apart from the obvious fact that $\Re(e^{ix})=\cos(x)$)?
The only reason that the result (and therefore the input) are complex is because arcosh(0) is undefined. Wolfram says that the expression on the right hand side resolves to $-1 + i$, and that makes sense considering that the function should be zero at $\pm{1}$ as expected.
Could just be my wishful thinking :)

3:55 AM
I think this is probably just giving me the values of x, not $b$ like I wanted... not exactly an irrational or transcendental number beginning with 7.615818...
Oh that's why I've been having trouble. I'm looking for the point at which two different zeroes lie on the same point, not just one specific zero.
I wouldn't even know how to begin to find that.

looks like there is no algebraic way to do
I guess he was lucky enough to guess that

4:22 AM
@Stupidquestioninc Note that $|2+11i|^2=125$ That means that $|\sqrt[3]{2+11i}|^2=5$. This hints greatly that $\sqrt[3]{2+11i}=1+2i$ or $2+i$, if it's going to be a reasonably simple number. At least that gives a place to start.
Was he given $2+11i$ by someone?

5:07 AM
Hm, I know what. Is there a test I can do for the number of zeroes that a function generates?
I can find the point at which the number of zeroes is only two perhaps.
The test would ideally confirm two zeroes at the locations $-1 + i$, $1 - i$.

5:30 AM
Say you have a set where x=[0, 1, 2, 3, 4...n] maps to y=[0, 1, 2, 3, 4,...n]. Now say y only has odd numbers i.e. y=[1,3,5,7...n]. The function would be $y=f(x)=2x+1$. What would the function be if the set y contained not multiples of 2 or 3 i.e. $y=[1, 5, 7, 11, 13, 15,...n]$. Assume $n$ is an arbitrary limit and we're only dealing with natural numbers.

5:43 AM
Alright, well I'm tired. I think this is indication enough for me to continue analyzing this error function. Maybe someone who knows complex analysis knows how to find the function of these zeroes for $b=t$ for $t$ time and for all values in [b_min, b_max]? desmos.com/calculator/90ayjh2keb
In the meantime, good night!

5:59 AM
Researchers will also recommend an open-access policy that promotes research being shared in online repositories.
> The Indian government is pushing a bold proposal that would make scholarly literature accessible for free to everyone in the country. The government wants to negotiate with the worldâ€™s biggest scientific publishers to set up nationwide subscriptions, rather than many agreements with individual institutions that only scholars can use, say researchers consulting for the government.
Is that possible?
Whole country, single prescription?

@robjohn Wow the $|\sqrt[3]{2+11i}|^2=5$ takes monstor trig function
$\sqrt{{\sqrt[4]{125}\cos(\frac{\arctan(11/2)+2\pi}{2})}^2+{i\sin({\frac{{arctan{(11/2)+2\pi}}{2})}^2}$
or is there any easy way to do so

6:57 AM
@robjohn hmm Yes 1+2i and 2+i and sqrt[3]2+11i 's magnitude squared is same
but I still have doubts
feeling of unsatisfactory
I will try to come up with answer
looks like I have an idea but I have fatigue now

1 hour later…
8:33 AM
@robjohn you mean by magnitude?

8:49 AM
Mornin'

Afternoon

@Stupidquestioninc $|z|$ is the magnitude or absolute value of $z$

or distance of z from the origin?

I know I mean we are trying to guess by finding norm right?
sorry I was tired so I wrote "you mean by magnitude "
so answer has norm 5 and question has norm 125
hence I need to look in complex plane to guess integer answer
if it's rational it's gonna be even more painful
may be I need to rephrase
$\norm(z^3)=\norm(2+11i)=125=5^3$ so we are finding $\norm(z)=5$
but finding norm(z) is kinda dumb imo
since there is a lot of pair of number where norm is 5

9:32 AM
@Stupidquestioninc |z|^2=5. There are two simple things to try: $(1+2i)^3=-11-2i$ and $(2+i)^3=2+11i$ If neither had worked, it would require some harder computations, like perhaps the cubic formula, but luckily it doesn't.

considering the time in the US, I am not surprised

Funnily enough, most of the activity from Europe appears to come in the early hours of the morning

9:52 AM
@robjohn ok just say that it is a lucky guess by considering taking integral solution

@Stupidquestioninc Yes. I asked where he got the problem. If it was from someone, it would no doubt have a nice solution so $5^3=125$ is a very good start.

@robjohn This problem was from Bombelli it was written in visual complex analysis and some lecture on complex analysis.
0

When a polynomial equation with integer coefficients arises in your research, e.g., $$x^3-15x-4=0\ ,$$ then you "naturally" check whether it has integer solutions. In the case at hand the constant $4$ indicates that such solutions would be from the set $$\{-4,-2, -1,1,2,4\}\ .$$ It is easily seen...

10:08 AM
Does anyone have any thoughts on this question? I asked it several days ago and have been continually coming back and thinking about it, but I still don't have a good answer. math.stackexchange.com/questions/3842835/…

2 answer didn't satisfy but for the other one by jose I think it is little bit ok
little bit

10:51 AM
@Stupidquestioninc Bombelli just observed that!

@user91500 doesn't answers my question XD

@Stupidquestioninc See the book Galois Theory by Ian Stewart page 27

math.stackexchange.com/questions/1728376/… Trying to solve exactly the same problem as this one. I defined $\delta = \frac{1}{2}$, which means that $|x| < 1/2$. And $|x^2 - 1| > \frac{3}{4}$. But how does one proceed from this to create the relationship between $\delta$ and $\epsilon$?

11:14 AM
@user91500 ok I will try
@user91500 hmm u mean page 26 right?

11:31 AM
@EdwardEvans you mean late in the night

11:58 AM
@Alessandro early hours of the morning means super late at night

4 hours later…
4:13 PM

Suppose $G$ is a topological group in which every open neighbourhood of $1$ contains a compact open subgroup of $G$. Let $H$ be a normal subgroup and $\pi : G \to G/H$ the natural projection and suppose $U \subset G/H$ is an open neighbourhood of $1$. Then $\pi^{-1}(U)$ is an open neighbourhood of $1$ in $G$, so it contains a compact open subgroup $K$. Since $\pi$ is continuous $\pi(K) \subset U$ is a compact subgroup of $G/H$ contained in $U$, but why is it open?
Is $\pi$ an open map? Lol

4:27 PM
Ah okay it is open. Why, then, should I care if $H$ is a closed normal subgroup of $G$? What bit of "every open neighbourhood of $1$ contains a compact open subgroup of $G$" wouldn't be preserved under the quotient of $G$ by a not necessarily closed normal subgroup?

4:43 PM
Isn't the projection $G\to G/H$ always open since it is the quotient by a group action? (the translation action of $H$ on $G$)

Yeah I know that now, but why would one care about $H$ being closed?
Is there something in the thing I wrote above that I'm assuming that I can't assume unless $H$ is closed?

hm doesn't look like it to me
People always work with closed subgroups for some reason though

Well if $H$ is closed then $G/H$ is Hausdorff, which is about the only justification I could find for caring about $H$ being closed
rofl

yeah that seems like a good reason
Also open subgroups are actually clopen

right but what would a clopen subgroup break
idk

4:53 PM
Dunno
It probably works anyway but "closed" is needed for something else

5:09 PM
Weeeell I showed that a closed subgroup of a locally profinite group is locally profinite, and this was to show that a quotient of a locally profinite group by a closed normal subgroup is locally profinite
so I suppose that's the point, but idk it seems to work without $H$ being closed so whatever

I don't know what locally profinite means
Even though you already told me once

yeah I know, I surpressed the words above but locally profinite iff every open nbhd of 1 contains a compact open subgroup

5:25 PM
Hi.

Currently (re)making a lecture for a bunch of youngins
What have you been up to lately, Edward?

Nice, just reading for seminars atm :)
and not shutting up about it on here because I'm somewhat out of my depth rofl

sure, I have nothing else to do until November so I may as well get a head start on things so I can identify the prerequisites I may need to work on before starting the semester
In my case, point-set topology

5:32 PM
Oh is it like a class that is a regular seminar?

Seminars are basically weekly talks held by students following a piece of literature
idk if it's different where you are

Seminars here are just what they call the weekly talks done by people, grouped according to subfield. E.g. we have a symplectic seminar, a geometric group theory seminar, a representation theory seminar, etc.
But the talks are usually just one-off things that a speaker talks about, usually their own research.

I guess you can call those seminar courses

yeah that's what I'd have called a seminar back in the UK actually. But here they just call "seminar courses" seminars
and seminars are also seminars
rofl

So what's this seminar on, @EdwardEvans?

5:39 PM
I have one on elliptic curves and another on the Langlands program

5:53 PM
Is this the right place to ask for help crafting a question?
Hi I'm new
is says to just ask, so ok
why do mathematicians disagree on stuff?

I disagree that mathematicians disagree on stuff :)

aren't there finitists?
for example

@EdwardEvans Good luck

6:52 PM
Finitism is less the position that you can't do math with infinity (which is pretty much undeniable---almost every mathematician is working contrary to this), and more the position that you ought to not use infinity when doing math.
It's merely making a value judgment about math done with or without infinity. It's like programmers arguing about which programming language is best to use. They aren't saying "C++ is not programming" when they say "Java is better than C++".

I'm an ultrainfinitist, I only believe in sets with cardinality $\geq\aleph_{17}$.
3

@anakhro It's not correct that finitism makes a normative claim, because there are finitists that have produced research in infinitary mathematics
I think a more accurate statement is that finitism claims that infinitary mathematics is "non-real", or does not accurately reflect the real natural of the universe, or something like this

7:09 PM
@MikeMiller I don't see what contradicts with what I said.

I think that believing that mathematics should accurately reflect the universe or stuff like that is already wrong

It's just not a normative claim
Nobody says you ought not to do infinitary math except Zeilberger and he's a troll before he's a finitist
I don't care about their particular claims but nobody is really telling their colleagues to quit

That's not what I meant.
and @AlessandroCodenotti I agree, and that would be something with regards to the philosophy of mathematics, rather than actual mathematics.

well what about the 4 color proof
math ppl disagree about that too
and there, it's hard to separate math from math philosophy, because if you reviewed that proof, you have to recommend publication or not

That's a better example. But really that's just about what constitutes a good proof.

7:21 PM
well can you tell me what ppl were actually arguing about?

Whether it should be accepted as a proof, since it can't be checked by human

but it can be check, its just exteremly laborious
but certainly within human capacity

Cannot be realistically checked*

It's like an extra degree of separation. In order to check the proof, you have to check the program which performed the computation.

wasnt it 100s of examples?

7:23 PM
Right, I was referring to the computation itself when I said it can't be checked by a human. Of course the correctness of the program can be checked

ok
so not whether it was possible or impossible

" This new proof is similar to Appel and Haken's but more efficient because it reduces the complexity of the problem and requires checking only 633 reducible configurations. Both the unavoidability and reducibility parts of this new proof must be executed by computer and are impractical to check by hand."

whether it was done
aha
ok so some people didn't like that a computer was doing part of the proof?

Actually was the "reducing the number of cases to a finite one" step also computer assisted or fully human?

There were numerous problems with earlier proofs, many of which were also attempted with computers.

7:26 PM
so computers have been wrong?
that was the objection?

When you say objection, what do you mean? Objection to what, precisely?

I'm referring to that fact that there was controversy

Mathematicians generally accepted the proof as a final judgement. The controversy was more about what could be gained from the proof and other ancillary things that didn't really attempt to de-legitimize the result, merely the comment on the nature of computer-proven results.

yes, I have heard that
thats what you mean by good proof
like, ok yes, you can do that
but it doesn't advance understanding very much
I'd rather do things a different way

Yeah, and that's fine.
There are other events that have occurred about disagreements among mathematicians
But they are very off to the side, or niche.

7:35 PM

Several notable mathematicians have come out saying they do not think that the results of the theory are clear enough and thus do not seem ready for publishing.

excellent
but some people say that he has shown something to be true
"Mochizuki and a few other mathematicians claim that the theory indeed yields such a proof but this has so far not been accepted by the mathematical community."

Indeed. So there is a problem there.

do you have any idea what's going on?
why do they disagree?

"Proving" is roughly convincing and explaining.
Some people can offer explanations but fail to convince.

7:41 PM
that seems to describe many things that aren't math though
like I could try to prove that socialism is flawed

Well in math the point is to come up with a proof that is rigorous enough to convince the vast majority.
Mochizuki has failed to do this.
It could very well be the case that he has proven something, but he has failed to demonstrate this sufficiently according to people in that subfield.

so what's happening is that Mochizuki is explaining his ideas well enough
didn't Galios also famously make huge leaps of logic?

No, he isn't explaining his ideas well enough.
Otherwise he'd be convincing others.

isn't
typo
so then, is it your position that if Mochizuki was more rigorous, and took smaller steps, he would be more convincing?

And Galois notably failed to pass mathematical exams. However they are unsure why, proposing that it was possibly because the examiners were unable to understand his thought processes. His success was found through his writing which was well-understood by contemporaries, though at the time not being recognized as important as it is today.

7:50 PM
is that a quote?

No.
I am not sure what the specific issues of clarity are with IUTT. I probably couldn't understand one bit of it due to not being a researcher in any adjacent subfield.

but isn't that a general truth about math

You'd be better off asking a mathematician who has read the IUTT papers, or reading one of the public denouncements of the work.

and I don't see how you got from step 3 to step 4
wouldn't you break it down into smaller steps?

psitae is Mochizuki trying to collect evidence that people approve of intergalactic teichmüller theory confirmed

7:52 PM
haha
no

@psitae sometimes you can be mistaken in your steps and there is no way from 3 to 4.
Or maybe you just need to re-write the steps.
Or maybe you need to write more.

but presumably if you teaching me some well-established theory with a vast majority of consensus then 4 would follow from 3

Probably. But "some well-established theory" doesn't describe IUTT accurately.

right
I'm not talking about edge cases anymore
just "normal" math
actually, we can include cases where 4 doesn't follow from 3
the general truth I'm getting at is, the way to resolve the disagreement is to break things down in the way in which i described

Not always. It really depends on the problem.
People learn things very differently and can sometimes understand things written one way, but not another.

8:00 PM
so I say 1+1-1+1 ... = 1/2
and you say that's nonsense

go on

I think that's a workable example
how should we resolve that disagreement
or I have another example, thinking about it
you say that something that is true can't contradict something else that is true
and I don't see how you can be so sure that that is self-evident
how do we resolve that disagreement?

@Alessandro thanks

When will the talks be?

Probably some time in february or march, they're both pretty late
I think both the 12th talk
Ah elliptic curves is 11

8:15 PM
@psitae These are particular examples where you have completely hidden proofs and explanations.
The issue isn't with the explanation. It's that there is no explanation.

do you accept that "something that is true can't be contradicted by something else that is true"?
btw thank you so much for helping me through this

@Alessandro actually, have you ever seen a seminar not run because not enough people signed up? There's 13 talks scheduled and so far only 5 people have signed up for talks, and there's a further 6 people in the "Sammelgruppe"

@psitae I think that claim is missing lots of context.

I accept that
what context do you want?

Depending on interpretation, the statement is true or false.

8:27 PM
I can think of real world stuff, like
I want to goof oof and not do my homework, and I want to get good grades
is there anything like that that's mathematical?
i.e. provide an example in math where the law of contradiction is false
maybe this?

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