/sci/ - Science & Math

>>12238272
In between serious and genius level, and this is all I need for my research so I won't go further.

>>12238272
in space

>>12238272
decimals

>>12238317
such is the story of the based retard

>>12238272
>cohomology
>genius level

>>12238272
Im at the level letters are still black

>>12238296
Math geniuses please answer my question
If a point doesnt measure anything and a straight line is made of points, how does a straight line measure things?

>>12238336
Knowing what it is and knowing how to let a computer solve your equations for you isn't the same as writing a formal proof

>>12238343
A point does measure something, it measures it in one dimension. A line is two dimensions. You're conceptualizing a line as it is drawn from a pencil, but that drawn line is in reality three dimensions. A two dimensional line is infinitely thin and can not exist in reality, it is theoretical.

>>12238346
>A point does measure something, it measures it in one dimension
How can something that doesnt have width and length exist?
I mean, try to visualize it, how would a point even look like? If you zoom in it, it would look like a circle

>A two dimensional line is infinitely thin
Why? Isnt width part of the 2 dimensions?

>>12238272
A bit on every level except the final one, which probably means this is poorly organized since I'm not a seriously autistic about math or anything.
>one-time pad decryption
Good meme

>>12238346
>A point does measure something, it measures it in one dimension
Everywhere I looked it says points are adimensional, they have no dimension, no area, no length, no volume, no surface, nothing, its "zero" dimensional

https://en.m.wikipedia.org/wiki/Point_(geometry)

>>12238343
How is it so that an unknowledgable person like me, that only barely knows the black words in the chart, knows something that math geniuses dont? (that points have no dimension)
Why do the math geniuses here talk out of their asses?

>>12238272
I know some of the genius level shit, but not all because my field is specific and I don't have time to preoccupy myself with other math

also, at what level would you put stuff like isometric embedding/convex integration?

>>12238352
If it has a length and a width, that makes it a rectangle.

You're stuck thinking of theoretical geometric constructs as only belonging on a piece of paper. For instance, when you think of a line, you're probably thinking of a long thick black line from a pencil. But that line is only drawn to help you imagine the line, it's not the line itself, for if it were the line, it would have length, but also width. If it had a length and a width, that would make it a rectangle, not a line

>>12238376
Accidentally clicked submit. I meant to add: Now imagine a theoretical rectangle, one made up of four points, and four lines that connect those points. Each of those lines are infinitely thin, for if they had width, the would be a rectangle. However if each of those lines are actually rectangles, then those rectangles must each be made up of 4 points, and 4 lines that connect those points. But those 4 lines are also rectangles, and on and on it does.

>>12238272
took some upper level undergrad courses from the serious bracket... I miss those days

>>12238376
>If it has a length and a width, that makes it a rectangle
I meant length and width in the usual sense, where there is a vertical component and an horizontal component to the size, so a circle would have length and width too but varying for each part of the circle

>>12238388
>Now imagine a theoretical rectangle, one made up of four points, and four lines that connect those points
done

>Each of those lines are infinitely thin, for if they had width, the would be a rectangle
I dont know how to imagine such a thing

>However if each of those lines are actually rectangles, then those rectangles must each be made up of 4 points, and 4 lines that connect those points. But those 4 lines are also rectangles, and on and on it does
Yes, in imagination, sure
If you do it on a piece of paper you will probably be limited to an atomic level

>>12238427
>However if each of those lines are actually rectangles, then those rectangles must each be made up of 4 points, and 4 lines that connect those points. But those 4 lines are also rectangles, and on and on it does
>Yes, in imagination, sure
>If you do it on a piece of paper you will probably be limited to an atomic level
That also reminds me of some crazy shit I saw

>>12238423
Again, you are still thinking of a line as drawn from a pen or the line on a computer screen. A line has no vertical component, it is infinitely and perfectly thin. Thinner than the thinnest thing you can possibly imagine, thinner than a monoatomic scalpel, thinner than the thread that can cut the monoatomic scalpel in half. That is because the line does not live in the reality of three dimensions, it lives in it's own reality of a theoretical two dimensions

>>12238427
And that is why you cannot draw a line, you can make a scratch on your piece of paper that leaves an imprint of graphite on it, and that imprint may resemble an idea of a line, and you can use that idea to help you work through an imaginary problem you are trying to solve, but in the end, what you have drawn is a tool. A tool to help you work through some thought experiment, something that only lives on as an idea, a concept, that concept being that in some theoretical space, two 1 dimensional points are connected, and that connection is thus called a line

> inb4 someone says they still don't get it

>>12238343
Good question, don't listen to the other moron. Points measure zero dimensional things (like discrete sets of points, in which case "measure" means "count.") Lines measure 1-dimensional things.
How is it possible that a line can do this? It's actually surprising that it is. This is a field of math called measure theory, which people usually don't learn until late into undergrad. Basically the way it works is you say, well I want the interval [a, b] to have length b-a. So you define that to be the length of that interval. So what's the length of any other set of real numbers? You take the set, cover it in a sequence of intervals like [a,b], and take finer and finer covers (more precise). each time you compute the total length of the cover. the limit of this sequence of lengths is the length of your set.
turns out this is really hard to justify as a good notion of length (e.g, if a set contains a subset, the subset is shorter, or, if you split a set into two pieces, the lengths add up, lots of little things like that) it's called "lebesgue measure."
so lebesgue measure has nothing to do with points, or how close those points are to one another. in fact, without starting with the length of intervals we'd have no idea what to do. this is because all the points that make up the line each have lebesgue measure 0. this is what you probably mean when you say they're zero dimensional. then anything with countably many points has lebesgue measure zero.
but a line has uncountably many points, which is a lot bigger. the whole point of measure theory is finding a way around the issue that a bunch of length zero things come together to form a length 1 thing, and this issue will never be solved if you try to start with points instead of starting with intervals.
but solving this issue comes with other problems. now because of all this uncountability business there's room to create sets which are so nasty that there is no way to assign a length to them.

>>12238437
>Again, you are still thinking of a line as drawn from a pen or the line on a computer screen.
Im thinking on a way that makes sense to me based on my experience

>A line has no vertical component, it is infinitely and perfectly thin.
The please show me such object, you have all the drawing technology to show me that, if it does exists, without the constraints of technique
Im saying youre describing a rectangular circle or a triangular circle

>Thinner than the thinnest thing you can possibly imagine
If it has any thinness at all, a thinness higher than zero, it stands to reason that it has 2 dimensions, length and width

>And that is why you cannot draw a line, you can make a scratch on your piece of paper that leaves an imprint of graphite on it, and that imprint may resemble an idea of a line, and you can use that idea to help you work through an imaginary problem you are trying to solve

If a line cannot be represented, and a draw imprint of graphite only resembles the idea of a line, there is no guarantee that anything done with such imprint with be transferable to the abstraction called line

>but in the end, what you have drawn is a tool. A tool to help you work through some thought experiment, something that only lives on as an idea, a concept

See above, this reasoning doesnt seem coegent to me

>that concept being that in some theoretical space, two 1 dimensional points are connected, and that connection is thus called a line

I linked the wikipedia article, it says that points arent one dimensional, they are zero dimensional, which makes even less sense to me

Now that I think about it, to get your abstract point you talk about, you would have to "zoom out" until that black dot almos disappeared (even then it would still have two dimensions, that is, length and width), and even then you wouldnt be close to the idea of a point. With that said, wouldnt the universe be able to be put inside a little dot if you zoomed out enough?

>>12238459
stop responding to the schizo he has no idea what he's talking about
also lines dont exist, neither do rectangles, we live in a 3d world.
they are theoretical objects, in the sense that we know what the real numbers are and we call that "a line" as well as appropriate embeddings of it in other spaces
also yes there are rigorous ways to understand what it means for a rectangle to approach a line by getting thinner and thinner

>>12238343
A point is zero dimensional, but it can exist within a space of higher dimensions such as a 2 dimensional space. A straight line is one dimensional, and just like points, can exist in a space of higher dimensions. A straight line can be used to measure things in the dimension which the line is in by using a line as a unit of measure, or in the case of a line with infinite length, by partitioning the line in equal segments and using the length of the segments as a unit of measure.

Lines are composed of the integral of infinitely many points in a direction, therefore it doesn’t matter that a point has no dimension

>>12238459
> If it has any thinness at all, a thinness higher than zero, it stands to reason that it has 2 dimensions, length and width
You didn't read the rest of the post
> If a line cannot be represented, and a draw imprint of graphite only resembles the idea of a line, there is no guarantee that anything done with such imprint with be transferable to the abstraction called line
Well I guess you're just way too smart for mathematicians.

Also I'm super drunk right now and kept calling points 1 dimension and lines 2, which would make my infinite rectangles pretty interesting

>>12238458
these sets are called "unmeasurable sets." but they're super weird and never show up in practice so they're not something to worry about. an example of an unmeasureable set would be: take the real numbers, for any x in the real numbers consider the set {x+q, q is rational}. this set is measurable. but, we have a bunch of these sets, pick one point from each such distinct set and put them together in another set. the resulting set will be unmeasurable. you can check this because an infinite number of copies of itself must have measures that add to 1. but infinitely many of the same number cant add to 1.

ok, why is the lebesgue measure the right one? why didnt we say [0,1] has length 3, [1,2] has length -4, etc. we could have done those things and we would have gotten different measures. but the lebesgue measure is special because it is translation invariant. i.e. if you move a set left or right on the number line, it wont change length just from moving. turns out the lebesgue measure is the only one that does this. so this is why we care about lebesgue measure, and how we measure the length of lines even though they are made of zero-length points.

>>12238458
>>12238488
> Guize, what's line?
> Ignore the guy trying to help you conceptualize the idea, here's a formal definition using concepts you've never even fucking heard of
> T-thanks anon. That was really helpful, now I understand. You're so smart, can I suck your dick?

>>12238458
>Points measure zero dimensional things (like discrete sets of points, in which case "measure" means "count.")
I think I understand what this means, you dont have to measure something zero dimensional, just say "it exists" and how many are there, like "there is something", nothing is said about the shape or form or that something, though it is counted
But how can one count something (that is, say how many there are, 1, 2, 3,...) that cannot be measured, seen, imagined, shown, represented or found? When I say "there is something", is because I can the visual difference between something and nothing
>Basically the way it works is you say, well I want the interval [a, b] to have length b-a. So you define that to be the length of that interval. So what's the length of any other set of real numbers? You take the set, cover it in a sequence of intervals like [a,b], and take finer and finer covers (more precise). each time you compute the total length of the cover. the limit of this sequence of lengths is the length of your set.
>turns out this is really hard to justify as a good notion of length (e.g, if a set contains a subset, the subset is shorter, or, if you split a set into two pieces, the lengths add up, lots of little things like that) it's called "lebesgue measure."
So lebesgue measure is a way to explain how lines can measure anything, it does that by saying the length of any line will simply be defined as the difference between two numbers "a" and "b", an interval [a,b] in other words, for real numbers it also says the length of an interval can be infinitely divided in smaller intervals
The last part about reals is what he said here
>>12238437
>A line has no vertical component, it is infinitely and perfectly thin. Thinner than the thinnest thing you can possibly imagine
The first part is interesting because it defines a line as the same thing as the intuitive distance between two objects, you can see the two objects arent stuck together

>>12238514
you mean the guy who is drunk and is spouting tons of nonsense about 2 dimensional lines and fractals?
OP asked how lines can have length, measure theory is how. not some dumb shit about lines being thin rectangles.

>>12238534
Yes, all that is right.
I think what gets hairy is that there are these disparate notions of:
>points in the real numbers
>adding/subtracting real numbers
>the order of real numbers, i.e. which are bigger than others
>the topology of real numbers, i.e. which are closer to others
>the metric structure of real numbers, i.e. what's the distance between two numbers
>the lebesgue measure on real numbers, i.e. how long are sets of real numbers
Each of these notions is directly influenced by all the notions above it, and lebesgue measure has to work together with all the notions to come up with something more interesting than "uhhh the length of a set of real numbers is just the number of points in the set" cause then if we measured things with this zero-dimensional perspective most sets would just have infinite length and you'd have no idea why [0, 1] is half as long as [0, 2].

>>12238543
Oh shit son, I thought he was asking what a line even was. Well shit, all you had to do to get him to understand was ask him to plot a rectangle using a standard graph using points such as [1,1], [1,5] [5, 1] and [5,5], then connect them. You can calculate the difference by just counting the spaces between. Making a rectangle dispels the concept that lines have width, and using the points dispels the idea that a zero dimensional object is useless. From there, you can draw curves, find midpoints, etc., all using lines. You want formal proofs, then you want more maths.

>>12238458
>so lebesgue measure has nothing to do with points, or how close those points are to one another.
How not? If it defines length as the size of an interval of numbers (size being determined by the subtraction of the biggest number by the smallest) you can count points and say the length between them
That solves the problem of the representation of intuitive length, but not the problem of points or lines

>this is what you probably mean when you say they're zero dimensional
Not really, unless i didnt understand your post, by zero dimensional i say what i understand, an object with no length, no width, no height, just something roughly undefined like "presence"

>More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built, meaning that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy. In particular, the geometric points do not have any length, area, volume or any other dimensional attribute

>then anything with countably many points has lebesgue measure zero.
but a line has uncountably many points, which is a lot bigger
I thought it was an axiom of maths that any number multiplied by zero would be zero as well? When you say
>a line has uncountably many points
"uncountably" is an adjective with the meaning of quantity, but how can there be quantity that cannot be represented by any known number like 10 or 100? If it is just a vague description, like "very big", it still implies a limited size, same for uncountable (so big you can't count), so any number of "zero dimensional" points should still not be able to form a line, it would only result in "nothing"

>the whole point of measure theory is finding a way around the issue that a bunch of length zero things come together to form a length 1 thing
I have a simpler idea, this may even be what your post was about and I was too dumb to understand it

>>12238458
>the whole point of measure theory is finding a way around the issue that a bunch of length zero things come together to form a length 1 thing, and this issue will never be solved if you try to start with points instead of starting with intervals.
I still have a small article to read from a philosopher who said he spent 30 years thinking about this point and line problem where he says he thinks he found the answer, so he could have a bttwr answer than me, this is mine though

Why not define a point, or a dot, as a simple two dimensional circle, and that will be considered the smallest unit and the smallest dimension in geometry, and it even could be said to have "size zero", even that wasnt the real case in reality, (as you obviously can see the point if you zoom in enough, though that would be increasing its size to more than zero), more accurately its size could be defined as a very close approximation to zero (like 0.00000000...1)?

There would be no such thing as a zero or one dimension, the fundamental dimension would be the second dimension, any and every object would be based on points, which in themselves would be based on the two vertical and horizontal lengths (two dimensions, each being inseparable, that is, not possible to talk about an object with zero vertical length but not zero width and vice-versa), of course these points' lengths wouldnt be literally zero, but they would be as close to zero as needed, (0.000...1), such that every geometric form would only be something close to what it represents

For further dimensions, like the third, you would just need to stack up a point in another dimension (height), such that you would get a very small tube that would be the basis of every 3 dimensional object

>>12238466
>also lines dont exist, neither do rectangles, we live in a 3d world.
if they dont exist how can you talk about them?

>>12238479
>You didn't read the rest of the post
I did, I thought you just repeated your point in the following paragraphs

>Also I'm super drunk right now and kept calling points 1 dimension and lines 2, which would make my infinite rectangles pretty interesting
Its interesting how this board seems to be full of alcoholics that seem to post only when i post as well

>>12238488
>take the real numbers, for any x in the real numbers consider the set {x+q, q is rational}. this set is measurable. but, we have a bunch of these sets, pick one point from each such distinct set and put them together in another set. the resulting set will be unmeasurable.

To pick one point from each distinct set, you must have looked into each set, that means you counted each set or at least could have counted. The resulting set ks measurable if you do a comparison between each point you add, so as to get the smallest and the biggest numbers

>>12238657
Oh you're still here. For the record and the rest of the anons here, I explained using the standard Cartesian graphs using points and explaining the difference between an idea and a model of the idea (line on paper) because he said he's still on a level where the letters are black... so just before Elementary Algebra. So yeah, cool, lebesgue measures, neat. What?

Anyways, here ya go: >>12238571
Plus all that other shit I said about whatever. Ask someone else, I'm gonna fuck off

>>12238488
>you can check this because an infinite number of copies of itself must have measures that add to 1
If the resulting set is consisted of only the same number over and over, by your definituon, the set is still measurable but the length is zero

>but infinitely many of the same number cant add to 1.
You start saying a set is countable if you can take the difference between the smallest and the biggest element, and now you say its defined by the number of elements it has, this is incoherent
And add means adding, which means addition, if you can add elements in a set it means it is countable or measurable

>why didnt we say [0,1] has length 3, [1,2] has length -4, etc. we could have done those things and we would have gotten different measures
It seems like a matter of convinience and consistency to me

>>12238514
>Ignore the guy trying to help you conceptualize the idea, here's a formal definition using concepts you've never even fucking heard of
I appreciate what you were trying to do, I think thats the important part of the discussion

>>12238272
2+2=5
Fuck wh!temales.

How to be good at math.

That's where im at

>>12238343
>If a point doesnt measure anything and a straight line is made of points, how does a straight line measure things?
You and I being in different places doesn't measure anything. You and I taking note of the fact that we're in different places let's us measure something. At the same time, a single point doesn't tell us anything other than the point exists. Any particular number of points doesn't tell us anything other than those points exists. Our noting the points can be related to each other in such a way that we can say something meaningful about that relationship is what lets us say meaningful things about those points (i.e. this is why a "straight line" is made up of points, because we can relate those points in such a way as to say, "there's a line").
You're conflating abstraction with reality but not really using either one, at the same time. This is quite literally something you should have grasped in a foundations course.

>>12238272
I am literally right behind “serious math” with Fourier series. I plan to take my first “serious math” class next semester.

>>12238769
How can people be good at math. How can I be good at math

>>12238773
https://4chan-science.fandom.com/wiki/Mathematics

>>12238773
Not that guy. I'm personally just barely into serious math.
Unless you're a once in a generation savant whose the right kind of autistic to be Be Good At Math™, the recurring theme is practice. Even those savants practiced math - literally, all they fucking do is math. The singular unifying factor among professors, researchers, and even geniuses has always been consistency and practice.
If you want to be good at math tomorrow, you should be practicing math right now.

>>12238775
Based.
Anything else?

>>12238782
Thank you for the advice

>>12238785

Textbooks:
http://gen.lib.rus.ec/
https://b-ok.cc/

Always get books with their solutions manual, even if it means getting an edition or two back. Even if you know an answer, look at the solution anyways, you might be solving it in a roundabout inferior way when there's a much better way of doing it

>>12238272
Are One-Time pad decryption and Random Sequence Extrapolation just utter memes? Not familiar with the others in that category so no clue how serious these are

>>12238793
Thanks

>>12238272
This pic is not well sorted but anyways: yang mills

>>12238437
>A line has no vertical component, it is infinitely and perfectly thin
no it just doesn't define the property width, it only defines length

>>12238568
>you'd have no idea why [0, 1] is half as long as [0, 2]
you can just say [0, 1] is a subset of [0, 2] and [0, 2] = [0, 1] union [1, 2] and 1-0=2-1. come on now..

>>12238427
don't listen to >>12238388
>Each of those lines are infinitely thin
NO, lines don't define the width property. when you define width you get 2d objects

Just give each line an unit surface. The shorter the line, the thicker it is. An infinitely short line would be therefore an infinitely thick line.
Then upscaling, give every surface unit volume.

>>12238272
will any of this ever bare any tangible benefits to our daily lives or are we just paying a bunch of nerds to play with numbers?

>>12239056
You made the bouncing accordion brick wall in my mind punch an imaginary stick figure by suddenly growing a third dimension. Stop that you

>>12239072
Sometimes it takes awhile for math to find useful applications. For the most extreme example I can think of, prime numbers were first written about in detail by the ancient Greeks, but had no practical applications until the 1970s, with the invention of public key cryptography. Or consider imaginary numbers; the first serious work on them was done in the 16th century, and calling them imaginary was originality a derogatory term Descartes used to mock them, but in the long run they have proven to be really useful in electrical circuit design and signal processing.

>>12238272
before genius
I ain't even gonna bother with the other useless shit

>>12238272
poincare conjecture

>>12238272
Why is control theory so deep?
Should be next to Laplace and Fourier transforms.
It's literally EE math.

>>12239186
I think the list is ordered by how difficult it is to write formal proofs for and not for how difficult it is to learn or use

>>12239199
Formal proofs for control theory either pertain functional analysis, systems of differential equations and/or finite dimensional vector space linear algebra.
Nothing too fancy really.

>>12238272
Chaos theory

>>12239205
There is differential geometric control which bumps up the level

>>12239205
yeah but that's only true of entry level linear control. there are far more complicated kinds of control systems.

>>12239199
write a proof that 2 + 2 = 4

>>12239199
yeah? what's so hard about formal proofs in "cohomology"?

>>12239334
Bro, do you even Principia Mathematica?

>>12238773
I unfortunately don't consider myself smart at all. However, If I'm having a hard time in a class, I try to find another textbook on the same topic. Reading another approach to the same topic can really help.
>>12238782
I agree with all of this. Learning the material well is important but that won't get you good at math. Practice is just as important! Good luck anon!

>>12239368
what the fuck is this shit
tranlsate into english please

>>12239412
it's an attempt to formalize all of math into 100% formal and symbolic language. in particular, from this proposition it will follow, when arithmetical addition has been defined, that 1+1=2.

>>12238272
Counting above human... You can exist and live without putting numbers on objects you know. So human > counting.

>>12238272
>first semester cs
>learn boolean algebra
>series math
kiss my feet niggers

>>12239435
fuck you nigger

the fuck is the octopus?

>>12238585
>you can count points and say the length between them
You literally cannot though. A continuum has uncountably many points. Any set which is Lebesgue measurable can be approximated by unions of intervals - which are uncountable.
>I thought it was an axiom of maths that any number multiplied by zero would be zero as well?
That's not an axiom, it is immediate from the definition of zero. Also, it is true for finite or countably many operations. When uncountability comes into play, you cannot assume such things, I think because it doesn't really make sense to consider adding up things more than countably many times.
> but how can there be quantity that cannot be represented by any known number like 10 or 100?
Try any transcendental number, like pi or e. More importantly, uncountable refers to the size of the set being larger than countable. Look up Cantor's diagonal argument if you want to see why the real numbers (or any interval) are not countable.
>I have a simpler idea, this may even be what your post was about and I was too dumb to understand it
I'm pretty sure simpler ideas will run into paradoxes or fail with pathological examples, as anon explained. That's why we formalize this with measure theory.

>>12238643
You are basically describing a discretized space. It's fine, but it's archaic, and it doesn't really address the question at hand, rather it just gets rid of the use of real numbers. We then lose important concepts like continuity - rather they become useless - if we only consider a discrete space. Also, you are missing a lot of definitions and you make a lot of contradictions to prior accepted definitions in math.

Random sequence extrapolation of course. That's why I can get these dubs. Check em

>>12238666
>that means you counted each set or at least could have counted
No. There are uncountably many such sets, so you cannot have counted. The axiom of choice is what allows one to pick one point from each set. Measurability is countably additive, but it is not uncountably additive.

>>12238696
>You start saying a set is countable if you can take the difference between the smallest and the biggest element
He never said that
>If the resulting set is consisted of only the same number over and over, by your definituon, the set is still measurable but the length is zero
No, because there are uncountably many elements in the set.

>>12239381
I'll try thanks a lot!

>>12239435
Gödel shattered that dream

>>12238272
Fuck math, engineering subjects get you money

>>12238272
Why is "serious math" empty?

>>12238272
Also the last bracket doesn't make sense.
The capacity of the human brain is everything until that bracket, not just that bracket.
You could say that is the limit of the capacity.

>Boolean algebra
>Not near the surface
What is this shit?

>>12238272

so deppp

how mathpilled are you?

>>12242633
That's way better than OP.

>>12238343
a straight line isnt made of points. the proof is that if you gave me a list of points that makes up a line i can always add one thats also on the line that is between two of the ones in the list. this is actually one of zenos paradoxs i believe.
t. math/physics fourth year undergrad

>>12239186
exactly, when I saw fourier series that far down I cringed at the retard that made this list

>>12238272
Decimals?

>>12238272
Years of studying and I still have yet to fully comprehend counting.

>>12238272
a bit past serious math

I skipped calculus and other boring crap, I'm doing abstract algebra. The image makes no sense, it implies a linear progression where there is none. You can learn maths in any order and find yourself in all levels of the picture. Is this some sort of quantum superposition?

I got to Algebraic Topology and said "this is stupid" then got a real job in Software.

> Random Matrices

OP confirmed idiot

>>12238272
>one-time pad decryption
what a meme, there is a braindead simple proof that that's impossible

>>12245098
Four colour theorem was considered brain dead simple to prove impossible. Until it wasn't.

Finished my degree :)
Get my certificate through the post mid November as graduation ceremonies have been cancelled. Not sure what to do with my life next, whether to do PhD (i have an offer) or just go into work.

But differential/algebraic geometry were the last subjects i did if you must know. Chaos Theory wasn't a subject on it's own at my uni, it was part of my 4th year Analysis class.

>>12245083
>I skipped calculus and other boring crap, I'm doing abstract algebra.
sure smells like undergrad category theorist

>>12238272
People actually believe this joke chart? Because it was clearly made as a joke.

>>12238272
Topics I've studied recently range from series all the way down to homeomorphism

>>12238272
>one time pad decryption

Isn’t that basically impossible?

>>12238272
Who made that shit up?

>>12245724
everything in the last tier is either trivially impossible (random sequence extrapolation) or gibberish (poly-dimensional topology)

>>12238272
>r/badmathematics

>>12243722
You're going to piss off the" real number" schizos with that

>>12238272
tfw only at vector spaces

>>12238272
Extrapolation of random sequence, I almost guessed lottery once, but in all tosses 70% completion. I bet, suddenly 0% completion and then 70% again after I didn't bet.

Same mathematics everywhere not cheats, when I bet right numbers, they changed, but I haven't been examining those new numbers, maybe they ware product of one more precision point switch on that numbers. But I was so embarrassed, I felt like getting slapped without no meaning.

>>12246557
I was in probabilistic loop, but somebody touched me, and it all went gone. Even computer software, don't be rude to members attempting to win a game, lottery is not much competitive sport and you don't need that much resources anyway, only if you'd like to achieve status without cooperation.

>>12238810
You don't have to be a genius to do one time pad decryption, you just have to not be an autist that can only do math. Mathcels can't see that and think it takes a genius to do it

>>12238272
Game theory isn't advanced mathematics, it's glorified sociology. Any random person can learn it by playing enough CoD.

>>12238272
>hairy ball theorem
>holy shit that can't be real
>looks up
>mfw

>>12238272
> one time of decryption

this is solved. It’s called a brute force approach

trivial transcendental number generators should be on this list

>>12238272
I'm halfway between serious math and genius level without being in STEM. This image can use some improvement.

>>12238272
You lost me after vectors.

>>12238343
>a point doesnt measure anything
retard