Could it be that most of higher mathematics, eg stuff like arithmetic geometry, is just nonsense...

At best they are approximations

There are no circles or spheres in the real world

>no spheres
>earth
Nigga u wat

I didn't know spheres, or even ellipsoids, had mountains and valleys

I completely agree with you, at some point, academia becomes so esoteric that unless you're completely involved and obsessed with the subject that you can understand what's happening, and even then, most of it is jsut work that's been fabricated in order to justify all the "grant money" that they're getting from the government.

This is why all research should be privately funded

The earth is a sphere moron.

But then only companies decide the progress of science, and unfortunately that's not something I'd like. A double knifed sword unfortunately.

>not something I'd like

didn't kno u were the fkn arbiter of what happens in the academy jeez

Sure, but how many branches of mathematics abolish the thought of the infinite? Because infinity clearly doesn't have any parallels to the physical world. I figure that was what OP was on about when he said "nonsense".

And as for , keep in mind that it's perfectly viable to have mathematics which don't correspond to our current understanding of reality. Not only because different maths model different systems and methods which are useful in different contexts and situations, but also because math for the sake of math is a fun diversion and good practice in creativity and inductive and deductive logic.

So the north pole is infinity or?

...

Yes the world is a Bloch sphere. Get with the times.

Of course it's nonsense. It happens to be so that nonsense helps us understand sensible things, though.

The Earth's surface is homotopy equivalent to the sphere under the most sensible topology (metric topology from being embedded in R^3), and the fibrant replacement is a CW complex: the sphere.

Topological results apply to the Earth. For example, I can tell you that there is a loop around Earth's surface at any given moment such that every point has the same temperature, or pressure, or sea level. Isn't that cool to you?

>a loop where every point on
>the surface of the sea level
>has the same distance to earth's
>core

Are you fucking with me?
How could that be true

Take a math class and you'll find out. Oh wait, math class is just a way for the evil hippie liberal media to control you, meaning you did do the right thing when you dropped out of high school.

I am majoring in chemistry. But ok

If it didn't exist, then the Ulam-Borsuk theorem is false, because I used that theorem to arrive at the conclusion. Assigning sea level to every point on the surface of the Earth is continuous with respect to the topology I described. So, we have a map [math] s:S^{2}\to \mathbb{R} [/math]. I forgot the details of my proof (I wrote it a year ago), but I basically found a way that Ulam-Borsuk generalizes up to guaranteeing a nondegenerate 1-sphere being assigned to a fixed value rather than just a nondegenerate 0-sphere.

The loop may be a small loop, mind you. Choose some island; you can imagine that there has to be some ring around it with the same sea level, since all of its sides go down into the ocean. That sort of thing can satisfy this existence theorem.

since when did adding positive numbers turn into negative fractions

Wow
>only true for radii of 0

You know that such a makroscopic thing like a beach of an island sounds pretty retarded if you image what sea is made of.

Water molcules

So you statement would be true if you observe for an infinite amount of time, but not at every instantaneous moment

Really makes me think

So what? Approximately true models give approximately accurate results, by continuity.

The Earth is most certainly not a sphere. Spheres don't have differing elevation levels.

I guess geometry is fucked then.
>implying you can draw a "line"

>reddit

...

Since when did adding an infinite amount of rational number give a finite result? You need a whole lot of machinery for that.

What are you even saying?

If regard the water as part of the surface of the Earth, the theorem works. It's still homeomorphic to a 2-sphere.

If you regard only the ground, it's still a 2-sphere, modulo overhangs. Please clarify what you are saying, because the topology I defined takes into account that everything is made of molecules.

>reddit

It literally isn't, retard.

Difference from a sphere are litterally less than the variations on a cue ball

>redditposting
Could you go back to gorillaposting? At least gorillas are intelligent.

>what is chaos theory

Which also isn't a sphere.

>implying you can ever know whether your axioms are true

laughing_hume.jpg

When someone brilliant revolutionizes mathematics by inventing a new field, like Grothendieck's algebraic geometry or Lurie's work on infinity-categories, it's natural that few other people at the time will understand. Sometimes it takes many years for enough people to understand and enough details to be filled in before the mathematical community decides that yes, it does make sense. Sometimes they decide that no, it doesn't really make sense and the guy writing this shit is a complete loon.

It's pretty tough, you have to put a lot of faith into people's abilities to referee papers and books. Every so often you'll hear a horror story about someone publishing a paper in a prestigious journal and then 10 years later someone finds an error and the result ends up being totally wrong. By and large though, these papers are relatively minor and don't purport to change the face of mathematics or anything. I'd still wager that at least 95% percent of all math papers don't contain major errors or reference papers which do.

It's kind of hard to maintain the ideal of complete rigor, I guess that's what I'm trying to get at.

when someone reads "arithmetic geometry" and assumes they meant "analytic geometry"

Axioms can't be false. Why does nobody on this board understand the concept of an axiom? It's not even complicated.

You don't really think arithmetic geometry is high-level do you?

when someone doesn't realize that smooth embeddings don't need to be conformal

Look at this brainlet who quotes Hume without knowing what Hume actually said.

> most of it is jsut work that's been fabricated in order to justify all the "grant money"

LOOOOOL no, I assure you, there are people who do mathematics because they think it's important, and acquire grant money by being able to convince others of the same. And historically yes, mathematics has been important.

>there exists no intermediate between hard and easy
(You)

what is convergence

Look at this brainlet who doesn't know what a quote is

You don't know what that is? It's simple algebra, user.

Do you really need the Ulam-Borsuk theorem? If you assume the temperature function $S^2\to \mathbb{R}$ is smooth and non-constant, then Sard's theorem assures us that there is at least one regular value, so if you take its inverse-image then you get a closed 1-manifold (i.e. a disjoint union of circles) where the temperature function is constant.

>clearly means true to life

It's advanced enough that most mathematicians never learn it.

It's an oblate spheroid you insignificant mouthbreathing brainstem.

Is there a version of Sard's theorem for just continuous functions? My result only relies on the temperature function being continuous, so maybe that is why I needed Ulam-Borsuk. I don't know very much analysis, though. Sorry.

That's a ball, it's boundary is a sphere .

Kek. Someone cut the British vs American English differences in spheres, balls, circles, disks, and circumferences.

Well, it's not completely bizarre math papers don't usually have errors? I wouldn't expect that. Why is that?