Why isnt there a unified theory of math

You have a unified theory for physics?

>>9067694
no but physicists strive for one

mathematicians don't think about their own unified theory in their field though

why

ZFCNBGKPTG set theory?

>>9067692
if you knew what you were talking about you'd understand that's a silly question.

>>9067692
Because we can construct whatever mathematical fairytale lala land we want as long as it logically consistent.

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>>9067692

Math is based on axioms, and anyone can build a completely valid (don't get nitpicky, Gödel posters) mathematical system based on whatever axioms they like. There are, in a sense, an infinite number of universes for mathematicians to consider, while physicists are only responsible for describing one.

>>9067692
It's impossible. By Godel's incompleteness theorem, many theorems don't have proofs. Furthermore, more math papers in each field are published every year than can possibly be read, and it is likely that most published proofs are incorrect, since most large open-source programs have bugs even after being reviewed by hundreds of programmers. Even Gauss's original proof of Fundamental Theorem of Algebra is incorrect because it relies on the Jordan curve theorem. Furthermore, engineers never learn proofs but can still apply math effectively.

>>9067766
>engineers never learn proofs but can still apply math effectively.

Why isn't there a unified theory of PDEs?
Why are retarded theorems on primes so difficult to solve?

>>9067692
Gödels completeness theorem (mind you, not the incompletness one) says first order logic proves all things provable in a model, and that's as good as it gets. And it's good.

https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem

In that sense, there is one.

>>9067766
Engineers can still apply math effectively?

Let's say they do some calculations and make conclusions from it and then do something valuable.

>>9067692
>>9067697
>>9067694
There will be an analogous result in physics to the incompleteness theorems within the coming century. Mark my words.

>>9067692

Because not so long ago, mathematicians sought out to prove all of mathematics. They thought they could eventually "solve" math, and that any theorem could eventually be proved given enough time and hard work.

Then some FUCKSTICK named Godel, who wasn't even a fucking mathematician, but instead was a type of shitstain philosopher known as a Logician ruined everything for everyone by writing a completely rigorous and true proof saying that any logic system that possesses operations like arithmetic will inherently have unprovable statements.

No one believed it until they did and it ruined fucking everything because not only did a goddamn philosopher ruin math, he showed that math is essentially philosophy with unknowable, unanswerable questions.

And to make things worse, this logic may apply to physics as well, since physics uses arithmetic. It's horrible. I wiSH GODEL NEVER EXISTED THE WORLD IS INHERENTLY UNKNOWABLE I FUCKING HATE PHILOSOPHERS

>>9067692
Because a bunch of lazyshits believed in Gödel's schizophrenia before he killed himself. It might even be a conspiracy against mathematics.

>>9067907
Yeah that makes no sense.

>>9067917
The superdeterminism theorem is coming, just you wait

>>9067925
That might make some sense, but it has nothing to do with incompleteness theorems.

>>9067931

Not that guy but it does, because the incompleteness theoresm pertain to arithmetic like operations which certainly includes the realm of physics.

It is entirely likely that physicists will discover that their field has unanswerable questions, in fact, I would venture to say that it is certain.

>>9067961
Even if the field progresses to the point where no further experimental evidence can be gathered that wouldn't be anything like the incompleteness theorems.
And the mathematical incompleteness theorems are not relevant to physics, because physics is not mathematics. If irreconcilable problems were found in the current foundations of mathematics it would be entirely acceptable for physical theories to simply ignore the issue.

>>9067961
But that kind of incompleteness doens't really apply to physics.
Physics is happy to use mathematical results that aren't logically proven if they produce the right results in reality. And if something has to be taken as an axiom then that's fine if it gives the right results

>>9067961
The closest thing to an incompleteness theorem in physics would be say proving a GUT or ToE is fundamentally impossible.

>>9067986
The big problem I think is that there are theorems which can be assumed as true or false and they will lead to different results. In physics this may mean that assuming something as an axiom in one area may break physics in another area, or that the "axiom" adequately describes phenomena, but only part of the time, or only certain kinds of phenomena.
I honestly don't know how physics could produce a unified theory of everything by using assumptions that may be inconsistent

>>9068014
I think those kinds of conflicting assumptions would either be a result of the theory being practised being wrong like an approximation and we wait for someone to come up with a better theory, the end result has either got to be a GUT or as this guy says >>9068013

Personally (which counts for nothing on an anonymous Mongolian cartoon board) I think it would be unlikely that we can't describe all of physics with a GUT when all of physics is physically happening all at once, just seems like a contradiciton

>>9068021
It may be possible to describe all of physics, but we would have to transcend physics and create a logical system that *contains* physics. Godel's theorem basically says that an axiomatic system (like physics or mathematics) can't be fully described using the same system. But it is possible to go "a level up" and describe the system using another system that contains it.

In other words, if we are to "solve" physics with a theory of everything, we would (probably) come up with another system that describes and contains physics. But then this system would not be able to fully describe itself...
Maybe a ToE is possible, but it may require structures beyond the field as we understand it.

>>9068032
>we would have to transcend physics and create a logical system that *contains* physics
Why?

>>9068038
Because Godel's theorem states that any system of logic that is sufficiently technical enough (axiomatic) and possesses arithmetic like operations *cannot* fully describe itself. This does have implications for physics, but as a whole, the community is unsure of what extent. It certainly means that physics will have some statements that are unprovable or knowable, but we aren't sure if the phenomena described will be relevant to a ToE

Assuming that the statements are relevant to the ToE, then the only way to get around this is to create a system of logic that contains physics, which is certainly possible. Then using the structures of the containing system, one could probably describe a ToE.

>>9068032
I disagree with needing a logical system that contains physics. With the different nature of science from maths physics does have some more freedom in not strictly needing logical proofs for everything, and we could kinda of cheat like with renormalisation.
I think it could be possible we come up with a GUT that has a description for everything that is as accurate as we can measure with no anomalous results that aren't explained by the GUT without the problem of needing to turn some phenomena into axioms like "this happens just because" since problems about those kinds of things fall more under metaphysics

>>9068053
We can agree to disagree. I am not a logician or a trained physicist, so much of what I am saying is conjecture. But if physicists eventually realize they cannot produce a GUT, I will not be surprised.

I *will* be surprised if a GUT does turn up, however.

>>9067692
One main reason would be that any math is grounded in the axioms you choose. Change your axioms and you have a different kind of math, so how would one unify two completely different mathematical systems? Physics, on the other hand, is an empirical science, and so we assume there only exists one physics, viz. the physics that best describes the universe. As such, it makes sense here to seek a unified theory of physics.

>>9068060
I do see it could be possible that we do prove that a perfect GUT could be impossible bc of Godel but that may only manifest itself when we make measurements that are so precise to the point of ridiculousness, and for all intents and purposes we do have what we would today think of as a functional GUT that only falls apart when looking at some near immeasurable scale. If that is the case it would probably come down to opinion if it is a true GUT, and if it is proved we will never be satisfied then maybe most serious scientists would be satisfied

Thanks for the civil discussion

people say Godel is the greatest logician of the 20th century

but remember that he believed in god

Because 0=infinity

The people saying "Godels theorems" dont know what the fuck they are talking about.

Gottlob Frege and Bertrand Russell were working towards a logical foundation to mathematics. They werent successful. Russell basically gave up, and Frege retired. Frank Ramsey and Wittgenstein were the next generation of that tradition of mathematical philosophy, but Ramsey died and Wittgenstein changed his mind. Anyway, David Hilbert literally held a convention where he declared his intent to start a new approach to discovering the foundations to mathematics called Formalism, and Godel was part of that effort. But the original Logicists, didnt see it as a continuation. Ramsey, Frege, and Wittgenstein all saw Formalism as pretty confused.

>>9067879
apparently no unified theory of even ODEs can exist, since if one would exist, an ODE can be modelled to show that the halting problem has a solution, which would be incorrect.

>>9067697
Because physics is trying to guess how nature works and they call collections of guesses a "theory". A "theory" in physics might be correct or might be wrong.

In mathematics, there is no theory about something in the same sense as above. You don't try to make an educated guess about how things work. It is just pure truths derived from certain intuitively "obvious" axioms by using simple logic.

>>9068204
How about the subset of ODEs that have a nice solution?

Wtf, I have yet to find some branch that doesn't use set theory as it's language.

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>>9067913
topkek

The unified theory of mathematics is 0=infinity.

>>9067692
*there

>>9068204
>halting """problem""" has a """solution"""
>>>/g/
Retard.

>>9067692
>Math
>Theories

You seem to be high on some meth right now.

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>>9067913 >>9067697 >>9067766 >>9067893 >>9068052

Godel & Most Philosophers ruined Math.

Most Philosophers are a bunch of retarded screaming "I don't know nothing" & "you cannot know nothing"

Philosophers preach pseudoscience bullshit garbage that "looks deep & profound"

>>9068200 Gottlob Frege and Bertrand Russell tried solve the mess that Godel left.

Godel
>I don't know nothing! You cannot know nothing!
Socrates
>I don't know nothing! You cannot know nothing!
Plato
>I don't know nothing! You cannot know nothing!
Kant
>I don't know nothing! You cannot know nothing!
Hegel
>I don't know nothing! You cannot know nothing!
Scientists
>I have a Theory

>>9070294
wow, you really know jack all about philosophy

>>9070336
Kant's Critique of Pure Reason says that Absolute Truth cannot be reached by our Senses or Intellect. So basically
>I don't know nothing! You cannot know nothing!

>>9070336 >>9070294

Hegel said that Absolute Truth cannot be reached, Momentary Socially Constructed Truth changes over time by Dialectics. So basically
>I don't know nothing! You cannot know nothing!

>>9070336
Plato in his Theory of Forms preached that We only can reach the Truths in our inner mind. We can never understand plenty the reality around us. So basically
>I don't know nothing! You cannot know nothing!

>>9070336
Socrates, the greatest Philosopher of all time said "I know that I know nothing"

So basically
>I don't know nothing! You cannot know nothing!

So basically most of Philosophy are a bunch of retarded who "dunno nuthin" wanna looks like a "deep & profound" intellectual.

>>9070349
>>9070351
>>9070356
>>9070362
cute trick.
but its natural that the truths are multitude, obviously so. philosophy is just creating a set of premises and then taking them to their logical conclusions. you know a lot but know very little. god is down here bud, you arent going to find him up there.

>>9067692
Most everything in math can be related to physics somehow, you just don't know how.

>>9067913
Godel was a mathematician. You know, a mathematical logician? It's obvious you don't study math

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>>9067692
Haven't some people tried that? Pic related.

https://mathoverflow.net/questions/29232/the-unification-of-mathematics-via-topos-theory

>>9067692
What the fuck do you even mean by this?

There is nothing to unify in math. It's entirely abstract.

There is stuff to unify in physics - the physical world exists outside of the math we use to model it.

>>9067692
What the fuck is a "unified theory"? Do you mean set theory and logic? That's the implicit foundation that the average mathematician works with.

>>9067692
>Why isnt there a unified theory of math
...bcoz you have not yet made it, fgt pls