The title basically. Any mathematical theorem holds only in the axiomatical system its in (obviously some systems are stronger than others but still). If you change the axioms, the theorem might be wrong and there is really nothing stopping you from changing the axioms (unless you think they're "interesting"). So in their pursuit of rigour and certainty, mathematicians have made everything relative.

Now, don't get me wrong, this is precisely why i love pure math. I love the honesty and freedom of it. But sometimes if feel like it's all just a game. What do you guys think?

It is unfortunately very late, and my undergrad physics friends and I got quickly distracted by the names and units of the derivatives and antiderivatives of position. It then occurred to me that when going from velocity to displacement (in terms of units), it goes from meters per second to meters. In my very tired and delusional state, this made no sense because taking the integral of one over a variable with respect to a variable is the natural log of that variable (int{1/x} = ln |x|). So, from a calculus standpoint, the integral of velocity is displacement and the units should go from m/s to m ln |s| (plus constants of course).

This deranged explanation boils down to the question: what is the log of a number with a unit? Does it in itself have a unit?

I am asking this from a purely mathematical and calculus standpoint. I understand that position is measured in units of length and that the definition of an average velocity is the change in position (meters) over the change in time (seconds) leading to a unit of m/s. The point of this question is not to get this kind of answer, I would like an explanation to the error in the math above (the likely option) or have a deeply insightful and philosophical question that could spark discussion. This answer also must correspond to an indefinite integral, as if we are integrating from an initial time to a final time the units inside the natural log cancel and it just scales the distance measurement.

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So I got into an interesting and lengthy conversation with a mathematician and philosopher about the possibility of infinite collections.

I have a very basic and simple understanding of set theory. Enough to know that the natural and real numbers cannot be put into a one to one correspondence.

In the course of the discussion they made a suprising statement that we turned over a few times and compared to the possibility of defining an infinite distant on a line or even better a ray. An infinite segment. I disagreed.

However, a segment contains an infinite number of points (uncountable real numbers), and it is infinitely divisible (countable rational numbers), but, and this seemed philosophically interesting, a segment cannot be defined as having an infinite number of equally discrete units.

Im am not realy great at math so maybe this will not make any sense , but why is multiplication first. From what i could find online multiplication is the oldest and most powerful calculation operation, but what is that was wrong from the start did we possibly hinder our progress. Mathematicians say Math is the language of the universe and if we ever discover aliens we could communicate with them through math because math is math and its the same everywhere. But what if we started learning the universal language of the universe all wrong maybe somewhere else subtraction is first and they are light-years more advanced then us.

Sorry if there are some grammar mistakes english is not my first language.

there's a room that is colored white that contains an object shaped like a box colored black, inside there's an abstract mechanism that flips a 2-sided coin painted yellow that either results into an head or a cross, you have to guess the results of each coin toss but there's no way to look directly inside the box without breaking the mechanism and going against it's fixed rules. what is the right way to calculate and achieve the exact same results as the mechanism flipping the unviewable coin object?

For example, Euler's number is often interpreted as being directly related to exponential growth. Or there are lots of ways to interpret the Golden Ratio, such as the "most irrational" number, or as the ratio of growth for successive addition, or as an answer to the quadratic x^2 -x -1=0. I was just curious if there are any other interesting ways to interpret or approach numbers like pi, e, or some other number I haven't mentioned.

I want to start by clarifying that this post is not about whether informal proofs are good or bad, but rather how we tend to forget that most proofs we deal with are informal.

We often hear, "Math is objective because everything is proved." But if you press a mathematician familiar with proof theory, they will likely admit that most proofs are more about intuitive logic applied to an intuitive understanding of ZFC (Zermelo-Fraenkel set theory with Choice). This weakens the common claim of math being purely objective.

Think of it like a programmer who confidently claims they know exactly what their code will do, despite not fully understanding the compiler—which could be faulty. Similarly, we treat mathematical proofs as unquestionably correct, even though they’re often based on shared assumptions that aren’t rigorously examined each time.

Imagine your professor just walked through a complex proof. If a classmate said, “I don’t believe the proof,” most students and professors would likely think poorly of them. Why? Because we’re taught that “it doesn’t matter if you believe it—proofs are objectively correct.” But is that really the case?

I believe this dynamic—where we treat proofs as beyond skepticism—occurs often, and it raises the question: Why? Is it because we are expected to defer to the consensus of mathematicians? Is it some leftover from Platonism? Or maybe it's because most mathematicians are uninterested in philosophy, preferring to avoid these messy questions. It could also be that teachers want to motivate students and don’t want to introduce doubts about the objectivity of math, which might be discouraging for future mathematicians.

What do you think? I highly value any opinion you can give me on both my question and propositions. As a side note, you might as well throw in the general aversion to not mention rival schools to the kind of formalism that is common today. Because "duh they are obviously wrong" which is a paraphrase from a professor I know personally. Thank you.

I’m just wondering if i am looking at things correctly. So from my understanding the core “logic based statements” or axioms are described sometimes as statements that are assumed to be true but I kind of look at it like statements that coincide with basic human logic.

But if that is the case then doesn’t the scientific method just output systems of logic that just “work the best” and give the most consistent output.

Square-free integers are the integers which prime factorization has exactly one factor for each prime that appears in them. The square-free integers have an even number of prime factors or an odd number of prime factors. I am curious whether the order of the square-free integers with the even number of prime factors and the odd number of prime factors could be controlled by a random walk.

After some time of thought and reading, I've come to this conclusion.

I don't think it's controversial to say that mathematics is invented. The Platonist conception of mathematics does not hold up to the logical incompleteness of math's foundations. (Gödel's Incompleteness Theorem) I think it's much more accurate to view math, in its entirety, as the creation of axioms and the "discovery" of their consequences. Euclidean and Non-Euclidean Geometry are a great example, where using a different fifth postulate gives you different geometries, and each different geometry is fully determined when the axioms are.

Same with zero-ring arithmetic, which you get by assuming 0 has a reciprocal, and which yields a result in which every number equals 0. By starting with different assumptions, you can develop different maths. Some axioms and their consequences are more useful than others, but use or function does dictate existence or fundamentality.

I imagine that there are an infinite number of maths, each dictated by a unique combination of axioms. They are a priori because they constitute knowledge obtained without any experience whatsoever. Using invented axioms, which form part of an infinite possibility of combinations, you can know that some statement conforms to some axiom. If a=a, then 2=2. I think the idea of a quantity can exist independent of the intermediaries we use in the real world, for example, if there are 3 pencils, the quality of there being 3 of them is not contained within any of them, it is a relation between objects that is subjectively imposed by the observer. Even though humans "discovered" the idea of numbers through direct observation of their surroundings, the idea of the integer 3 is perfectly logically consistent within an independent system of axioms, even if you've never seen 3 pencils.

I haven't gone very far into this area of philosophy, but I find it deeply interesting. Please be kind in the comments if you disagree, and especially if I'm factually wrong!

Dont be a bully.

How can I turn a diameter into a height vector? I want to measure boobs and I have bust size but I just want to know the height from the beginning of chest to the tip of nipple. Is there a way I can calculate it easily?

No harassment, please.

I don’t really know what field of mathematics this belongs in so will post here, but here is a bit of a thought experiment I haven’t been able to find anything written on.

You have an infinitely flexible/elastic 1 meter hollow rubber tube. One end (let’s call it end A) is slightly smaller than the other such that it can be inserted into the other end of the tube (let’s call this end B) making a loop. The tube surfaces are also frictionless where in contact with other parts of the tube.

So one end of the tube has been inserted into the other end. You slide the inserted end 10 cm in. Now you push it in 10 more cm. The inserted end of the tube (A) has travelled 20 cm through end B toward the other end of the tube - itself! The inserted end is now 80 cm from itself. Push it in 30 more cm. End A is now 50 cm from itself.

What happens as you push it in further? It seems the tube is spiraled up maybe but that isn’t nearly as interesting as the end of the tube getting closer and closer to itself. End A can’t reach itself and eventually come out of itself. There is only one end A. So what happens at the limit of insertion and what exactly is that limit?

I can’t get my head around this because even inserted 99 cm, end A is 1 cm away from coming out of itself. So if there was a tiny camera inside this dense spiral of tubing, outside of but pointed at end A, it seems as you peer into end A, you would see end A coming up the tube 1 cm away from coming out of itself. But would there be another end A 1 cm from coming out of that end A? And another about to come out of that end A? And so on. I say this because there is only one end A so anywhere you see end A, it has to be in the same condition as anywhere else you see end A. But there is only one end A. So this clearly can’t happen. So what really goes on here? And again, what is the limit (mathematically I guess) to pushing one end of a tube into the other end of the same tube?

I’m assuming this has been milked to death in this forum, but when I look at how godels work is implicated in our models of physical systems, I see a wide diversity in opinion.

My path is in neuroscience, but I am of the opinion that our current frameworks involve assuming brain behavior correlations are bilinear and that reductionism and building our knowledge from the ground up may help get rid of some implied magic or some implied notion of cognition just magically emerging from nothing.

I also dabbled with a project idea involving looking at how specific rule sets lead to different types of emergence in boo lean/classical systems and seeing if I could develop rulesets based off of quantum rulesets or rather logic developed from how qubits and quantum circuits behave to make a larger argument about the incompatibility of boo lean logic and quantum systems.

I am admittedly terrible at math, but godel and turings work has interested me and I can’t get a solid answer about the implications of the incompleteness theorems past a point of “all models of the known universe will be incomplete to some degree” and the other extreme of “it only means that proofs are incomplete”

I was wondering what your take was on godels work and it’s implications in our models of any complex system(s).

There is too little space... joke in the link.

https://gist.github.com/godcodehunter/750ab86eacb426b15581ed1357df3990

You'll be lying under the table for 0 hours!

P.S.S.S.S.S.S.S.S...∞

Metaphysics is bullshit, 🤘🤘🤘🤘🤘🤘
All philosophers are bums. 🤘🤘🤘🤘🤘
The ultimate purpose of existence 🤘🤘
Is to live f*cking awesome

I am conducting some reasoning on solving one basic theorem, I am not entirely sure of its validity.
If basically I am doing some reasoning about the non-existence of the cube a^2*a^n for n>0

https://preview.redd.it/wt78c16zmeed1.png?width=1892&format=png&auto=webp&s=23f39dded320a775db0116d4f873fe809a3c105b

https://gist.github.com/godcodehunter/750ab86eacb426b15581ed1357df3990

I understand that this is not the place for simple questions. But I'm too stupid and there's no one to help me, I like math but I just can't wait. I would like to get some help, help me I'm completely confused...

Asking for a friend. I'm round about 99.999% sure it'd stay irrational

Hello everyone I’m reading a book on Arithmetic by Nicomachus, if anyone is familiar with this work or related subjects, can you please explain to me what does he mean by saying ( the self is Even X Even) what I knew from the context is that when numbers (even in name and value) are reduced to half, the result will pan out to the indivisible monad, such as take 64 (32, 16, 8, 4, 2, 1). What does Nicomachus imply by the word (self)? Is it OUR SELF ? and which part exactly? Is it the soul? My head is messed up 😗

Thanks