**8.146 soft-question questions.**

What are some notable or somehow generally useful examples of sequences defined by linear or non-linear recurrence relations?
I myself cannot think of anything other than Fibonacci numbers:
$$
F_0 = ...

I begin this post with a plea: please don't be too harsh with this post for being off topic or vague. It's a question about something I find myself doing as a mathematician, and wonder whether others ...

So I recently finished studying Spivak's calculus (excluding the chapter on construction of the real number system) and I'm almost done with Abbott's understanding analysis, what should my next step ...

I'm pretty good at "school math." When I solve a problem, all I need to do is repeat the steps that I learned. Most of the "school math" questions on a worksheet are basically the same but with ...

While trying to understand set theory from categorical perspective i.e. elementary theory of category of sets (Thanks to Lawvere), I am confronted with the situation where I need to construct ...

What is the meaning, when it is the irrationality of a constant?
I understand that irrational means can't be represent as a fraction.

I am a layman interested in mathematics, and I would like to hear mathematicians' views on the following: Is it normal to be picky about mathematical stuff you find interesting?
I ask because 80% of ...

A purported existence of a standard model of such theory as ZFC has been a cause of discomfort for a number of experts.
Taking a strong Platonist view of entities and their collections, etc., in a ...

What is calculus from the first principle?
This is a very difficult concept to understand. Can anyone give me a simple explanation of it.

I would be very glad if someone could point me to modern reviews/surveys on these topics.
To be concrete, I'll provide some examples:
S. Smale, Differentiable dynamical systems
D. V. Anosov, On the ...

How did the ancient Greeks discover formulas for volume and surface area of different objects, e.g. of a sphere? They did not know about integrals, so there must another way?

I'm a maths teacher and want to create a calendar for my classroom.
I'm looking to compile some interesting facts about each of the numbers 1 through to 31.
The hard part is they must be at a ...

In the past, how did they calculate the angles and sides of a right angle triangle without using a calculator?

A long time ago I studied mathematics at the University of Stockholm. I had a romantic view of modern algebra and manage to make the first two algebra courses by self studies in order to immediately ...

I always find myself wanting for a clear explanation (to a college algebra student) for the fact that horizontal transformations of graphs work in the opposite way that one might expect.
For example, ...

What is the purpose of taking the curl of both sides of Maxwell's third equation? I'm fully able to follow this wave equation derivation, but I don't understand the initial premise of taking the curl ...

I am a high school student who has finished the standard hs math curriculum. After working through an intro to proofs, logic and set theory (Velleman's How to Prove It), I am looking to study some ...

I was reading about Hodge conjecture on Wikipedia but it started with the assumption that $X$ is smooth projective.
If $X$ is a smooth quasi-projective variety, then corresponding to smooth sub-...

A circle is divided into 360 little parts called degrees.
Why or how did they choose that figure? Is there a very strong reason for that or it just a accidentally choose.

Many math textbooks and papers often introduce certain variables that are different, but the symbols chosen to represent these variables are often very similar.
For example, if one variable is ...

$D \subset \mathbb R$ and we have two functions $U: D \to \mathbb R$ and $L: D \to \mathbb R$, with the given property that $\forall x \in D: U(x) > L(x)$.
Because $U(x) \neq L(x)$ there are ...

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...

I am studying linear algebra and I am trying to get a better intuition on how I should think about finite dimensional real inner product spaces.(I am doing this since for example in Analysis it is ...

Everyone in high school learnt about Pythagoras theorem: $a^2+b^2=c^2$
Why It is so important that we have study it in school?

e.g. $12$ can be expressed as a product of its factors: $2 \times 6, 3 \times 4$. The composites can be decomposed further.
$12$ can also be expressed as a sum of its ...

Derivatives, both ordinary and partial, appear often in my mathematics courses. However, my teachers have never really given a good example of why the derivative is useful. My questions:
Other than ...

This question is related to rough path theory. A link to wikipedia is: https://en.wikipedia.org/wiki/Rough_path
I can understand to an extent how to calculate signatures given a path. I am interested ...

I'm a math teacher. Next week I'll give a special lecture about number theory curiosities. It will treat special properties of numbers — the famous story with Ramanujan, taxicab numbers, later numbers ...

There are some really inspiring examples of blind mathematicians. However in my experience I also think problems inside my head using words. So I was wondering if there are some examples of deaf ...

This has been rangling around my head for awhile. With the death of Hilbert's program via Gödel's Incompleteness Theorems (and the prior damage done to Logicism via Russell's Paradox), have ...

edu-active.com is a website promoting events, internship and job opportunities and interesting projects, but it sadly mostly posts about political, social sciences which isn't really my interest. So I ...

What are the basic things (about when and how) to be kept in mind while proposing a conjecture in Mathematics. Should it accompany solid efforts at proof. When should any one think of proposing a ...

Looking up dictionary definitions of algebra geometry is pretty unsatisfying as they are usually along the lines of
"the branch of mathematics in which letters and other general symbols
are used ...

I don't know if this is the best place to ask this, but I couldn't think of another place where I could get lots of responses from people with mathematical experience. As I quite enjoy and devote a ...

What is the most unusual proof that
$$1+2+\cdots+n=\frac{n(n+1)}{2}?$$
Consider, for example, the following. We have
$$1+x+x^2+\cdots+x^n=\frac{x^{n+1}-1}{x-1},$$ thus differentiating we obtain
$$1+2x+...

One of my acquaintance who is a math major undergraduate once told me that most students at his level focus on problem solving and ignored understanding proofs of major theorems, for example ...

Has anyone written a paper on the mathematics of version control systems?
The background for this question: Many people are now studying the mathematics of computer systems.
However, one aspect of ...

I am trying to make a list of basic operations or relations on sets, such as:
Union
Intersection
Complement
Inclusion
as well as ways of building new sets:
Subset
Cartesian product
Power set
...

I would like to know more about this formula (via the Worldwide Center of Mathematics website):
$$\frac{(x+y)^n}{x}=\sum_{k=0}^n\binom{n}{k}(x-ak)^{k-1}(y+ak)^{n-k}$$
What is $a$? Does the formula ...

I learned recently that there are mathematical objects that can be proven to exist, but also that can be proven to be impossible to "construct". For example see this answer on MSE:
Does the existence ...

I have been studying preadditive categories similar to specific types of rings. See for instance here. The clearer answer I have found is in this article. The result shown is that the category of ...

Some (neccesary) background and motivation for my question:
In some of my undergraduate math classes, specifically my proofs course, I have been required to use the $\Rightarrow$ symbol to denote any ...

I have a question about the irrationality of $e$:
In proving the irrationality of $e$, one can prove the irrationality of $e^{-1}$ by using the series $$e^x = 1+x+\frac{x^2}{2!} + \cdots + \frac{x^...

What topics should absolutely every applicant have studied.
I believe on overview of essential topics would include
Linear Algebra
Topology
Real and Complex Analysis
Geometry
Algebra
I am hoping to ...

I want to teach a short course in probability and I'm looking for some counterintuitive examples for it. Results that seems to be obviously false but they true or vice versa...
I already found some ...

In some kind of old mathematical text, writers use notations like following.
I guess at the left side it is written as "G".
My question is where can I find a list that contains that kind of ...

The book I'm reading introduces polynomials over a field and proves the statement that a polynomial of degree $n$ has at most $n$ zeros. They do this by using division algorithm and induction.
Then ...

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