Highest scored questions

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are ...

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $\frac{\textrm{d}y}{\textrm{d}x}$ is not a ratio. Couldn't it be interpreted as a ratio, because ...

So this is supposed to be really simple, and it's taken from the following picture: Text-only: It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will it ...

I hesitate to ask this question, but I read a lot of the career advice from MathOverflow and math.stackexchange, and I couldn't find anything similar. Four years after the PhD, I am pretty sure that ...

What is wrong with this proof? Is $\pi=4?$

Background. If $R$ is a commutative ring, it is easy to prove $\dim(R[T]) \geq \dim(R)+1$, where $\dim$ denotes the Krull dimension. If $R$ is Noetherian, we have equality. Every proof of this fact I'...

As I have heard people did not trust Euler when he first discovered the formula (solution of the Basel problem) $$\zeta(2)=\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$$ However, Euler was Euler ...

Here's my issue I faced; I worked really hard studying Math, so because of that, I started to realised that I understand things better. However, that comes at a big cost: In the last few years, I had ...

In my linear algebra class, we just talked about determinants. So far I’ve been understanding the material okay, but now I’m very confused. I get that when the determinant is zero, the matrix doesn’t ...

$\pi$ Pi Pi is an infinite, nonrepeating $($sic$)$ decimal - meaning that every possible number combination exists somewhere in pi. Converted into ASCII text, somewhere in that infinite string of ...

This is a problem that has haunted me for more than a decade. Not all the time - but from time to time, and always on windy or rainy days, it suddenly reappears in my mind, stares at me for half an ...

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament,...

So we all know that the continued fraction containing all $1$s... $$ x = 1 + \frac{1}{1 + \frac{1}{1 + \ldots}}. $$ yields the golden ratio $x = \phi$, which can easily be proven by rewriting it as $x ...

Let $(X,\tau), (Y,\sigma)$ be two topological spaces. We say that a map $f: \mathcal{P}(X)\to \mathcal{P}(Y)$ between their power sets is connected if for every $S\subset X$ connected, $f(S)\subset Y$ ...

Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of "proof". I receive responses like: "surely if Collatz is true up ...