Linked Questions

It's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true". Now, I know a fair few examples of things that are obviously true and that can be proved ...

As I procrastinate studying for my Maths Exams, I want to know what are some cool examples of where math counters intuition. My first and favorite experience of this is Gabriel's Horn that you see in ...

Given the set of standard axioms (I'm not asking for proof of those), do we know for sure that a proof exists for all unproven theorems? For example, I believe the Goldbach Conjecture is not proven ...

I've studied quite a bit of group theory recently, but I'm still not able to grok why normal subgroups are so important, to the extent that theorems like $(G/H)/(K/H)\approx G/K$ don't hold unless $K$ ...

QUESTION: What are some simple math problems whose answers are highly unintuitive, and what makes them so? There are plenty of unintuitive and frankly baffling results in math, like the Banach-Tarski ...

Why does the result of cutting a Möbius strip down the middle lengthwise have two full twists in it? I can account for one full twist--the identification of the top left corner with the bottom right ...

In "Angle Trisection, the Heptagon, and the Triskaidecagon", published in the American Mathematical Monthly in March 1988, Andrew Gleason discusses what regular polygons can be constructed with ...

ESPN recently posted a story demonstrating that the "hot hand" concept is, in fact, real. Part of the justification is this example based on coin flips from a paper by Adam Sanjurjo and ...

$13^{11^{7^{5^{3^2}}}}\bmod100=37$, according to WolframAlpha. My calculations provided the same result, however upon consideration, I realized that they don't make sense, even though the result is ...

I have been doing some questions from an exam review with no solution and I have no idea how to work this problem. I know that $Pr(A_1) = \frac{1}{2}$, $Pr(A_2) = \frac{1}{2}$, $Pr(A_3) = \frac{1}{2}$,...

Take a random 12 digit random binary string, each bit equiprobable 0 or 1. Select a bit that is preceded by 3 0s equiprobably at random. The probability that the bit is 1 is ~66%. Why? Why is this ...

I know that $\sum\limits_{n=1}^\infty n^{-2}=\pi^2/6$, but shouldn't the sum of rationals be rational? Is this akin to $\sum\limits_{n=1}^\infty n=-1/12$? Or does that mean that, somehow, $\pi^2/6$ is ...