## Top new questions this week:

### Why is 987654321/123456789 = 8.0000000729?

Many years ago, I noticed that $987654321/123456789 = 8.0000000729\ldots$. I sent it in to Martin Gardner at Scientific American and he published it in his column!!! My life has gone downhill since …

(arithmetic) (rational-numbers)

### What is $-i$ exactly?

We all know that $i$ doesn't have any sign: it is neither positive nor negative. Then how can people use $-i$ for anything? Also, we define $i$ a number such that $i^2 = -1$. But it can also be seen …

(soft-question) (complex-numbers)

### Why is $\varphi$ called "the most irrational number"?

I have heard $\varphi$ called the most irrational number. Numbers are either irrational or not though, one cannot be more "irrational" in the sense of a number that can not be represented as a ratio …

(number-theory) (irrational-numbers) (golden-ratio)

### What is a proof?

I am just a high school student, and I haven't seen much in mathematics (calculus and abstract algebra). Mathematics is a system of axioms which you choose yourself for a set of undefined entities, …

(logic) (proof-writing) (proof-theory) (big-picture)

### Yitang Zhang: Prime Gaps

Has anybody read Yitang Zhang's paper on prime gaps? Wired reports "$70$ million" at most, but I was wondering if the number was actually more specific. EDIT$^1$: Are there any experts here who can …

(number-theory) (elementary-number-theory) (prime-numbers) (math-history) (prime-twins)

### explaining the derivative of $x^x$

You set the following exercise to your calculus class: Q1. Differentiate $y(x) = x^x$. A student submits the following solution: Let $g(a)=a^x$ and $f(x)=x$. Then $y(x) = g(f(x))$, so by …

(calculus) (teaching) (fake-proofs)

### How do you respond to "I was always bad at math"?

Here in the U.S., it is my experience that over 75% of adults I meet socially will volunteer that phrase or a variation upon learning that I am a mathematician. I find this frustrating, since almost …

(soft-question)

## Greatest hits from previous weeks:

### Software for drawing geometry diagrams

What software do you use to accurately draw geometry diagrams?

(geometry) (big-list) (math-software)

### Results that came out of nowhere.

Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups. …

(soft-question) (math-history) (big-list)

### Ulm and Frattini Subgroups

Let $A$ be an abelian group. We define $U(A)=\cap (nA), n\in \mathbb N$ be the Ulm subgroup of $A$. The Frattini subgroup of $A$ is $\Phi(A)=\cap(pA)$ ($p\in \mathbb P$). I was trying to show that …

(abstract-algebra) (group-theory)