## Top new questions this week:

### A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of …

(soft-question) (self-learning)

### Are there surfaces with more than two sides?

I'm watching a naive introduction to the Möbius band, the lecturer asks if it's possible to construct a one sided surface and then she says that there is one of these surfaces, namely the Möbius band. …

(general-topology) (geometry)

### When does $(uv)'=u'v'?$

In any calculus course, one of the first thing we learn is that $(uv)'=u'v+v'u$ rather than the what I've written in the title. This got me wondering: when is this dream product rule true? There are …

(calculus) (real-analysis) (analysis) (differential-equations) (derivatives)

### Limit is found using polar coordinates but it is not supposed to exist.

Consider the following 2-variable function: $$f(x,y) = \frac{x^2y}{x^4+y^2}$$ I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$. I used polar coordinates instead of …

(analysis) (limits) (multivariable-calculus)

### Is it possible that "A counter-example exists but it cannot be found"

Then otherwise the sentence "It is not possible for someone to find a counter-example" would be a proof. I mean, are there some hypotheses that are false but the counter-example is somewhere we …

(logic) (proof-theory)

### Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? …

(soft-question) (education)

### How find this $x,y$ such this equation $x^x+x=y!$

Find all pairs of positive integers $(x,y)$,such $$x^x+x=y!$$ I find the $$(x,y)=(1,2)$$ is such it. and $$(x,y)=(2,3)$$ I think this equation have other roots. and maybe use inequality to …

(number-theory)

## Greatest hits from previous weeks:

### Why are mathematical proofs that rely on computers controversial?

There are many theorems in mathematics that have been proved with the assistance of computers, take the famous four color theorem for example. Such proofs are often controversial among some …

(soft-question) (proof-writing)

### Why is Euclid's proof on the infinitude of primes considered a proof?

I've expressed Euclid's proof on the infinitude of primes on Mathematica: f[x_] := Product[Prime[n], {n, 1, x}] + 1 TableForm[Table[{f[x], PrimeQ[f[x]]}, {x, 1, 20}]] Which results in: …

(number-theory) (prime-numbers)

### Solving integral $\int\frac{\sin x}{1+x\cos x}dx$

How I can find the anti-derivative? $$\int\frac{\sin x}{1+x\cos x}dx$$

(homework) (integration)

### Use of "I" in mathematics papers

Some people consider the use of "I" in a paper to be a great evil. Others, however, consider the use of the passive voice to be an even greater evil. I will be presenting a paper at a competition, …

(article-writing)