Maybe one of the strange things about quantum mechanics comes from the mental dificulty of reconciling the fact that a system in a superposition of several states, when measured or …

QUESTION I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to …

It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed …

"No". That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. Yet, I am a mathematics educator who was o …

Hi friends, Does anybody know of a pdf version of the following paper ? Ramanujan, S. “Modular Equations and Approximations to Pi.” Quart. J. Pure Appl. Math. 45, 350-372, 1913-1 …

I hope this question is not too simple, but I would like to know the asymptotic behaviour of the following function $f: \mathbb{N}^{+} \rightarrow \mathbb{Q}$ where $$ f(n) = \sum_ …

I am doing research on automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning. I have found several researc …

Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to …

Here is a basic, though very important, example: Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the poss …

EDIT (30 Nov 2012): MoMath is opening in a couple of weeks, so this seems like it might be a good time for any last-minute additions to this question before I vote to close my own …

I am writing a paper about a flaw that I found in a published paper. There, the statement is called “Theorem 2”. In my paper, I am reproducing the other paper’s definitions, and st …

Hi! I am looking for notions of general position that are stronger than linear general position. To illustrate, 3 points in linear general position don't lie on a line. I want a …

Let $n \in \mathbb N$, and $s: \mathbb N \rightarrow \mathbb N,\ p: (\mathbb N \rightarrow \mathbb N) \rightarrow \mathbb N$ be defined as follows: $$ s(x) = x + 1; \\ p(f) = c(1), …

Recently, while looking for articles and documents to learn about the Riemann Hyopthesis, I came across a strange funny document of a chinese "mathematician" called Jiang Chun-Xuan …