The gm.general-mathematics tag has no wiki summary.

**-2**

votes

**0**answers

31 views

### Green`s function [on hold]

Find the Green's function $G(x,y, x',y')$ for Laplace's equation in
$0<x'<a$, $0<y'<b$; with $G=0$, $x'=0$, $G_{x'}=0$, $x'=a$, $G_{y'}=0$, $y'=0$, $G=0$, $y'=b$,
and $0<y'<b$, ...

**0**

votes

**0**answers

76 views

### Can someone help me find a Mathematical documentary that aired on British television within the past 10 years about Leibniz? [on hold]

I have been searching for a documentary that aired on British television between around 2006 and 2012 which was centred around the German Mathematician, Gottfried Leibniz. All that I can remember ...

**17**

votes

**3**answers

868 views

### Which way for reading the proofs?

I am a master student in mathematics. For me a large part of doing mathematics is thinking about, reading and verifying the proof of theorems that I find them in my field of study. I can do this ...

**1**

vote

**6**answers

3k views

### Proofs by induction [closed]

Background
I'm interested in the issue of "explanatory" mathematical proofs and would like to try to find out what intuitions mathematicians have about induction, because there seems to be some ...

**25**

votes

**5**answers

2k views

### Collaboration or acknowledgment?

This post is a sequel of: When should a supervisor be a co-author?
This time the topic is about the interaction between two professional mathematicians (in particular junior-senior, but not ...

**14**

votes

**2**answers

755 views

### What are the applications of operator algebras to other areas?

Question: What are the applications of operator algebras to other areas?
More precisely, I would like to know the results in mathematical areas outside of operator algebras which were proved by ...

**84**

votes

**20**answers

11k views

### Mathematical habits of thought and action which would be of use to non-mathematicians

Once again I come to MO for help with something I'm writing for the public.
Which habits of mathematicians -- aspects of the way we approach problems, the way we argue, the way we function as a ...

**40**

votes

**8**answers

3k views

### Published results: when to take them for granted?

Two kinds of papers. There are two kinds of papers: self-contained ones, and those relying on published results (which I believe are the vast majority).
Checking the result. Of course, one should ...

**9**

votes

**11**answers

3k views

### What advanced Area of Mathematics can be delved into with only basic Calculus and Linear Algebra

Hello Mathoverflow Community,
I would really appreciate some advice on this:
All I know is Basic Calculus and Basic Linear Algebra,
I want to start learning more advanced material on my own while ...

**61**

votes

**6**answers

2k views

### Good ways to engage in mathematics outreach?

Greetings all, I have often heard that it would be good if we as a community did more in the way of mathematics outreach: more to explain what it is we do to the community at large, more to expose ...

**19**

votes

**5**answers

2k views

### Where do surreal numbers come from and what do they mean?

I know about Conway's original discovery of the surreal numbers by way of games,
as well as Kruskal's way of viewing surreal numbers in terms of asymptotic behavior
of real-valued functions, leading ...

**3**

votes

**1**answer

431 views

### Mathematics of Computer science and AI [closed]

Computer science and Artificial Intelligence have been fertile grounds for research for decades, not only for Engineers but particularly for Mathematicians. What kinds of Mathematics have emerged ...

**0**

votes

**2**answers

221 views

### link to a paper by Ramanujan

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, 1913-1914.
It's ...

**2**

votes

**2**answers

450 views

### Popular books written by great mathematicians [closed]

I read:
H. Poincare. Value of science
F. Klein. Development of Mathematics in the 19th Century
J.E. Littlewood. A Mathematicians Miscellany
G.H. Hardy. A Mathematician’s Apology
R. Courant, ...

**6**

votes

**1**answer

142 views

### Compiling self-referential forms

Fix $1\leq d\in\mathbb{N}$ and set $D:=\{0,1,\ldots,d-1\}$.
Consider the system of equations
\begin{equation}
x_i=c_i + \sum_{j\in D}\delta_{x_j,i}
\end{equation}
with $c_i\in D$ given and $x_i\in D$ ...

**0**

votes

**3**answers

780 views

### Simplifying finite sum over 1/(ax+b)

Can I simplify:
\begin{equation}
\sum_{x=x_0}^{x_1} \frac{1}{ax+b}
\end{equation}

**6**

votes

**2**answers

349 views

### Are there any organized websites for seminar/conference videos?

These days, there are many conference centers and universities recording seminars and conference talks and make them available on the web. Some examples:
http://www.fields.utoronto.ca/video-archive
...

**105**

votes

**15**answers

13k views

### When should a supervisor be a co-author?

What are people's views on this? To be specific: suppose a PhD student has produced a piece of original mathematical research. Suppose that student's supervisor suggested the problem, and gave a few ...

**3**

votes

**1**answer

94 views

### Extension of an involutive automorphism

Suppose that $g$ is a complex semi-simple Lie algebra and $g'$ its reductive subalgebra.
If $\tau$ is an involutive automorphism of $g'$, can $\tau$ be extended to an involutive automorphism of $g$ ...

**45**

votes

**6**answers

5k views

### Does a referee have to check carefully the proof ?

I have always checked very carefully the papers I was refereeing when I wanted to suggest "accept". Actually I spend almost as much time checking the maths of a paper I referee than checking the maths ...

**14**

votes

**5**answers

577 views

### Mathematics of privacy?

I wonder to which extent the current public debate on privacy issues (not only by state sniffing, but e.g. by microtargetting ads too an issue) offers interesting questions in mathematics?
Can we ...

**1**

vote

**1**answer

211 views

### Concept of synchronizability

This thread is about the concept of synchronizability. It's a concept I tried to formalize in its most general sense but without success. The goal of this thread is therefore to try to formalize it in ...

**2**

votes

**2**answers

152 views

### Websites for Math Shopping [closed]

I was wondering if anyone knows about good websites or stores to buy math related products. On etsy there are normal distribution plushes and famous mathematicians in coasters. However when I search ...

**1**

vote

**2**answers

153 views

### iterative solution better than analytic solution? [closed]

My supervisor and I were discussing a specific optimisation problem this afternoon.
To be simple: solve for $R$ in the equation $Rx=y$, where $x$, $y$ are made of samples in two difference ...

**41**

votes

**17**answers

8k views

### Is rigour just a ritual that most mathematicians wish to get rid of if they could?

"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 one of the panelists ...

**6**

votes

**1**answer

409 views

### Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...

**0**

votes

**1**answer

166 views

### How to solve $e^{f(x)} + a f(x) + bx = 0$ [closed]

How should determine solutions to equations of this form?
$$e^{-f(x)} + b f(x) = ax$$
Here $f(x)>0$ is real valued. Also $a>0$, $b>0$.

**8**

votes

**2**answers

995 views

### The impact of large cardinals in mathematics [closed]

What are the main applications of large cardinals in ordinary mathematics, and what is the philosophy behind using them. In particular:
Question 1. What is the philosophy behind accepting large ...

**6**

votes

**5**answers

1k views

### Proof or citation?

I'm writing an article. I suppose that I'll submit it to a more or less decent journal (in English). I have doubts about the following: I have a lemma (with quite a trivial proof). I don't want to ...

**5**

votes

**1**answer

212 views

### Constructing a function from preimages

This question was inspired by Can we build a continuous function from "fibers"/preimages defined over a topological base?
Let $X,Y$ be sets and $L\subseteq \mathcal{P}(Y)$. Suppose $L$ has ...

**25**

votes

**15**answers

2k views

### Objects which can't be defined without making choices but which end up independent of the choice

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. And sometimes ...

**-4**

votes

**1**answer

85 views

### geometry formula adjacent neighbour of a N dimensional cube [closed]

A question from a curious.
How many adjacent N dimensional cube there is when they are regularly distributed on a "grid".
By N dimensional cube I mean:
a point is a OD cube
a segment is a 1D cube
...

**31**

votes

**6**answers

2k views

### Negative impact of wrong or non-rigorous proofs

The recent talks of Voevodsky (for example, http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf), which describe subtle errors in proofs by him as well as others, as well ...

**53**

votes

**26**answers

5k views

### Proof synopsis collection

I hate to keep going with the big lists, but the question about one-sentence summaries of topics/areas spurred this question...and I just can't help myself!
Definition (Fraleigh): A proof synopsis ...

**1**

vote

**0**answers

316 views

### Conjectures on fractions where each digit appears once in numerator and denominator

This is a highly redacted version of a question that was asked before. Please see Criteria of considering relevance of the question to the domain of research topics for details.
Some numerical ...

**2**

votes

**7**answers

2k views

### Books about polynomials [closed]

Hi,have you a good reference (books) for the study of polynomials with one variable or many variables ? Thanks for your help.
Don't hesitate to correct my English.

**6**

votes

**10**answers

873 views

### Examples of “Unusual” Classifications

When one says "classification" in math, usually one of a handful of examples springs to mind:
-Classification of Finite Simple Groups with 18 infinite families and 26 sporadic examples (assuming one ...

**7**

votes

**6**answers

425 views

### Do you have examples of such “transitive” elements?

(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.)
Let $A$ be a set ...

**3**

votes

**1**answer

521 views

### Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions.
In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...

**25**

votes

**1**answer

636 views

### Applications of Lawvere's fixed point theorem

Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism $A \to X^A$ which is point-surjective (meaning that $\hom(1,A) \to \hom(1,X^A)$ is surjective), then ...

**52**

votes

**8**answers

5k views

### Have you solved problems in your sleep? [closed]

I have hit upon major (for me—relative to my trivial accomplishments)
insights in my research
in various sleep-deprived altered states of consciousness,
e.g., long solo car-drives extending ...

**4**

votes

**5**answers

289 views

### procedure-based (as opposed to definition-based) concepts

Euler's work on divergent series was guided by computational procedures, rather than any definition of the "value" of such a series. E.g., he was happy to have half a dozen procedures that indicated ...

**33**

votes

**33**answers

4k views

### Structures that turn out to exhibit a symmetry even though their definition doesn't

Sometimes (often?) a structure depending on several parameters turns out to be symmetric w.r.t. interchanging two of the parameters, even though the definition gives a priori no clue of that symmetry. ...

**2**

votes

**0**answers

79 views

### Jacobi triple product for multidimensional lattices

The Jacobi triple product identity gives as a special case a product formula for the theta function of a 1-dimensional lattice. Is there a more general product formula for the theta function of an ...

**11**

votes

**9**answers

1k views

### math circles video lectures for school children?

Hello,
I am from India. I find the mathoverflow amazing.
I have a question: Are there any good quality video lectures on school math topics?
There are a lot of high quality lectures available on ...

**-1**

votes

**1**answer

229 views

### What is an example of a non-axiomatic mathematical system? [closed]

In this wikipedia article on the foundations of mathematics, it says:
In practice, most mathematicians ... do not work from axiomatic systems
Is this correct? If so, what is an example of this?

**3**

votes

**4**answers

810 views

### Another Chicken or Egg: Sequence or Series

This is a side question which is more motivated by teaching than research.
First, I am trying to convince myself that sequences appear before series (as numerical approximations to "interesting" ...

**82**

votes

**90**answers

11k views

### What would you want to see at the Museum of Mathematics?

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 question as "no ...

**14**

votes

**12**answers

2k views

### Why semigroups could be important?

There is known a lot about the use of groups -- they just really appear a lot, and appear naturally. Is there any known nice use of semigroups in Maths to sort of prove they are indeed important in ...

**49**

votes

**6**answers

6k views

### Still Difficult After All These Years

I think we all secretly hope that in the long run mathematics becomes easier, in that with advances of perspective, today's difficult results will seem easier to future mathematicians. If I were ...