## All Questions

75k views

### Examples of common false beliefs in mathematics. [closed]

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent p …
17k views

### Polynomial bijection from QxQ to Q?

Is there any polynomial $f(x,y)\in{\mathbb Q}[x,y]{}\$ such that $f:\mathbb{Q}\times\mathbb{Q} \rightarrow\mathbb{Q}$ is a bijection?
16k views

### Thinking and Explaining

How big a gap is there between how you think about mathematics and what you say to others? Do you say what you're thinking? Please give either personal examples of how your tho …
11k views

### Ideas on how to prevent a department from being shut down. [closed]

[Please stop upvoting. I don't want to get a gold badge out of this...] [Too late... is there a way to give a medal back?] Dear community, the VU University Amsterdam, my employ …
64k views

### Philosophy behind Mochizuki’s work on the ABC conjecture

Mochizuki has recently announced a proof of the ABC conjecture. It is far too early to judge its correctness, but it builds on many years of work by him. Can someone briefly explai …
9k views

### Polynomial representing all nonnegative integers

Lagrange proved that every nonnegative integer is a sum of 4 squares. Gauss proved that every nonnegative integer is a sum of 3 triangular numbers. Is there a 2-variable polynomi …
9k views

### Refereeing a Paper [closed]

I've refereed at least a dozen papers in my (short) career so far and I still find the process completely baffling. I'm wondering what is actually expected and what people tend to …
44k views

### Mathematical “urban legends” [closed]

When I was a young and impressionable graduate student at Princeton, we scared each other with the story of a Final Public Oral, where Jack Milnor was dragged in against his will t …
33k views

### What are some examples of colorful language in serious mathematics papers? [closed]

The popular MO question "Famous mathematical quotes" has turned up many examples of witty, insightful, and humorous writing by mathematicians. Yet, with a few exceptions such as W …
64k views

### Proofs without words [closed]

Can you give examples of proofs without words? In particular, can you give examples of proofs without words for non-trivial results? (One could ask if this is of interest to mathe …
5k views

### Two commuting mappings in the disk

Suppose that $f$ and $g$ are two commuting continuous mappings from the closed unit disk (or, if you prefer, the closed unit ball in $R^n$) to itself. Does there always exist a poi …
11k views

### Which journals publish expository work?

I wonder if anyone else has noticed that the market for expository papers in mathematics is very narrow (more so than it used to be, perhaps). Are there any journals which publi …
43k views

### A single paper everyone should read? [closed]

Different people like different things in math, but sometimes you stand in awe before a beautiful and simple, but not universally known, result that you want to share with any of y …