# Tagged Questions

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

1k views

### What are some results that shook the foundations of one or more fields of mathematics? [closed]

An example would be the proof that $\sqrt{2}$ is not rational, which was a violation of some fundamental assumptions that mathematicians at the time made about numbers. Another would be Russell's ...
74 views

### Website for Mathematics enigmas?

I seek some website just for the pleasure of solving mathematics enigmas. I know this website : Brilliant.org I just want to know if you know some others good sites ! Thank you
12k views

### What is the smallest unknown natural number?

There are several unknown numbers in mathematics, such as optimal constants in some inequalities. Often it is enough to some estimates for these numbers from above and below, but finding the exact ...
476 views

### Space on which all real-valued continuous functions achieve maximum but not compact?

A friend is writing a book for non-mathematicians; he has asked me some questions... One possible direction I suggested was whether a topological space (metric space can probably be assumed given what ...
3k views

### What is the most unusual proof you know that $\sqrt{2}$ is irrational?

What is the most unusual proof you know that $\sqrt{2}$ is irrational? Here is my favorite: Theorem: $\sqrt{2}$ is irrational. Proof: $3^2-2\cdot 2^2 = 1$. (That's it) That is a ...
240 views

### What are some interesting blogs about general topology?

We have several question asking about book recommendations for general topology - for example the posts linked to Best book for topology? or the posts mentioned in the relevant section of List of ...
170 views

### Comprehensive Linear Algebra Text

Occasionally I come across a fact from linear algebra that I have not seen before. These facts are often obscured in search engines by either introductory texts or unrelated papers, and it is ...
269 views

### What are statements about the natural numbers where induction is impossible or unnecessary to prove?

I'm looking for statements like "for all natural numbers, ____" where induction would be impossible or unnecessarily complicated. This is for pedagogical reasons. When students first learn induction, ...
377 views

### Challenging problems in algebra (book recommendation) [closed]

Could you suggest me a book/web page where I can find challenging/hard problems in algebra (possibly with solutions) for an undergraduate student (groups, rings, fields, Galois theory)? Thanks in ...
124 views

### All possible total orderings of a finite set are isomorphic. What are some other examples of this phenomenon?

All possible total orderings of a finite set are isomorphic. I find these kinds of results remarkable. Here's a few more. Assume that $S$ is a finite set. Then: All possible field structures on $S$ ...